├── LICENSE ├── README.md ├── data ├── inv_aniso_model_aniso.mat ├── inv_aniso_model_iso.mat ├── inv_iso_model_iso.mat ├── inversion_data.mat ├── protocol.mat └── synt_data_for_inversion.mat ├── figures ├── forward_validation_model1.fig ├── forward_validation_model1.png ├── forward_validation_model2.fig ├── forward_validation_model2.png ├── inv_aniso_model_aniso.fig ├── inv_aniso_model_aniso.png ├── inv_aniso_model_iso.fig ├── inv_aniso_model_iso.png ├── inv_iso_model_iso.fig └── inv_iso_model_iso.png ├── functions ├── Calc_data_weight.m ├── CtC_anis.m ├── calcul_alpha_anis.m ├── calcul_u_S_anis.m ├── cglscd.m ├── deriv2D.m ├── distance_weighting.m ├── find_k.m ├── gauss_newton_inversion_anis.m ├── geometric_factor.m ├── getAperture.m ├── gradient_product_anis.m ├── grille2d_elect.m ├── integration_U.m ├── matrix_coeff_anis.m ├── tri_electr_pos.m └── vec2model.m └── scripts ├── drawing ├── script_drawing_aniso.m └── script_drawing_iso.m ├── forward ├── script_analytical_anis_2layers.m └── script_analytical_anis_semiInfiniteSpace.m ├── inversion └── script_preparation_inversion.m ├── script_drawing.m ├── script_forward_validation.m └── script_inversion.m /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # AIM4RES user guide 2 | 3 | AIM4RES is a finite-differences forward and inverse anisotropic modeling open source MATLAB library. By considering the resistivity as a tensor, allowing for the anisotropy estimation, AIM4RES provides three model sections from Electrical Resistivity Tomography data: highest resistivity ρ1, lowest resistivity ρ3 and the angle of anisotropy θ. Details about the theory will be found in the article _AIM4RES, an open-source 2.5D finite differences MATLAB library for anisotropic electrical resistivity modeling_ currently in review. 4 | 5 | ## Library description 6 | 7 | The library is open source and freely available for any purpose. It contains 4 folders: 8 | * _functions_: this folder contains all the needed functions for AIM4RES proper functioning. Each function contains a header describing its purpose, the needed input and its outputs. A description of the 3 major structures __param__, __XYZ__ and __Inv__ are thoroughly explained below. 9 | 10 | * _scripts_: this folder contains the executable example scripts. 11 | 12 | 13 | * _data_: this folder contains the data used the scripts previously described, and the output data resulting from the scripts. These latter allow for direct parameters exploration or drawing without previous calculation (for the inversion). 14 | 15 | * _figures_: this folder contains the .fig files obtain from the previous scripts, and correspond to the figures presented in the article. 16 | 17 | All scripts are executable form the folder __./aim4res__ 18 | 19 | ### Prerequisites 20 | 21 | Having a working MATLAB distribution, installed on any operating system. No installation is needed for this library and it is directly usable in a MATLAB environment. 22 | 23 | ## What AIM4RES has inside 24 | 25 | ### Key functions 26 | 27 | AIM4RES is based on some key functions, which functioning is described in the accompanying article: 28 | 29 | * *calcul_u_S_anis* drives forward modeling as well as sensitivity calculation, 30 | 31 | * *matrix_coeff_anis* is the function building the capacitance matrix thoroughly described in the article and is called by *calcul_u_S_anis*, 32 | 33 | * *gauss_newton_inversion_anis* drives the inverse modeling. This function needs the two structures __param__ and __XYZ__ and return the __Inv__ structure. 34 | 35 | ### Key parameters 36 | 37 | Three structures are needed in the modeling process: 38 | 39 | * __param__: parameters structure. Some of its items are computed by the different functions. The others are user filled out: 40 | * **flag.geo_factor**: geometric factor associated to each measurements. Needed for the apparent resistivity calculation used in the inverse modeling, 41 | * **cell_size**: determine the block size. Assuming a raw block is 1 m2, **cell_size** slices it dividing its horizontal dimension by **cell_size(1)** and its vertical dimension by **cell_size(2)**, 42 | * **nb_pad_bloc**, **nb_raff**, **nb_surr** and **fact** are described in *grille2d_elect.m* header, 43 | * **rho.xx**, **rho.zz**, **rho.xz** and **rho.yy**: synthetic model resistivity components (ρxx, ρzz, ρxz and ρyy), 44 | * **flag.inv.p**: determines wether inverse modeling computes only the two ρxx and ρzz components (**flag.inv.p** = 2) ; or the three ρxx, ρzz and ρxz components (**flag.inv.p** = 3), 45 | * **data_nb**: ρxx, ρzz or ρxz components size, 46 | * **K**: geometric factor, 47 | * **MEAS.Res**: resistance data (U/I), synthetically computed or measured on the field, 48 | * **anis_init**: homogeneous initial anisotropy considered in the inversion, 49 | * **const_ind**, **const_vect** and **const_TrueFalse**: respectively constrained model cells indices, constrained model cells resistivity value and application (or not) of the constraints, 50 | * **const.***: other constraints parameters (see *script_preparation_inversion.m*), 51 | * **inv.***: inverse modeling features 52 | * **invparam** = 'log resistivity', 'resistivity' or 'resistance' according to the desired inversion. 'log resistivity' is highly recommended, 53 | * **fct_reg** = 'flatness' or 'smoothness', depending on wether first derivative or second derivative is prefered as regularization, respectively, 54 | * **appl_fct_reg** = 'model' or 'model perturbation' 55 | * **dataweight**: see *Calc_data_weight.m* header, 56 | * **alx**, **alz**, **als**: see *CtC_anis.m* header 57 | * **BETA**: regularization coefficient. Usually higher for the anisotropic problem than for the isotropic one, 58 | * **rms_model** 59 | * **tol**: tolerance threshold iteration criterion, 60 | * **maxit**: maximum amount of iterations, 61 | * **weight**: weights applied on the regularization matrix (true of false), 62 | * **weightMinit** and **weightMaxit**: respectively first and last iteration for the weigthing application, 63 | * **weightFun**: 'Distance weighting' or 'Sensitivity weighting' (see Li and Oldenburg, 1996) 64 | * **alp**: Armijo coefficient. 65 | 66 | 67 | * __XYZ__: geometric structures 68 | * **surface_electrode**, **borehole1_electrode** and **borehole2_electrode**: respectively surface, first borehole and second borehole admissible coordinates. Can contain unused coordinates but __*MUST*__ contain all the used coordinates (x: first column, z: second column), 69 | * **MEAS.***: quadrupoles coordinates 70 | * **C1**: current electrode 1 coordinates. nth row = nth measure (x: first column, z: second column) 71 | * **C2**:current electrode 2 coordinates, 72 | * **P1**:potential electrode 1 coordinates, 73 | * **P2**:potential electrode 2 coordinates, 74 | * **areas**: area formed b the quadrupoles. nth row = nth measure. 75 | 76 | 77 | * __Inv__: inverse modeling products 78 | * **rho.***: ρ1, ρ2, ρxx, ρzz, ρxz and θ inverted sections at each iteration, 79 | * **D**: data weighting matrix (see *Calc_data_weight.m* header), 80 | * **d_cal**: apparent resistivity computed on the inverted model at each iteration 81 | * **rho_app_pos_index**: indices of the considered measures at each iteration. Inverse modeling considers logarithmic values of apparent resistivity, **rho_app_pos_index** only keep positive apparent resistivities, 82 | * **rms**: root mean square value at each iteration, 83 | * **beta_weighting**: weighting coefficient stored at each iteration, 84 | * **sens_weighting**: weighting sections stored at each iteration, 85 | * **Ki2**: χ2 value stored at each iteration, 86 | * **CTC**: regularization matrix stored at each iteration 87 | 88 | ## Running the tests 89 | 90 | Ready for use scripts have been added to AIM4RES library. They reproduce the figures presented in the article. These scripts can be edited for any use to adapt any ERT data. 91 | 92 | Scripts are to be executed from AIM4RES root folder: 93 | 94 | * *script_forward_validation.m*: forward modeling considering the two synthetic models described in the article. The script waits for user input to compute the two different forward modeling proposed. 95 | 96 | * *script_inversion.m*: inverse modeling considering the synthetic model described in the article. The script waits for user input to determine if synthetic data have to be computed beforehand from *script_preparation_inversion.m*, or if already existing MATLAB file is to be considered ('synt_data_for_inversion.mat'). 97 | 98 | * *script_drawing.m*: script producing the figures presented in the article. 99 | 100 | 101 | ## Authors 102 | 103 | * **Simon GERNEZ** 104 | 105 | * **Abderrezak BOUCHEDDA** 106 | 107 | Members of the [Laboratoire d'Interprétation et Acquisition des Mesures en Géosciences](https://github.com/groupeLIAMG) of INRS-ETE University, Quebec, Canada. 108 | 109 | ## License 110 | 111 | This project is licensed under the GNU GENERAL PUBLIC LICENSE. See LICENSE.txt for details. 112 | -------------------------------------------------------------------------------- /data/inv_aniso_model_aniso.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Simoger/AIM4RES/940b771bc74b5e8bb41aadf90db59591a5dfc957/data/inv_aniso_model_aniso.mat -------------------------------------------------------------------------------- /data/inv_aniso_model_iso.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Simoger/AIM4RES/940b771bc74b5e8bb41aadf90db59591a5dfc957/data/inv_aniso_model_iso.mat -------------------------------------------------------------------------------- /data/inv_iso_model_iso.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Simoger/AIM4RES/940b771bc74b5e8bb41aadf90db59591a5dfc957/data/inv_iso_model_iso.mat 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| % % 9 | % In: % 10 | % ----------- % 11 | % wt: weigths applied on the regularization matrix % 12 | % param.param.inv.alx: smoothing parameter in x direction % 13 | % param.param.inv.alz: smoothing parameter in z direction % 14 | % param.h_x: x step % 15 | % param.h_z: z step % 16 | % % 17 | % Out: % 18 | % ----------- % 19 | % CTC: model weighting matrix % 20 | % Cx: model weighting matrix in x direction % 21 | % Cx: model weighting matrix in z direction % 22 | % % 23 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 24 | %%========================================================================% 25 | % Copyright (C) 2019 Simon GERNEZ and Abderrezak BOUCHEDDA % 26 | %%========================================================================% 27 | % % 28 | % Contacts: % 29 | % % 30 | % Simon GERNEZ % 31 | % simon.gernez@ete.inrs.ca % 32 | % Institut National de la Recherche Scientifique % 33 | % Centre Eau-Terre-Environnement % 34 | % http://www.ete.inrs.ca/ % 35 | % % 36 | % Abderrezak BOUCHEDDA % 37 | % Abderrezak.Bouchedda@ete.inrs.ca % 38 | % Institut National de la Recherche Scientifique % 39 | % Centre Eau-Terre-Environnement % 40 | % http://www.ete.inrs.ca/ % 41 | % % 42 | % This program is free software; you can redistribute it and/or modify % 43 | % it under the terms of the GNU General Public License as published by % 44 | % the Free Software Foundation; either version 2 of the License, or % 45 | % (at your option) any later version. % 46 | % % 47 | % This program is distributed in the hope that it will be useful, % 48 | % but WITHOUT ANY WARRANTY; without even the implied warranty of % 49 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % 50 | % GNU General Public License for more details. % 51 | % % 52 | % You should have received a copy of the GNU General Public License % 53 | % along with this program; if not, write to the Free Software % 54 | % Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA% 55 | 56 | %%========================================================================% 57 | 58 | %% Calculation 59 | 60 | param.h_x = [param.h_x ; param.h_x(end)]; 61 | param.h_z = [param.h_z ; param.h_z(end)]; 62 | 63 | %smoothing parammeters 64 | alx = param.inv.alx; 65 | alz = param.inv.alz; 66 | 67 | nx = param.nb_col; 68 | nz = param.nb_ligne; 69 | 70 | %Smallness parameter 71 | als = param.inv.als; 72 | wts = wt(:); 73 | 74 | % derivative matrix 75 | [Cx,Cz] = deriv2D(param.h_x,param.h_z,param.flag.reg_fct); 76 | 77 | if ~isempty(param.const.WGx) 78 | Cx = spdiags(param.const.WGx,0,nx*nz,nx*nz)*Cx; 79 | end 80 | 81 | if ~isempty(param.const.WGz) 82 | Cz = spdiags(param.const.WGz,0,nx*nz,nx*nz)*Cz; 83 | end 84 | 85 | if isfield(param.const,'Wti') 86 | Ci = spdiags(param.const.Wti,0,nx*nz,nx*nz); 87 | else 88 | Ci = speye(nx*nz,nx*nz); 89 | end 90 | 91 | %% Create a weighted smallness term 92 | 93 | % Weights certain points more than others 94 | 95 | Wts_1 = spdiags(wts(1:nx*nz), 0, nx*nz, nx*nz); 96 | Wts_2 = spdiags(wts(nx*nz+1:2*nx*nz), 0, nx*nz, nx*nz); 97 | 98 | if nb_composantes == 3 99 | Wts_3 = spdiags(wts(2*nx*nz+1:end), 0, nx*nz, nx*nz); 100 | end 101 | 102 | % Assemble the Anisotropic derivative operator 103 | Gs = [alx*Cx ; alz*Cz]; 104 | 105 | % Assemble the 2d weighting matrix 106 | CTC = (Gs'*Gs + als * Ci); 107 | % if flag == 0 108 | % CTC = (Gs'*Gs + als * Ci); 109 | % else 110 | % CTC = (Gs'*Gs + als * speye(nx*nz,nx*nz)); 111 | % end 112 | 113 | if nb_composantes == 2 114 | CTC = sparse( blkdiag(Wts_1',Wts_2') * blkdiag(CTC,CTC) * blkdiag(Wts_1,Wts_2) ); 115 | elseif nb_composantes == 3 116 | CTC = sparse( blkdiag(Wts_1',Wts_2',Wts_3') * blkdiag(CTC,CTC,CTC) * blkdiag(Wts_1,Wts_2,Wts_3) ); 117 | end 118 | end -------------------------------------------------------------------------------- /functions/calcul_alpha_anis.m: -------------------------------------------------------------------------------- 1 | function alpha = calcul_alpha_anis(a,k,rho,sigma,pos,normale) 2 | 3 | %%========================================================================% 4 | % % 5 | % calculation of nu for mixed boundary condition % 6 | % % 7 | %%========================================================================% 8 | % % 9 | % In: % 10 | % ------- % 11 | % r: distance between current source frontiers points % 12 | % k: wave number vector % 13 | % rho: resistivity values % 14 | % sigma: conductivity values % 15 | % pos: positions vector % 16 | % normale: normale direction vector % 17 | % % 18 | % Out: % 19 | % ----------- % 20 | % nu: mixed boundary condition coefficient % 21 | % % 22 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 23 | %%========================================================================% 24 | % Copyright (C) 2019 Simon GERNEZ and Abderrezak BOUCHEDDA % 25 | %%========================================================================% 26 | % % 27 | % Contacts: % 28 | % % 29 | % Simon GERNEZ % 30 | % simon.gernez@ete.inrs.ca % 31 | % Institut National de la Recherche Scientifique % 32 | % Centre Eau-Terre-Environnement % 33 | % http://www.ete.inrs.ca/ % 34 | % % 35 | % Abderrezak BOUCHEDDA % 36 | % Abderrezak.Bouchedda@ete.inrs.ca % 37 | % Institut National de la Recherche Scientifique % 38 | % Centre Eau-Terre-Environnement % 39 | % http://www.ete.inrs.ca/ % 40 | % % 41 | % This program is free software; you can redistribute it and/or modify % 42 | % it under the terms of the GNU General Public License as published by % 43 | % the Free Software Foundation; either version 2 of the License, or % 44 | % (at your option) any later version. % 45 | % % 46 | % This program is distributed in the hope that it will be useful, % 47 | % but WITHOUT ANY WARRANTY; without even the implied warranty of % 48 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % 49 | % GNU General Public License for more details. % 50 | % % 51 | % You should have received a copy of the GNU General Public License % 52 | % along with this program; if not, write to the Free Software % 53 | % Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA% 54 | 55 | %%========================================================================% 56 | 57 | %% Calculation 58 | 59 | eps = 10^-10; 60 | nk = length(k); 61 | nr = length(a); 62 | alpha = zeros(nr,nk); 63 | normale = normale(:); 64 | 65 | x = pos(:,1); 66 | z = pos(:,2); 67 | 68 | 69 | % scal = 2*[x z]; % [sigma . grad(a)] dot product 70 | scal = [sigma.xx.*(2.*x.*rho.xx + 2.*z.*rho.xz) + sigma.xz.*(2.*x.*rho.xz + 2.*z.*rho.zz), ... 71 | sigma.xz.*(2.*x.*rho.xx + 2.*z.*rho.xz) + sigma.zz.*(2.*x.*rho.xz + 2.*z.*rho.zz)]; 72 | scal_norm = scal*normale; 73 | scal_norm = (1./rho.yy).*scal_norm; 74 | 75 | for j=1:nk 76 | % K0 = besselk(0,(k(j)*sqrt(a)),0); 77 | % K1 = besselk(1,(k(j)*sqrt(a)),0); 78 | K0 = besselk(0,(k(j)*sqrt(a))); 79 | K1 = besselk(1,(k(j)*sqrt(a))); 80 | alpha(:,j) = k(j)./(2*sqrt(a)).*(K1./(K0+eps)).*scal_norm; 81 | end 82 | 83 | end 84 | 85 | 86 | 87 | 88 | -------------------------------------------------------------------------------- /functions/calcul_u_S_anis.m: -------------------------------------------------------------------------------- 1 | function [u,S] = calcul_u_S_anis(param,XYZ,rho,sens_calc) 2 | 3 | %%========================================================================% 4 | % % 5 | % Calculation of potential u and sensitivity S in anisotropic media % 6 | % % 7 | %%========================================================================% 8 | % % 9 | % In: % 10 | % ----------- % 11 | % sens_calc: sensitivity calculation % 12 | % sens_calc == 0: don't calculate sensitivity matrix % 13 | % sens_calc == 1: calculate sensistivity matrix % 14 | % param: parameters structure % 15 | % XYZ: electrodes position structure % 16 | % % 17 | % Out: % 18 | % ----------- % 19 | % u: calculated potential % 20 | % I = 1 == > u = resistance (= u/I = u/1) % 21 | % S: sensitivity matrix (if sens_calc == 1) % 22 | % % 23 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 24 | %%========================================================================% 25 | % Copyright (C) 2019 Simon GERNEZ and Abderrezak BOUCHEDDA % 26 | %%========================================================================% 27 | % % 28 | % Contacts: % 29 | % % 30 | % Simon GERNEZ % 31 | % simon.gernez@ete.inrs.ca % 32 | % Institut National de la Recherche Scientifique % 33 | % Centre Eau-Terre-Environnement % 34 | % http://www.ete.inrs.ca/ % 35 | % % 36 | % Abderrezak BOUCHEDDA % 37 | % Abderrezak.Bouchedda@ete.inrs.ca % 38 | % Institut National de la Recherche Scientifique % 39 | % Centre Eau-Terre-Environnement % 40 | % http://www.ete.inrs.ca/ % 41 | % % 42 | % This program is free software; you can redistribute it and/or modify % 43 | % it under the terms of the GNU General Public License as published by % 44 | % the Free Software Foundation; either version 2 of the License, or % 45 | % (at your option) any later version. % 46 | % % 47 | % This program is distributed in the hope that it will be useful, % 48 | % but WITHOUT ANY WARRANTY; without even the implied warranty of % 49 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % 50 | % GNU General Public License for more details. % 51 | % % 52 | % You should have received a copy of the GNU General Public License % 53 | % along with this program; if not, write to the Free Software % 54 | % Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA% 55 | 56 | %%========================================================================% 57 | 58 | %% Initialisation 59 | 60 | S = []; 61 | eps = 1e-5; 62 | position = param.pos; 63 | ind = param.ind; 64 | I = 1; % current intensity 65 | nb_ligne = max(size(param.h_z))+1; 66 | nb_col = max(size(param.h_x))+1; 67 | nb_t = nb_ligne*nb_col; 68 | nb_electrode1 = size(position.C,1); 69 | nb_electrode2 = size(position.P); 70 | nb_electrode2 = nb_electrode2(1,1); 71 | nb_electrode = nb_electrode1+nb_electrode2; % number of electrodes 72 | nb_k = length(param.k); % wave number 73 | nb_meas = param.data_nb; % measures number 74 | position1 = [position.C ; position.P]; 75 | u_P1 = zeros(2*nb_meas,1); 76 | u_P2 = zeros(2*nb_meas,1); 77 | 78 | if sens_calc == 0 % no sensitivity 79 | param.flag.sen = 0; % force to no sensitivity 80 | end 81 | 82 | if param.flag.sen == 1 83 | u1 = zeros(nb_col*nb_ligne,nb_electrode*nb_k); 84 | end 85 | 86 | qq = sparse(nb_col*nb_ligne,nb_electrode); 87 | ind_source = []; 88 | u = zeros(nb_meas,nb_k); 89 | 90 | %% Matrix coeff calculation 91 | 92 | [A1,Ak] = matrix_coeff_anis(param.h_x,param.h_z,param.grille,rho,param.k); 93 | 94 | % Ak shouldn't be complex 95 | try 96 | isreal(Ak) == false; 97 | catch 98 | error('complex Ak: Ak should be real') 99 | end 100 | 101 | for ii = 1:nb_electrode 102 | iind = find(abs(position1(ii,1)-param.grille(:,1)) < eps & abs(position1(ii,2)-param.grille(:,2)) < eps); 103 | qq(iind,ii) = I/2; 104 | ind_source = [ind_source;iind]; 105 | end 106 | 107 | %% Forward problem resolution 108 | 109 | if nb_t > 10^6 % if huge parameters number to estimate 110 | 111 | for j = 1:nb_k % loop for k 112 | 113 | A = A1 + sparse(1:nb_t,1:nb_t,Ak(:,j)); 114 | 115 | % Symmetric reverse Cuthill-McKee permutation 116 | p = symrcm(A); 117 | A = A(p,p); 118 | [~,up] = sort(p); 119 | %-------- 120 | setup.droptol = 10^-5; 121 | % LU precondit. 122 | [L1,U1] = ilu(A,setup); 123 | %-------- 124 | l1 = 0; 125 | l2 = 0; 126 | 127 | for i = 1:nb_electrode1 % loop for current electrode position 128 | 129 | q = qq(:,i); 130 | q = q(p); 131 | 132 | % resoudre Au = q 133 | [uu,~] = bicgstab(A,q,10^-9,20,L1,U1); 134 | 135 | uu = uu(up); % rearrangement after Cuthill-McKee permutation 136 | 137 | l2 = l2+param.L(i); 138 | 139 | u1(:,i+(j-1)*nb_electrode) = uu; 140 | 141 | u_P1((1+l1:l2)) = uu(ind.P1(1+l1:l2)); 142 | u_P2((1+l1:l2)) = uu(ind.P2(1+l1:l2)); 143 | 144 | l1 = l2; 145 | 146 | end 147 | 148 | u_P1C1(ind.C1C2(param.sign == 1)) = u_P1(param.sign == 1); 149 | u_P1C2(ind.C1C2(param.sign == -1)) = u_P1(param.sign == -1); 150 | u_P2C1(ind.C1C2(param.sign == 1)) = u_P2(param.sign == 1); 151 | u_P2C2(ind.C1C2(param.sign == -1)) = u_P2(param.sign == -1); 152 | 153 | u(:,j) = (u_P1C1-u_P1C2)-(u_P2C1-u_P2C2); 154 | 155 | end 156 | 157 | % integration into the spatial domain 158 | u = integration_U(u,param.wk,param.k,param.nbk1); 159 | 160 | else 161 | 162 | for j = 1:nb_k % loop for k 163 | 164 | A = A1 + sparse(1:nb_t,1:nb_t,Ak(:,j)); 165 | 166 | if param.flag.inv.p == 3 167 | [L,U] = lu(A); 168 | elseif param.flag.inv.p == 2 169 | % symmetric coefficient matrix if only 2 components, chol 170 | % more efficient than lu in that case 171 | R = chol(A); 172 | RT = R'; 173 | end 174 | 175 | l1 = 0; 176 | l2 = 0; 177 | 178 | q = qq; 179 | 180 | for i = 1:nb_electrode1 % loop for current electrode position 181 | if param.flag.inv.p == 3 182 | uu = (U\(L\(q(:,i)))); 183 | elseif param.flag.inv.p == 2 184 | uu = (R\(RT\(q(:,i)))); 185 | end 186 | 187 | l2 = l2+param.L(i); 188 | 189 | if param.flag.sen == 1 190 | u1(:,i+(j-1)*nb_electrode) = uu; 191 | end 192 | 193 | u_P1((1+l1:l2)) = uu(ind.P1(1+l1:l2)); 194 | u_P2((1+l1:l2)) = uu(ind.P2(1+l1:l2)); 195 | 196 | l1 = l2; 197 | end 198 | 199 | u_P1C1(ind.C1C2(param.sign == 1)) = u_P1(param.sign == 1); 200 | u_P1C2(ind.C1C2(param.sign == -1)) = u_P1(param.sign == -1); 201 | u_P2C1(ind.C1C2(param.sign == 1)) = u_P2(param.sign == 1); 202 | u_P2C2(ind.C1C2(param.sign == -1)) = u_P2(param.sign == -1); 203 | 204 | if isnan(XYZ.MEAS.C2(1,1)) && isnan(XYZ.MEAS.P2(1,1)) % pole-pole 205 | u_P2C1 = 0; 206 | u_P2C2 = 0; 207 | u_P1C2 = 0; 208 | elseif isnan(XYZ.MEAS.C2(1,1)) && ~isnan(XYZ.MEAS.P2(1,1)) % pole-dipole 209 | u_P2C2 = 0; 210 | u_P1C2 = 0; 211 | end 212 | 213 | u_k = (u_P1C1-u_P1C2) - (u_P2C1-u_P2C2); 214 | u(:,j) = u_k(:); 215 | 216 | end 217 | 218 | % integration into the spatial domain 219 | u = integration_U(u,param.wk,param.k,param.nbk1); 220 | 221 | end 222 | 223 | %% Sensitivity matrix calculation 224 | 225 | % we start with the calculation of the reciprocal potential pos. misses 226 | 227 | if sens_calc == 1 % sensitivity calculation 228 | 229 | if param.flag.inv.p == 2 230 | if nb_electrode2 ~= 0 % calculate reciprocal potential if P1 or P2 are not used as C1 or C2 231 | for j = 1:nb_k 232 | A = A1 + sparse(1:nb_t,1:nb_t,Ak(:,j)); 233 | [R,~,p] = chol(A,'vector'); % Cholesky decomposition with ordering 234 | [~,up] = sort(p); % ordering indices 235 | for i = 1:nb_electrode2 236 | q = qq(:,i+nb_electrode1); 237 | % Au = q 238 | uu = (R\(R'\(q(p)))); 239 | uu = uu(up); 240 | u1(:,i+nb_electrode1+(j-1)*nb_electrode) = uu; 241 | end 242 | end 243 | end 244 | 245 | elseif param.flag.inv.p == 3 246 | if nb_electrode2 ~= 0 % calculate reciprocal potential if P1 or P2 are not used as C1 or C2 247 | for j = 1:nb_k 248 | A = A1 + sparse(1:nb_t,1:nb_t,Ak(:,j)); 249 | [L,U,p] = lu(A,'vector'); 250 | [~,up] = sort(p); % ordering indices 251 | for i = 1:nb_electrode2 252 | q = qq(:,i+nb_electrode1); 253 | % Au = q 254 | uu = (U\(L\(q(p)))); 255 | uu = uu(up); 256 | u1(:,i+nb_electrode1+(j-1)*nb_electrode) = uu; 257 | end 258 | end 259 | end 260 | 261 | end 262 | 263 | n = size(ind.meas,1); 264 | 265 | rho.xx = rho.xx'; 266 | rho.xz = rho.xz'; 267 | rho.zz = rho.zz'; 268 | rho.yy = rho.yy'; 269 | 270 | rho.xx = rho.xx(:)'; % Mandatory step so that cells are considered 271 | rho.xz = rho.xz(:)'; % as an arranged vector as for inversion 272 | rho.zz = rho.zz(:)'; 273 | rho.yy = rho.yy(:)'; 274 | 275 | S.xx = zeros(nb_meas,nb_ligne*nb_col); 276 | S.zz = zeros(nb_meas,nb_ligne*nb_col); 277 | S.xz = zeros(nb_meas,nb_ligne*nb_col); 278 | % % Uncomment if lambda sensitivity is needed (if you don't know wether it is needed, assume it is not) 279 | % Slambda = zeros(nb_meas,nb_ligne*nb_col); 280 | 281 | rho.rho_1 = rho.rho_1'; 282 | rho.rho_2 = rho.rho_2'; 283 | rho.angle = rho.angle'; 284 | rho.rho_1 = rho.rho_1(:)'; 285 | rho.rho_2 = rho.rho_2(:)'; 286 | rho.angle = rho.angle(:)'; 287 | 288 | if strcmp(param.inv.invparam,'log resistivity') 289 | 290 | % dipole-dipole 291 | if ~isnan(XYZ.MEAS.C2(1,1)) && ~isnan(XYZ.MEAS.P2(1,1)) 292 | 293 | parfor i = 1:n 294 | 295 | u_1 = (u1(:,ind.meas(i,1):nb_electrode:end)-u1(:,ind.meas(i,2):nb_electrode:end));% u(c1)-u(c2) 296 | u_1R = (u1(:,ind.meas(i,3):nb_electrode:end)-u1(:,ind.meas(i,4):nb_electrode:end));% u(p1)-u(p2) 297 | 298 | % Gradient calculation 299 | g = gradient_product_anis(u_1R, u_1, param.h_x, param.h_z, param.k); 300 | 301 | % xx 302 | g.xx = integration_U(g.xx,param.wk,param.k,param.nbk1); % Inverse Fourier transform 303 | g.xx = reshape(g.xx,nb_ligne,nb_col); 304 | g.xx = reshape(g.xx',(nb_ligne)*(nb_col),1)'; % horizontally arranged 305 | 306 | % xz 307 | g.xz = integration_U(g.xz,param.wk,param.k,param.nbk1); % Inverse Fourier transform 308 | g.xz = reshape(g.xz,nb_ligne,nb_col); 309 | g.xz = reshape(g.xz',(nb_ligne)*(nb_col),1)'; % horizontally arranged 310 | 311 | % zz 312 | g.zz = integration_U(g.zz,param.wk,param.k,param.nbk1); % Inverse Fourier transform 313 | g.zz = reshape(g.zz,nb_ligne,nb_col); 314 | g.zz = reshape(g.zz',(nb_ligne)*(nb_col),1)'; % horizontally arranged 315 | 316 | % yy 317 | g.yy = integration_U(g.yy,param.wk,param.k,param.nbk1); % tr. Fourier inv. 318 | g.yy = reshape(g.yy,nb_ligne,nb_col); 319 | g.yy = reshape(g.yy',(nb_ligne)*(nb_col),1)'; % horizontally arranged 320 | 321 | % Calculation of the sensitivity (ln(resistivity)) 322 | Sxx(i,:) = (1./(rho.rho_1*u(i))).*(g.xx.*(cosd(rho.angle)).^2 + ... 323 | g.zz.*(sind(rho.angle)).^2 - ... 324 | g.xz.*cosd(rho.angle).*sind(rho.angle) + ... 325 | g.yy); 326 | 327 | Szz(i,:) = (1./(rho.rho_2*u(i))).*(g.xx.*(sind(rho.angle)).^2 + ... 328 | g.zz.*(cosd(rho.angle)).^2 + ... 329 | g.xz.*cosd(rho.angle).*sind(rho.angle)); 330 | 331 | Sxz(i,:) = -(rho.angle./u(i)).*(g.xx.*(1./rho.rho_2-1./rho.rho_1).*sind(2*rho.angle) + ... 332 | g.zz.*(1./rho.rho_1-1./rho.rho_2).*sind(2*rho.angle) + ... 333 | g.xz.*(1./rho.rho_2-1./rho.rho_1).*cosd(2*rho.angle)); 334 | 335 | % Uncomment if lambda sensitivity is needed (if you don't know wether it is needed, assume it is not) 336 | % s_m = sqrt(rho.rho_1.*rho.rho_2); 337 | % lambd = sqrt(rho.rho_2./rho.rho_1); 338 | % Slambda(i,:) = - ( d_phi.xx.*s_m.*(cosd(rho.angle).^2 - 1./lambd.^2.*sind(rho.angle).^2) ... 339 | % + d_phi.zz.*s_m.*(sind(rho.angle).^2 - 1./lambd.^2.*cosd(rho.angle).^2) ... 340 | % - d_phi.xz.*0.5.*s_m.*(1 + 1./lambd.^2).*sind(2*rho.angle)); 341 | 342 | end 343 | 344 | S.xx = Sxx; 345 | S.xz = Sxz; 346 | S.zz = Szz; 347 | % Uncomment if lambda sensitivity is needed 348 | % S.lambda = Slambda; 349 | 350 | % pole-pole 351 | elseif isnan(XYZ.MEAS.C2(1,1)) && isnan(XYZ.MEAS.P2(1,1)) 352 | 353 | parfor i = 1:n 354 | 355 | u_1 = u1(:,ind.meas(i,1):nb_electrode:end); % u(c1) 356 | u_1R = u1(:,ind.meas(i,2):nb_electrode:end); % u(p1) 357 | 358 | % Gradient calculation 359 | g = gradient_product_anis(u_1R, u_1, param.h_x, param.h_z, param.k, param.flag.inv.p); 360 | 361 | % xx 362 | g.xx = integration_U(g.xx,param.wk,param.k,param.nbk1); % Inverse Fourier transform 363 | g.xx = reshape(g.xx,nb_ligne,nb_col); 364 | g.xx = reshape(g.xx',(nb_ligne)*(nb_col),1)'; % horizontally arranged 365 | 366 | % xz 367 | g.xz = integration_U(g.xz,param.wk,param.k,param.nbk1); % Inverse Fourier transform 368 | g.xz = reshape(g.xz,nb_ligne,nb_col); 369 | g.xz = reshape(g.xz',(nb_ligne)*(nb_col),1)'; % horizontally arranged 370 | 371 | % zz 372 | g.zz = integration_U(g.zz,param.wk,param.k,param.nbk1); % Inverse Fourier transform 373 | g.zz = reshape(g.zz,nb_ligne,nb_col); 374 | g.zz = reshape(g.zz',(nb_ligne)*(nb_col),1)'; % horizontally arranged 375 | 376 | % yy 377 | g.yy = integration_U(g.yy,param.wk,param.k,param.nbk1); % tr. Fourier inv. 378 | g.yy = reshape(g.yy,nb_ligne,nb_col); 379 | g.yy = reshape(g.yy',(nb_ligne)*(nb_col),1)'; % horizontally arranged 380 | 381 | % Calculation of the sensitivity (ln(resistivity)) 382 | Sxx(i,:) = (1./(rho.rho_1*u(i))).*(g.xx.*(cosd(rho.angle)).^2 + ... 383 | g.zz.*(sind(rho.angle)).^2 - ... 384 | g.xz.*cosd(rho.angle).*sind(rho.angle) + ... 385 | g.yy); 386 | 387 | Szz(i,:) = (1./(rho.rho_2*u(i))).*(g.xx.*(sind(rho.angle)).^2 + ... 388 | g.zz.*(cosd(rho.angle)).^2 + ... 389 | g.xz.*cosd(rho.angle).*sind(rho.angle)); 390 | 391 | Sxz(i,:) = -(rho.angle./u(i)).*(g.xx.*(1./rho.rho_2-1./rho.rho_1).*sind(2*rho.angle) + ... 392 | g.zz.*(1./rho.rho_1-1./rho.rho_2).*sind(2*rho.angle) + ... 393 | g.xz.*(1./rho.rho_2-1./rho.rho_1).*cosd(2*rho.angle)); 394 | 395 | % Uncomment if lambda sensitivity is needed (if you don't know wether it's needed, assume it is not) 396 | % s_m = sqrt(rho.rho_1.*rho.rho_2); 397 | % lambd = sqrt(rho.rho_2./rho.rho_1); 398 | % Slambda(i,:) = - ( d_phi.xx.*s_m.*(cosd(rho.angle).^2 - 1./lambd.^2.*sind(rho.angle).^2) ... 399 | % + d_phi.zz.*s_m.*(sind(rho.angle).^2 - 1./lambd.^2.*cosd(rho.angle).^2) ... 400 | % - d_phi.xz.*0.5.*s_m.*(1 + 1./lambd.^2).*sind(2*rho.angle)); 401 | 402 | end 403 | 404 | S.xx = Sxx; 405 | S.xz = Sxz; 406 | S.zz = Szz; 407 | % Uncomment if lambda sensitivity is needed 408 | % S.lambda = Slambda; 409 | 410 | % pole-dipole 411 | elseif isnan(XYZ.MEAS.C2(1,1)) && ~isnan(XYZ.MEAS.P2(1,1)) 412 | 413 | parfor i = 1:n 414 | 415 | u_1 = u1(:,ind.meas(i,1):nb_electrode:end); % u(c1) 416 | u_1R = (u1(:,ind.meas(i,2):nb_electrode:end)-u1(:,ind.meas(i,3):nb_electrode:end)); % u(p1)-u(p2) 417 | 418 | % Gradient calculation 419 | g = gradient_product_anis(u_1R, u_1, param.h_x, param.h_z, param.k, param.flag.inv.p); 420 | 421 | % xx 422 | g.xx = integration_U(g.xx,param.wk,param.k,param.nbk1); % Inverse Fourier transform 423 | g.xx = reshape(g.xx,nb_ligne,nb_col); 424 | g.xx = reshape(g.xx',(nb_ligne)*(nb_col),1)'; % horizontally arranged 425 | 426 | % xz 427 | g.xz = integration_U(g.xz,param.wk,param.k,param.nbk1); % Inverse Fourier transform 428 | g.xz = reshape(g.xz,nb_ligne,nb_col); 429 | g.xz = reshape(g.xz',(nb_ligne)*(nb_col),1)'; % horizontally arranged 430 | 431 | % zz 432 | g.zz = integration_U(g.zz,param.wk,param.k,param.nbk1); % Inverse Fourier transform 433 | g.zz = reshape(g.zz,nb_ligne,nb_col); 434 | g.zz = reshape(g.zz',(nb_ligne)*(nb_col),1)'; % horizontally arranged 435 | 436 | % yy 437 | g.yy = integration_U(g.yy,param.wk,param.k,param.nbk1); % tr. Fourier inv. 438 | g.yy = reshape(g.yy,nb_ligne,nb_col); 439 | g.yy = reshape(g.yy',(nb_ligne)*(nb_col),1)'; % horizontally arranged 440 | 441 | % Calculation of the sensitivity (ln(resistivity)) 442 | Sxx(i,:) = (1./(rho.rho_1*u(i))).*(g.xx.*(cosd(rho.angle)).^2 + ... 443 | g.zz.*(sind(rho.angle)).^2 - ... 444 | g.xz.*cosd(rho.angle).*sind(rho.angle) + ... 445 | g.yy); 446 | 447 | Szz(i,:) = (1./(rho.rho_2*u(i))).*(g.xx.*(sind(rho.angle)).^2 + ... 448 | g.zz.*(cosd(rho.angle)).^2 + ... 449 | g.xz.*cosd(rho.angle).*sind(rho.angle)); 450 | 451 | Sxz(i,:) = -(rho.angle./u(i)).*(g.xx.*(1./rho.rho_2-1./rho.rho_1).*sind(2*rho.angle) + ... 452 | g.zz.*(1./rho.rho_1-1./rho.rho_2).*sind(2*rho.angle) + ... 453 | g.xz.*(1./rho.rho_2-1./rho.rho_1).*cosd(2*rho.angle)); 454 | 455 | % Uncomment if lambda sensitivity is needed (if you don't know wether it's needed, assume it is not) 456 | % s_m = sqrt(rho.rho_1.*rho.rho_2); 457 | % lambd = sqrt(rho.rho_2./rho.rho_1); 458 | % Slambda(i,:) = - ( d_phi.xx.*s_m.*(cosd(rho.angle).^2 - 1./lambd.^2.*sind(rho.angle).^2) ... 459 | % + d_phi.zz.*s_m.*(sind(rho.angle).^2 - 1./lambd.^2.*cosd(rho.angle).^2) ... 460 | % - d_phi.xz.*0.5.*s_m.*(1 + 1./lambd.^2).*sind(2*rho.angle)); 461 | 462 | end 463 | 464 | S.xx = Sxx; 465 | S.xz = Sxz; 466 | S.zz = Szz; 467 | % Uncomment if lambda sensitivity is needed 468 | % S.lambda = Slambda; 469 | end 470 | end 471 | end 472 | 473 | end 474 | -------------------------------------------------------------------------------- /functions/cglscd.m: -------------------------------------------------------------------------------- 1 | function [x, error, iter] = cglscd(J, x, b, BETA, CTC, dxc, D, P, max_it, tol, appl_fct_reg) 2 | 3 | %%========================================================================% 4 | % % 5 | % This function calculate resistivity perturabation by cg % 6 | % it resolves : % 7 | % for model reg. (J'*D'*D*J+ BETA CTC) x= J'*D'*D (d-dobs)-BETA(CTC*dxc) % 8 | % for model pert. reg. (J'*D'*D*J+ BETA CTC) x= J'*D'*D (d-dobs) % 9 | % % 10 | %%========================================================================% 11 | % % 12 | % In: % 13 | % ----------- % 14 | % J : Jacobian matrix % 15 | % x : initial guess vector % 16 | % b : d-dobs % 17 | % BETA : regularization coefficient % 18 | % CTC : C'*C where C is regularization matrix % 19 | % dxc : rho-rho_ref % 20 | % D : data weigthing matrix % 21 | % P : constraints vector to fix resistivity ( 0 fix, 1 unfix) % 22 | % max_it : maximum number of iteration % 23 | % tol : error tolerance % 24 | % appl_fct_reg : applied regularization ( model or model perturbation) % 25 | % % 26 | % Out: % 27 | % ----------- % 28 | % x REAL solution vector % 29 | % error REAL error norm % 30 | % iter INTEGER number of iterations performed % 31 | % % 32 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 33 | %=========================================================================% 34 | % Copyright (C) 2008 Abderrezak BOUCHEDDA % 35 | %=====oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo====% 36 | % contact: ---------->\\\//// % 37 | % |_ _| % 38 | % (@ @) % 39 | % **********oooO***(_)***Oooo********** % 40 | % * -----> Abderrezak BOUCHEDDA<----- * % 41 | % * Abderrezak.Bouchedda@ete.inrs.ca * % 42 | % * INRS-ETE * % 43 | % * http://www.ete.inrs.ca/ete * % 44 | % ************************************* % 45 | % |_______| % 46 | % |__|__| % 47 | % () () % 48 | % ooO Ooo % 49 | % This program is free software; you can redistribute it and/or modify % 50 | % it under the terms of the GNU General Public License as published by % 51 | % the Free Software Foundation; either version 2 of the License, or % 52 | % (at your option) any later version. % 53 | % % 54 | % This program is distributed in the hope that it will be useful, % 55 | % but WITHOUT ANY WARRANTY; without even the implied warranty of % 56 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % 57 | % GNU General Public License for more details. % 58 | % % 59 | % You should have received a copy of the GNU General Public License % 60 | % along with this program; if not, write to the Free Software % 61 | % Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA% 62 | % % 63 | %%========================================================================% 64 | 65 | %% Calculation 66 | 67 | iter = 0; 68 | 69 | if isempty(P) 70 | P = ones(size(x)); 71 | end 72 | 73 | x = P.*x; 74 | % M : jacoby preconditioner 75 | M = (sum((D*J).^2)'+BETA*diag(CTC)); 76 | M(M==0) = eps; 77 | M = 1./M; 78 | % 79 | zz = D*(b - J*x); % gradient initialisation 80 | 81 | if strcmp(appl_fct_reg,'model') 82 | 83 | b1 = (((D.^2)*b)'*J)' - BETA*CTC*(dxc); 84 | bnrm2 = norm( b1 ); 85 | 86 | if ( bnrm2 == 0.0 ) 87 | bnrm2 = 1.0; 88 | end 89 | 90 | r= P.*(((zz' * D )*J)'- BETA*CTC * (x+dxc)); 91 | 92 | error = norm( r ) / bnrm2; % error initialisation 93 | 94 | if ( error < tol ) 95 | return 96 | end 97 | 98 | for iter = 1:max_it 99 | 100 | z = M.* r; % modified gradient 101 | rho = (r'*z); 102 | 103 | if ( iter > 1 ) 104 | beta = rho / rho_1; % beta_k coefficient 105 | p = z + beta*p; % direction 106 | else 107 | p = z; % direction initialisation 108 | end 109 | 110 | q = D*(J*p); 111 | alpha = rho / (q'*q + (p'*BETA*CTC*p)); % step 112 | x = x + alpha * p; % descent 113 | zz = zz - alpha*q; 114 | r = P.*(((zz'*D)*J)' - BETA*CTC*(x+dxc)); % gradient 115 | error = norm( r ) / bnrm2; 116 | 117 | if ( error <= tol ) 118 | break 119 | end % stop criterion 120 | 121 | rho_1 = rho; 122 | 123 | end 124 | 125 | 126 | elseif strcmp(appl_fct_reg,'model perturbation') 127 | 128 | r= P.*((zz' * D )*J)'- BETA*CTC * x; 129 | b1=(((D.^2)*b)'*J)'; 130 | bnrm2 = norm( b1 ); 131 | error = norm( r ) / bnrm2; % error initialisation 132 | 133 | if ( error < tol ) 134 | return 135 | end 136 | 137 | for iter = 1:max_it 138 | 139 | z = M.* r; % modified gradient 140 | rho = (r'*z); 141 | 142 | if ( iter > 1 ) 143 | beta = rho / rho_1; % beta_k coefficient 144 | p = z + beta*p; % direction 145 | else 146 | p = z; % direction initialisation 147 | end 148 | 149 | q = D*J*p; 150 | alpha = rho / (q'*q + BETA *(p'*CTC*p)); % step 151 | x = x + alpha * p; % descent 152 | zz = zz - alpha*q; 153 | r = P.*((zz'*D)*J)'- BETA * CTC * x; % gradient 154 | error = norm( r ) / bnrm2; 155 | if ( error <= tol ) 156 | break 157 | end % stop criterion 158 | 159 | rho_1 = rho; 160 | 161 | end 162 | 163 | end 164 | end -------------------------------------------------------------------------------- /functions/deriv2D.m: -------------------------------------------------------------------------------- 1 | function [Cx,Cz] = deriv2D(pasx,pasz,flag) 2 | 3 | 4 | nxx=numel(pasx); % nombre d'elements dans la direction x 5 | nzz=numel(pasz); % nombre d'elements dans la direction z 6 | N=nxx*nzz; % nombre total d'elements 7 | %nx=(nxx-1)*nzz; 8 | nz=nxx*(nzz-1); 9 | Cx=sparse(N,N); 10 | 11 | 12 | 13 | 14 | 15 | if flag ==1 % first derivative 16 | 17 | pasz=(pasz(1:end-1)+pasz(1:end-1))/2; 18 | pasx=(pasx(1:end-1)+pasx(1:end-1))/2; 19 | pasx=1./pasx(:); % 20 | pasz=1./pasz(:); 21 | 22 | % in x direction 23 | for i=1:nzz 24 | 25 | Cx1 = sparse(1+(i-1)*nxx:nxx-1+(i-1)*nxx , 1+nxx*(i-1):nxx-1+nxx*(i-1) , -pasx , N , N); 26 | Cx2 = sparse(1+(i-1)*nxx:nxx-1+(i-1)*nxx , 2+nxx*(i-1):nxx+nxx*(i-1) , pasx , N , N); 27 | Cx=Cx+Cx1+Cx2; 28 | 29 | end 30 | 31 | % in z direction 32 | pasz=pasz'; 33 | 34 | pasz=repmat(pasz,nxx,1); 35 | pasz=pasz(:); % mise sous forme de vecteur 36 | % 37 | % 38 | Cz=sparse(N,N); 39 | Cz1 = sparse(1:(nzz-1)*nxx,1:(nzz-1)*nxx,-pasz,N,N); 40 | Cz2 = sparse(1:(nzz-1)*nxx,1+nxx:N,pasz,N,N); 41 | Cz=Cz+Cz1+Cz2; 42 | 43 | elseif flag==2 % second derivative 44 | 45 | ax=zeros(nxx,1); bx=ax; az=zeros(nzz,1);bz=az; 46 | ax(1)=0; 47 | ax(end)=3/((pasx(end-1)+2*pasx(end))*pasx(end)); 48 | bx(1)=3/((pasx(2)+2*pasx(1))*pasx(1)); 49 | bx(end)=0; 50 | 51 | az(1)=0; 52 | az(end)=3./((pasz(end-1)+2*pasz(end))*pasz(end)); 53 | 54 | bz(1)=3./((pasz(2)+2*pasz(1))*pasz(1)); 55 | bz(end)=0; 56 | 57 | 58 | ax(2:end-1)=4./((pasx(3:end)+2*pasx(2:end-1)+pasx(1:end-2)).*(pasx(2:end-1)+pasx(1:end-2))); 59 | bx(2:end-1)=4./((pasx(3:end)+2*pasx(2:end-1)+pasx(1:end-2)).*(pasx(2:end-1)+pasx(3:end))); 60 | az(2:end-1)=4./((pasz(3:end)+2*pasz(2:end-1)+pasz(1:end-2)).*(pasz(2:end-1)+pasz(1:end-2))); 61 | bz(2:end-1)=4./((pasz(3:end)+2*pasz(2:end-1)+pasz(1:end-2)).*(pasz(2:end-1)+pasz(3:end))); 62 | 63 | ax=kron(ones(nzz,1),ax); 64 | bx=kron(ones(nzz,1),bx); 65 | az=kron(az,ones(nxx,1)); 66 | bz=kron(bz,ones(nxx,1)); 67 | 68 | 69 | cx=-(ax+bx); 70 | cz=-(az+bz); 71 | % reordering to use spdiags function 72 | ax=[ax(2:end);0]; 73 | az=[az(nxx+1:end);zeros(nxx,1)]; 74 | bx=[0;bx(1:end-1)]; bx(2)=0; % to avoid null space matrix 75 | bz=[zeros(nxx,1);bz(1:end-nxx)]; bz(2)=0; % to avoid null space matrix 76 | 77 | Cx = spdiags([ax cx bx],-1:1, N, N); 78 | Cz = spdiags([az cz bz],[-nxx 0 nxx], N, N); 79 | 80 | end 81 | 82 | end 83 | 84 | 85 | 86 | 87 | -------------------------------------------------------------------------------- /functions/distance_weighting.m: -------------------------------------------------------------------------------- 1 | function Q=distance_weighting(param,beta) 2 | 3 | %%========================================================================% 4 | % % 5 | % Calculation of distance weigthing values % 6 | % % 7 | %%========================================================================% 8 | % % 9 | % In: % 10 | % ----------- % 11 | % param: parameters structure % 12 | % beta: weigthing coefficient % 13 | % % 14 | % Out: % 15 | % ----------- % 16 | % Q = weigthing values % 17 | % % 18 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 19 | %%========================================================================% 20 | % Copyright (C) 2019 Simon GERNEZ and Abderrezak BOUCHEDDA % 21 | %%========================================================================% 22 | % % 23 | % Contacts: % 24 | % % 25 | % Simon GERNEZ % 26 | % simon.gernez@ete.inrs.ca % 27 | % Institut National de la Recherche Scientifique % 28 | % Centre Eau-Terre-Environnement % 29 | % http://www.ete.inrs.ca/ % 30 | % % 31 | % Abderrezak BOUCHEDDA % 32 | % Abderrezak.Bouchedda@ete.inrs.ca % 33 | % Institut National de la Recherche Scientifique % 34 | % Centre Eau-Terre-Environnement % 35 | % http://www.ete.inrs.ca/ % 36 | % % 37 | % This program is free software; you can redistribute it and/or modify % 38 | % it under the terms of the GNU General Public License as published by % 39 | % the Free Software Foundation; either version 2 of the License, or % 40 | % (at your option) any later version. % 41 | % % 42 | % This program is distributed in the hope that it will be useful, % 43 | % but WITHOUT ANY WARRANTY; without even the implied warranty of % 44 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % 45 | % GNU General Public License for more details. % 46 | % % 47 | % You should have received a copy of the GNU General Public License % 48 | % along with this program; if not, write to the Free Software % 49 | % Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA% 50 | 51 | %%========================================================================% 52 | 53 | %% Calculation 54 | 55 | % Li and Oldenburg, 2000,Joint inversion of surface and three-component 56 | % borehole magnetic data, Geophysics. 57 | 58 | X = param.grille(:,1); 59 | X = reshape(X,param.nb_ligne,param.nb_col); 60 | X = X'; 61 | X = X(:); 62 | 63 | Z = param.grille(:,2); 64 | Z = reshape(Z,param.nb_ligne,param.nb_col); 65 | Z = Z'; 66 | Z = Z(:); 67 | 68 | h_x = [param.h_x ; param.h_x(end)]; 69 | h_z = [param.h_z ; param.h_z(end)]; 70 | 71 | h_xr = repmat(h_x(:)',length(h_z),1); 72 | h_zr = repmat(h_z(:),1,length(h_x)); 73 | dV = (h_xr.*h_zr)'; 74 | dV = dV(:); 75 | 76 | R0=min(dV)^(1/3); 77 | Q=0; 78 | pos = [param.pos.C ; param.pos.P]; 79 | % pos = pos(pos(:,2)==0 , :); 80 | % pos(pos(:,2)==0 , :) = []; 81 | n=length(pos); 82 | 83 | for i=1:n 84 | R = sqrt((X-pos(i,1)).^2 + (Z-pos(i,2)).^2); 85 | 86 | R=(R+R0).^3; 87 | R=(dV./R).^2; 88 | Q=Q+R; 89 | end 90 | 91 | Q=Q.^(beta/4); 92 | % Q(Q<1e-3) = 1e-3; 93 | 94 | Q = reshape(Q,param.nb_col,param.nb_ligne)'; 95 | Q(:,[1:param.nb_pad_bloc+param.nb_surr end-(param.nb_pad_bloc+param.nb_surr):end]) = 1; 96 | Q(end-(param.nb_pad_bloc+param.nb_surr):end,:) = 1; 97 | % Q(:,[1:param.nb_pad_bloc+param.nb_surr-3 end-(param.nb_pad_bloc+param.nb_surr)+3:end]) = 1; 98 | % Q(end-(param.nb_pad_bloc+param.nb_surr)+3:end,:) = 1; 99 | end -------------------------------------------------------------------------------- /functions/find_k.m: -------------------------------------------------------------------------------- 1 | function [k,wk,N] = find_k(N,k2) 2 | 3 | %%========================================================================% 4 | % % 5 | % 2.5D frequency process % 6 | % % 7 | %%========================================================================% 8 | % % 9 | % In: % 10 | % ----------- % 11 | % N : number of frequencies considered % 12 | % k2 : reference frequency % 13 | % % 14 | % Out: % 15 | % ----------- % 16 | % k : number of frequencies considered % 17 | % wk : reference frequency % 18 | % N : number of frequencies considered % 19 | % % 20 | %%========================================================================% 21 | % Copyright (C) 2019 Simon GERNEZ and Abderrezak BOUCHEDDA % 22 | %%========================================================================% 23 | % % 24 | % Contacts: % 25 | % % 26 | % Simon GERNEZ % 27 | % simon.gernez@ete.inrs.ca % 28 | % Institut National de la Recherche Scientifique % 29 | % Centre Eau-Terre-Environnement % 30 | % http://www.ete.inrs.ca/ % 31 | % % 32 | % Abderrezak BOUCHEDDA % 33 | % Abderrezak.Bouchedda@ete.inrs.ca % 34 | % Institut National de la Recherche Scientifique % 35 | % Centre Eau-Terre-Environnement % 36 | % http://www.ete.inrs.ca/ % 37 | % % 38 | % This program is free software; you can redistribute it and/or modify % 39 | % it under the terms of the GNU General Public License as published by % 40 | % the Free Software Foundation; either version 2 of the License, or % 41 | % (at your option) any later version. % 42 | % % 43 | % This program is distributed in the hope that it will be useful, % 44 | % but WITHOUT ANY WARRANTY; without even the implied warranty of % 45 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % 46 | % GNU General Public License for more details. % 47 | % % 48 | % You should have received a copy of the GNU General Public License % 49 | % along with this program; if not, write to the Free Software % 50 | % Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA% 51 | 52 | %% Code 53 | 54 | kk2=k2; 55 | k2=sqrt(k2); 56 | k1=0; 57 | 58 | [xk1,wk1]=Gausslp(N); 59 | [xk2,wk2]=Gausslgp(N-3); 60 | 61 | k=[(((k2-k1)*xk1+k1+k2)/2).^2 xk2+kk2]'; 62 | wk=[(k2-k1)*wk1/2 wk2]; 63 | 64 | end 65 | 66 | 67 | %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 68 | function p=Lgndrp(N) % Legendre polynomial 69 | if N<=0 70 | p=1; % n*Ln(t)=(2n-1)t Ln-1(t)-(n-1)Ln-2(t) 71 | elseif N==1 72 | p=[1 0]; 73 | else 74 | p=((2*N-1)*[Lgndrp(N-1) 0]-(N-1)*[0 0 Lgndrp(N-2)])/N; 75 | end 76 | end 77 | 78 | %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 79 | function p=Laguerp(N) %Legendre polynomial 80 | M=N:-1:0; 81 | p=factorial(N)*(((-1).^M)./factorial(M)).*((factorial(N))./(factorial(N-M).*factorial(M))); 82 | end 83 | 84 | %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 85 | function [t,w]=Gausslp(N) 86 | if N<0 87 | error('Gauss-Legendre polynomial of negative order?'); 88 | end 89 | t=roots(Lgndrp(N))'; % make it a row vector 90 | A(1,:)= ones(1,N); b(1)=2; 91 | for n=2:N 92 | A(n,:)=A(n-1,:).*t; 93 | if mod(n,2)==0 94 | b(n)=0; 95 | else 96 | b(n)=2/n; 97 | end 98 | end 99 | w= b/A'; 100 | end 101 | 102 | %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 103 | function [t,w]=Gausslgp(N) 104 | if N<0 105 | error('Gauss-Laguerre polynomial of negative order?'); 106 | end 107 | t=roots(Laguerp(N))'; % make it a row vector 108 | A(1,:)= ones(1,N); b(1)=1; 109 | for n=2:N 110 | A(n,:)=A(n-1,:).*t; 111 | b(n)=(n-1)*b(n-1); 112 | end 113 | w= b/A'; 114 | end -------------------------------------------------------------------------------- /functions/gauss_newton_inversion_anis.m: -------------------------------------------------------------------------------- 1 | function [param, XYZ, Inv] = gauss_newton_inversion_anis(param,XYZ) 2 | 3 | %%========================================================================% 4 | % % 5 | % Gauss Newton inversion % 6 | % % 7 | %%========================================================================% 8 | % % 9 | % In : % 10 | % ----------- % 11 | % param: parameters structure % 12 | % XYZ: electrodes position structure % 13 | % draw_plots: 0: no figure ; 1: dray figures % 14 | % % 15 | % Out : % 16 | % ----------- % 17 | % These structures are saved after each iteration in a iter_#.mat file: % 18 | % param: parameters structure % 19 | % XYZ: electrodes position structure % 20 | % Inv: inversion results at each iteration: % 21 | % Inv.rho: different rho components sections % 22 | % Inv.D: data weighting matrix (from Calc_data_weight.m) % 23 | % Inv.d_cal: apparent resistivities calculated at the ith iteration% 24 | % Inv.rho_app_pos_index: data considered. Negative apparent % 25 | % resistivities are ignored at each iter. % 26 | % Inv.rms: rms value % 27 | % Inv.beta_weighting: weigthing coefficients % 28 | % Inv.sens_weighting: weigthing section % 29 | % Inv.Ki2: Ki^2 value % 30 | % Inv.CTC: model regularization matrix (from CtC_anis.m) % 31 | % % 32 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 33 | %%========================================================================% 34 | % Copyright (C) 2019 Simon GERNEZ and Abderrezak BOUCHEDDA % 35 | %%========================================================================% 36 | % % 37 | % Contacts: % 38 | % % 39 | % Simon GERNEZ % 40 | % simon.gernez@ete.inrs.ca % 41 | % Institut National de la Recherche Scientifique % 42 | % Centre Eau-Terre-Environnement % 43 | % http://www.ete.inrs.ca/ % 44 | % % 45 | % Abderrezak BOUCHEDDA % 46 | % Abderrezak.Bouchedda@ete.inrs.ca % 47 | % Institut National de la Recherche Scientifique % 48 | % Centre Eau-Terre-Environnement % 49 | % http://www.ete.inrs.ca/ % 50 | % % 51 | % This program is free software; you can redistribute it and/or modify % 52 | % it under the terms of the GNU General Public License as published by % 53 | % the Free Software Foundation; either version 2 of the License, or % 54 | % (at your option) any later version. % 55 | % % 56 | % This program is distributed in the hope that it will be useful, % 57 | % but WITHOUT ANY WARRANTY; without even the implied warranty of % 58 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % 59 | % GNU General Public License for more details. % 60 | % % 61 | % You should have received a copy of the GNU General Public License % 62 | % along with this program; if not, write to the Free Software % 63 | % Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA% 64 | 65 | %%========================================================================% 66 | 67 | %% ------ Initialize ----------------------------------------- 68 | 69 | tic 70 | 71 | X = reshape(param.grille(:,1),param.nb_ligne,param.nb_col); 72 | Z = -reshape(param.grille(:,2),param.nb_ligne,param.nb_col); 73 | 74 | if strcmp(param.inv.invparam,'log resistivity') 75 | 76 | if isempty(param.const.rho_init) % if no initial model 77 | [K] = geometric_factor(XYZ,param.flag.geo_factor); 78 | nb_meas = length(param.MEAS.Res); 79 | mm = median(K.*param.MEAS.Res); 80 | 81 | if param.flag.inv.p == 2 82 | % solution_vector : [rho1_init ; rho2_init] 83 | solution_vector = log(mm)*ones(param.nb_ligne*param.nb_col,1); 84 | solution_vector = [solution_vector ; log(param.anis_init*mm)*ones(param.nb_ligne*param.nb_col,1)]; % + rho_2 initial 85 | elseif param.flag.inv.p == 3 86 | % solution_vector : [rho1_init ; rho2_init ; angles_init] 87 | solution_vector = log(mm)*ones(param.nb_ligne*param.nb_col,1); % rho_1 initial 88 | solution_vector = [solution_vector ; log(param.anis_init*mm)*ones(param.nb_ligne*param.nb_col,1)]; % + rho_2 initial 89 | solution_vector = [solution_vector ; log(60)*ones(param.nb_ligne*param.nb_col,1)]; % + angle initial 90 | end 91 | 92 | [rho]= vec2model(exp(solution_vector),param.nb_ligne,param.nb_col, param.flag.inv.p); 93 | 94 | % constraints 95 | if param.const_TrueFalse == true 96 | param.const.vect = log(param.const_vect); 97 | end 98 | 99 | else % if initial model (has to be a structure) 100 | nb_meas = length(param.MEAS.Res); 101 | 102 | if param.flag.inv.p == 2 103 | param.const.rho_init.xx = param.const.rho_init.xx'; 104 | param.const.rho_init.zz = param.const.rho_init.zz'; 105 | solution_vector = [param.const.rho_init.xx(:) ; param.const.rho_init.zz(:)]; 106 | end 107 | 108 | solution_vector = log(solution_vector(:)); 109 | [rho] = vec2model(exp(solution_vector),param.nb_ligne,param.nb_col, param.flag.inv.p); 110 | 111 | if param.const_TrueFalse == true 112 | param.const.vect = log(param.const_vect); 113 | end 114 | end 115 | 116 | if ~isempty(param.const.rho_ref) && param.const.rho_ref ~= 0 117 | param.const.rho_ref = log(param.const.rho_ref); 118 | end 119 | 120 | else 121 | errordlg('gauss_newton_inversion_anis function : inversion parameter type is not defined or not suitable',... 122 | 'inversion parameter Error'); 123 | 124 | end 125 | 126 | % define reference model 127 | if isempty(param.const.rho_ref) 128 | param.const.rho_ref=0; 129 | end 130 | 131 | % Set the constraints values 132 | if isfield(param,'const_ind') && param.const_TrueFalse == true 133 | param.const.P = ones(length(solution_vector),1); 134 | param.const.P(param.const_ind) = 0; 135 | solution_vector(param.const_ind) = param.const.vect; 136 | cglscd_init = ones(length(solution_vector),1); 137 | cglscd_init(param.const_ind) = param.const.vect; 138 | disp('Constraints added') 139 | else 140 | param.const.P = []; 141 | cglscd_init = ones(length(solution_vector),1); 142 | end 143 | 144 | % weight for matrix C 145 | wt = ones(size(solution_vector)); 146 | 147 | % allocate some numbers 148 | gc = 1; 149 | normg0 = 1; 150 | Ki2 = []; 151 | 152 | % data weight matrix calculation 153 | [D,dtw_pre] = Calc_data_weight(param); 154 | D_orig = D; 155 | dtw_pre_orig = dtw_pre; 156 | 157 | % flatness or smoothness or covariance matrix calculation 158 | [CTC,~,~] = CtC_anis(wt,param,param.flag.inv.p); 159 | 160 | %% Start Gauss-Newton loop 161 | 162 | itc = 0; 163 | 164 | while(norm(gc)/normg0 > param.inv.tol && itc < param.inv.maxit && norm(gc) > 1e-20) 165 | %% iteration count 166 | 167 | itc = itc+1; 168 | disp(['Iteration #',num2str(itc)]) 169 | toc 170 | 171 | if itc > 1 172 | param.inv.BETA = max(param.inv.BETA/2,10^-6); 173 | end 174 | 175 | % potential and sensitivity calculation 176 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 177 | 178 | disp(['Sensitivity calculus iteration #',num2str(itc)]); 179 | [d,S] = calcul_u_S_anis(param,XYZ,rho,1); 180 | 181 | K = geometric_factor(XYZ,param.flag.geo_factor); 182 | if strcmp(param.inv.invparam,'log resistivity') 183 | dobs = log((K.*param.MEAS.Res)); 184 | else 185 | dobs = (K.*param.MEAS.Res); 186 | end 187 | D = D_orig; 188 | dtw_pre = dtw_pre_orig; 189 | 190 | % We ignore for this each iteration the quadripoles measuring a negative apparent resistivity 191 | rho_app = (K'.*d); 192 | if strcmp(param.inv.invparam,'log resistivity') 193 | rho_app_pos_index = (rho_app > .1); 194 | end 195 | 196 | d = d(rho_app_pos_index); 197 | K = K(rho_app_pos_index); 198 | dobs = dobs(rho_app_pos_index); 199 | D = D(rho_app_pos_index,rho_app_pos_index); 200 | dtw_pre = dtw_pre(rho_app_pos_index); 201 | 202 | if param.flag.inv.p == 2 203 | J = [S.xx(rho_app_pos_index,:) S.zz(rho_app_pos_index,:)]; 204 | elseif param.flag.inv.p == 3 205 | J = [S.xx(rho_app_pos_index,:) S.zz(rho_app_pos_index,:) S.xz(rho_app_pos_index,:)]; 206 | end 207 | 208 | %% Weigthing ------------------------------------------------------ 209 | 210 | if param.inv.weight == true && itc >= param.inv.weightMinit && itc <= param.inv.weightMaxit 211 | % ----------------------------------------------------------------- 212 | 213 | % Distance weighting - recommended 214 | if strcmp(param.inv.weightFun,'distance') 215 | beta_weight_1 = .1; 216 | beta_weight_2 = .1; 217 | message_weight = strcat('Weighting based weighting function applied (iter #',num2str(itc),')'); 218 | disp(message_weight) 219 | wt1 = distance_weighting(param,beta_weight_1); 220 | wt2 = distance_weighting(param,beta_weight_2); 221 | wt1 = wt1'; 222 | wt2 = wt2'; 223 | % figure 224 | % imagesc(0:40,0:9,wt1(param.h_x==1/x, param.h_z==1/z));colormap jet;colorbar 225 | % wt = [wt1 , ones(size(wt2))]; 226 | % wt = [ones(size(wt1)) , wt2]; 227 | wt = [wt1 , wt2]; 228 | 229 | wt = wt(:); 230 | 231 | [CTC,~,~] = CtC_anis(wt,param,param.flag.inv.p); % 232 | 233 | 234 | % Sensitivity weighting 235 | elseif strcmp(param.inv.weightFun,'sensitivity') 236 | % message_weight = strcat('Sensitivity based weighting function applied (iter #',num2str(itc),', Ki = ',num2str(Ki),')'); 237 | % disp(message_weight) 238 | 239 | wt = (sum(J.*J)); 240 | 241 | beta_weight_1 = 0.1; 242 | beta_weight_2 = 0.1; 243 | 244 | wt1 = wt(1:param.nb_col*param.nb_ligne).^(beta_weight_1/4); 245 | wt1 = reshape(wt1,param.nb_col,param.nb_ligne)'; 246 | wt1(:,[1:param.nb_pad_bloc+20+1 , end-(param.nb_pad_bloc+16):end]) = 1; 247 | % wt1(end-(param.nb_pad_bloc+1):end,:) = 1; 248 | % wt1(:,[1:param.nb_pad_bloc+param.nb_raff(1)*(param.nb_surr) , end-(param.nb_pad_bloc+param.nb_raff(1)*(param.nb_surr)-1):end]) = 1; 249 | wt1(end-(param.nb_pad_bloc+param.nb_raff(2)*param.nb_surr):end,:) = 1; 250 | 251 | wt2 = wt(param.nb_col*param.nb_ligne+1:end).^(beta_weight_2/4); 252 | wt2 = reshape(wt2,param.nb_col,param.nb_ligne)'; 253 | wt2(:,[1:param.nb_pad_bloc+20+1 , end-(param.nb_pad_bloc+16):end]) = 1; 254 | % wt2(end-(param.nb_pad_bloc+1):end,:) = 1; 255 | % wt2(:,[1:param.nb_pad_bloc+param.nb_raff(1)*(param.nb_surr) , end-(param.nb_pad_bloc+param.nb_raff(1)*(param.nb_surr)-1):end]) = 1; 256 | wt2(end-(param.nb_pad_bloc+param.nb_raff(2)*param.nb_surr):end,:) = 1; 257 | 258 | wt = [wt1' , wt2']; 259 | % wt = [wt1' , ones(size(wt2'))]; 260 | 261 | fig1 = figure('visible','off'); 262 | subplot(121) 263 | imagesc(wt1); 264 | title('\omega_1') 265 | colormap jet; 266 | colorbar 267 | 268 | subplot(122) 269 | imagesc(wt2); 270 | title('\omega_2') 271 | colormap jet; 272 | colorbar 273 | 274 | set(gcf,'Visible','off','CreateFcn','set(gcf,''Visible'',''on'')') 275 | iterName = num2str(itc); 276 | pathName = strcat('./savefig/weightings',iterName,'.fig'); 277 | savefig(fig1,pathName) 278 | close 279 | 280 | [CTC,~,~] = CtC_anis(wt,param,param.flag.inv.p); % 281 | 282 | else 283 | error('Weighting function has to be param.inv.weightFun=''distance'' or param.inv.weightFun=''sensitivity''') 284 | 285 | end 286 | 287 | 288 | % Unweight the model after max_itc_weights iterations 289 | elseif param.inv.weight == true && itc > param.inv.weightMaxit 290 | beta_weight_1 = nan; 291 | beta_weight_2 = nan; 292 | wt = ones(size(solution_vector)); 293 | 294 | [CTC,~,~] = CtC_anis(wt,param,param.flag.inv.p); % 295 | 296 | 297 | % Conserve last applied weighting vector after max_itc_weights iterations 298 | else 299 | beta_weight_1 = nan; 300 | beta_weight_2 = nan; 301 | 302 | end 303 | 304 | if ~all(K'.*d > 0) 305 | disp('Negative apparent resistivity') 306 | disp(' ') 307 | end 308 | 309 | d = log(K'.*d)'; 310 | 311 | clear S 312 | 313 | %% Evaluate model perturbation 314 | 315 | [s,error_cglscd,~] = cglscd(J,cglscd_init, (dobs-d),param.inv.BETA,CTC,solution_vector-param.const.rho_ref,D,param.const.P, 1000, 10^-6,param.inv.appl_fct_reg); 316 | error_cglscd % indication of the iteration efficiency 317 | 318 | if itc == 1 319 | normg0 = norm(gc); 320 | end 321 | 322 | %% Test for convergence 323 | 324 | if max(abs(s)) < 1e-6 325 | errordlg('gauss_newton_inversion_anis function : STEP size too small CONVERGE ',... 326 | 'inversion stop'); 327 | end; 328 | 329 | % Try the step 330 | mu1 = 1; 331 | 332 | % Calculate the value of data objective function 333 | fd = 0.5*(d-dobs)'*(D.^2)*(d-dobs); 334 | 335 | %% Armijo Line search 336 | 337 | % Calculate the value of model objective function 338 | fm = 0.5*( (solution_vector-param.const.rho_ref)'*param.inv.BETA*CTC*(solution_vector-param.const.rho_ref) ); 339 | 340 | % Add them for the total Objective function 341 | fc = fd + fm; 342 | 343 | % Evaluate the gradient 344 | gc = (((D.^2)*(d-dobs))'*J)' + param.inv.BETA*CTC*(solution_vector-param.const.rho_ref); 345 | clear J 346 | 347 | for ils = 1 : 6 348 | 349 | disp(['Line search calculation #',num2str(ils)]); 350 | 351 | xt = solution_vector + mu1*s; 352 | 353 | %% Evaluate the new objective function 354 | 355 | if strcmp(param.inv.invparam,'log resistivity') == 1 % log parameters 356 | if ~isempty(param.const.rho_min) 357 | xt(exp(xt) < param.const.rho_min) = param.const.rho_min; 358 | end 359 | if ~isempty(param.const.rho_max) 360 | xt(exp(xt) > param.const.rho_max) = param.const.rho_max; 361 | end 362 | rho = vec2model(exp(xt),param.nb_ligne,param.nb_col,param.flag.inv.p); 363 | end 364 | 365 | [d] = calcul_u_S_anis(param,XYZ,rho,0); 366 | 367 | K = geometric_factor(XYZ,param.flag.geo_factor); 368 | dobs = log(K.*param.MEAS.Res); 369 | D = D_orig; 370 | dtw_pre = dtw_pre_orig; 371 | 372 | % We ignore for each iteration the quadripoles producing a negative apparent resistivity 373 | rho_app = (K'.*d); 374 | rho_app_pos_index = (rho_app > .1); 375 | 376 | d = d(rho_app_pos_index); 377 | K = K(rho_app_pos_index); 378 | dobs = dobs(rho_app_pos_index); 379 | D = D(rho_app_pos_index,rho_app_pos_index); 380 | dtw_pre = dtw_pre(rho_app_pos_index); 381 | 382 | if ~all(K'.*d > 0) 383 | disp('Negative apparent resistivity') 384 | disp(' ') 385 | end 386 | 387 | d = log(K'.*d)'; 388 | 389 | fd = 0.5*(d-dobs)'*(D.^2)*(d-dobs); 390 | fm = 0.5*((xt-param.const.rho_ref)'*param.inv.BETA*CTC*(xt-param.const.rho_ref)); 391 | ft = fd+fm; 392 | 393 | fgoal = fc - param.inv.alp*mu1*(s'*gc); 394 | 395 | if ft < fgoal 396 | break 397 | else 398 | mu1 = mu1/2; 399 | end; 400 | 401 | end % end line search 402 | 403 | rms_model = 100*sum(sqrt((((solution_vector-xt).^2)./(1e-10+solution_vector.^2))/(param.nb_ligne*param.nb_col))); 404 | 405 | if rms_model < param.inv.rms_model 406 | errordlg('gauss_newton_inversion function : rms_model < desired rms_model',... 407 | 'inversion convergence'); 408 | break; 409 | end 410 | 411 | %% Update model 412 | 413 | solution_vector = xt; 414 | 415 | e = (D*(d-dobs)); 416 | Ki = sum(e.^2) / nb_meas; 417 | 418 | % data reweigthing ( L1 or W-estimator) 419 | if ~strcmp(param.inv.dataweight.type,'const.weight') 420 | [D,~] = Calc_data_weight(param,e,dtw_pre); 421 | end 422 | 423 | Ki2 = [Ki2;Ki]; 424 | rms_data = 100*sqrt(sum((d-dobs).^2))/(norm(dobs)); % misfit in percentages 425 | 426 | % Stock inv. infos into Inv structure 427 | Inv.rho{itc} = rho; 428 | Inv.D{itc} = D; 429 | Inv.d_cal{itc} = d; 430 | Inv.rho_app_pos_index{itc} = rho_app_pos_index; 431 | Inv.rms{itc} = rms_data; 432 | Inv.beta_weighting{itc} = [beta_weight_1 ; beta_weight_2]; 433 | Inv.sens_weighting{itc} = wt; 434 | Inv.Ki2 = Ki2; 435 | Inv.CTC{itc} = CTC; 436 | 437 | % Display convergence info : # iter, Ki2, rmse 438 | [(1:itc)' , Ki2 , cell2mat(Inv.rms)'] %#ok 439 | 440 | str_save = strcat('iter_',num2str(itc),'.mat'); 441 | save(str_save,'param','XYZ','Inv') 442 | 443 | end 444 | 445 | end -------------------------------------------------------------------------------- /functions/geometric_factor.m: -------------------------------------------------------------------------------- 1 | function K = geometric_factor(XYZ,C1C2_config) 2 | 3 | %%========================================================================% 4 | % % 5 | % Geometric factor calculation % 6 | % % 7 | %%========================================================================% 8 | % % 9 | % In: % 10 | % ----------- % 11 | % XYZ: electrodes position structure % 12 | % C1C2_config: % 13 | % C1C2_config==1 (C1,C2) borehole electrodes % 14 | % C1C2_config==2 (C1,C2) surface electrodes % 15 | % C1C2_config==3 (C1) borehole electrodes ; (C2) surface electrodes % 16 | % C1C2_config==4 (C2) borehole electrodes ; (C2) surface electrodes % 17 | % % 18 | % Out: % 19 | % ----------- % 20 | % K: vector of the geometric factors corresponding to each quadrupole % 21 | % (Guo et al. 2014) % 22 | % % 23 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 24 | % Copyright (C) 2009 Abderrezak BOUCHEDDA 25 | %=====oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo====% 26 | % contact: ---------->\\\//// % 27 | % |_ _| % 28 | % (@ @) % 29 | % **********oooO***(_)***Oooo********** % 30 | % * -----> Abderrezak BOUCHEDDA<----- * % 31 | % * Abderrezak.Bouchedda@ete.inrs.ca * % 32 | % * INRS-ETE * % 33 | % * http://www.ete.inrs.ca/ete * % 34 | % ************************************* % 35 | % |_______| % 36 | % |__|__| % 37 | % () () % 38 | % ooO Ooo % 39 | % This program is free software; you can redistribute it and/or modify % 40 | % it under the terms of the GNU General Public License as published by % 41 | % the Free Software Foundation; either version 2 of the License, or % 42 | % (at your option) any later version. % 43 | % % 44 | % This program is distributed in the hope that it will be useful, % 45 | % but WITHOUT ANY WARRANTY; without even the implied warranty of % 46 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % 47 | % GNU General Public License for more details. % 48 | % % 49 | % You should have received a copy of the GNU General Public License % 50 | % along with this program; if not, write to the Free Software % 51 | % Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA% 52 | % % 53 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 54 | %%========================================================================% 55 | 56 | %% Calculation 57 | 58 | ind1 = find(C1C2_config == 1); 59 | ind2 = find(C1C2_config == 2); 60 | ind3 = find(C1C2_config == 3); 61 | ind4 = find(C1C2_config == 4); 62 | 63 | K = zeros(size(C1C2_config)); 64 | 65 | 66 | if ~isempty(ind1) 67 | if isnan(XYZ.MEAS.C2(1,1)) && isnan(XYZ.MEAS.P2(1,1)) % pole-pole 68 | r2=0; 69 | r3=0; 70 | r4=0; 71 | r21=0; 72 | r31=0; 73 | r41=0; 74 | elseif isnan(XYZ.MEAS.C2(1,1)) && ~isnan(XYZ.MEAS.P2(1,1)) % pole-dipole 75 | r2=0; 76 | r4=0; 77 | r21=0; 78 | r41=0; 79 | r3=1./((XYZ.MEAS.C1(ind1,1)-XYZ.MEAS.P2(ind1,1)).^2 +(XYZ.MEAS.C1(ind1,2)-XYZ.MEAS.P2(ind1,2)).^2).^.5; % C1-P2 80 | r31=1./((XYZ.MEAS.C1(ind1,1)-XYZ.MEAS.P2(ind1,1)).^2 +(-XYZ.MEAS.C1(ind1,2)-XYZ.MEAS.P2(ind1,2)).^2).^.5; %C1 mirror -P2 81 | elseif ~isnan(XYZ.MEAS.C2(1,1)) && ~isnan(XYZ.MEAS.P2(1,1)) % dipole-dipole 82 | r2=1./((XYZ.MEAS.C2(ind1,1)-XYZ.MEAS.P1(ind1,1)).^2 +(XYZ.MEAS.C2(ind1,2)-XYZ.MEAS.P1(ind1,2)).^2).^.5; % C2-P1 83 | r3=1./((XYZ.MEAS.C1(ind1,1)-XYZ.MEAS.P2(ind1,1)).^2 +(XYZ.MEAS.C1(ind1,2)-XYZ.MEAS.P2(ind1,2)).^2).^.5; % C1-P2 84 | r4=1./((XYZ.MEAS.C2(ind1,1)-XYZ.MEAS.P2(ind1,1)).^2 +(XYZ.MEAS.C2(ind1,2)-XYZ.MEAS.P2(ind1,2)).^2).^.5; % C2-P2 85 | r21=1./((XYZ.MEAS.C2(ind1,1)-XYZ.MEAS.P1(ind1,1)).^2 +(-XYZ.MEAS.C2(ind1,2)-XYZ.MEAS.P1(ind1,2)).^2).^.5; %C2 mirror -P1 86 | r31=1./((XYZ.MEAS.C1(ind1,1)-XYZ.MEAS.P2(ind1,1)).^2 +(-XYZ.MEAS.C1(ind1,2)-XYZ.MEAS.P2(ind1,2)).^2).^.5; %C1 mirror -P2 87 | r41=1./((XYZ.MEAS.C2(ind1,1)-XYZ.MEAS.P2(ind1,1)).^2 +(-XYZ.MEAS.C2(ind1,2)-XYZ.MEAS.P2(ind1,2)).^2).^.5; %C2 mirror -P2 88 | else 89 | errordlg('geometric factor function : array type is not defined '); 90 | end 91 | 92 | r1=1./((XYZ.MEAS.C1(ind1,1)-XYZ.MEAS.P1(ind1,1)).^2 +(XYZ.MEAS.C1(ind1,2)-XYZ.MEAS.P1(ind1,2)).^2).^.5; % C1-P1 93 | r11=1./((XYZ.MEAS.C1(ind1,1)-XYZ.MEAS.P1(ind1,1)).^2 +(-XYZ.MEAS.C1(ind1,2)-XYZ.MEAS.P1(ind1,2)).^2).^.5; % C1 mirror -P1 94 | 95 | K(ind1)=(4*pi)./(r1+r11-r2-r21-r3-r31+r4+r41); 96 | end 97 | 98 | if ~isempty(ind2) 99 | if isnan(XYZ.MEAS.C2(1,1)) && isnan(XYZ.MEAS.P2(1,1)) % pole-pole 100 | r2=0; 101 | r3=0; 102 | r4=0; 103 | elseif isnan(XYZ.MEAS.C2(1,1)) && ~isnan(XYZ.MEAS.P2(1,1)) % pole-dipole 104 | r2=0; 105 | r4=0; 106 | r3=1./((XYZ.MEAS.C1(ind2,1)-XYZ.MEAS.P2(ind2,1)).^2 +(XYZ.MEAS.C1(ind2,2)-XYZ.MEAS.P2(ind2,2)).^2).^.5; % C1-P2 107 | elseif ~isnan(XYZ.MEAS.C2(1,1)) && ~isnan(XYZ.MEAS.P2(1,1)) % dipole-dipole 108 | r2=1./((XYZ.MEAS.C2(ind2,1)-XYZ.MEAS.P1(ind2,1)).^2 +(XYZ.MEAS.C2(ind2,2)-XYZ.MEAS.P1(ind2,2)).^2).^.5; % C2-P1 109 | r3=1./((XYZ.MEAS.C1(ind2,1)-XYZ.MEAS.P2(ind2,1)).^2 +(XYZ.MEAS.C1(ind2,2)-XYZ.MEAS.P2(ind2,2)).^2).^.5; % C1-P2 110 | r4=1./((XYZ.MEAS.C2(ind2,1)-XYZ.MEAS.P2(ind2,1)).^2 +(XYZ.MEAS.C2(ind2,2)-XYZ.MEAS.P2(ind2,2)).^2).^.5; % C2-P2 111 | else 112 | errordlg('geometric_factor function : array type is not defined '); 113 | end 114 | 115 | r1=1./((XYZ.MEAS.C1(ind2,1)-XYZ.MEAS.P1(ind2,1)).^2 +(XYZ.MEAS.C1(ind2,2)-XYZ.MEAS.P1(ind2,2)).^2).^.5; % C1-P1 116 | 117 | K(ind2)=(2*pi)./(r1-r2-r3+r4); 118 | end 119 | 120 | if ~isempty(ind3) 121 | if ~isnan(XYZ.MEAS.C2(1,1)) && ~isnan(XYZ.MEAS.P2(1,1)) % dipole-dipole 122 | r2=1./((XYZ.MEAS.C2(ind3,1)-XYZ.MEAS.P1(ind3,1)).^2 +(XYZ.MEAS.C2(ind3,2)-XYZ.MEAS.P1(ind3,2)).^2).^.5; % C2-P1 123 | r3=1./((XYZ.MEAS.C1(ind3,1)-XYZ.MEAS.P2(ind3,1)).^2 +(XYZ.MEAS.C1(ind3,2)-XYZ.MEAS.P2(ind3,2)).^2).^.5; % C1-P2 124 | r4=1./((XYZ.MEAS.C2(ind3,1)-XYZ.MEAS.P2(ind3,1)).^2 +(XYZ.MEAS.C2(ind3,2)-XYZ.MEAS.P2(ind3,2)).^2).^.5; % C2-P2 125 | r21=0; %C2 mirror -P1 126 | r31=1./((XYZ.MEAS.C1(ind3,1)-XYZ.MEAS.P2(ind3,1)).^2 +(-XYZ.MEAS.C1(ind3,2)-XYZ.MEAS.P2(ind3,2)).^2).^.5; %C1 mirror -P2 127 | r41=0; %C2 mirror -P2 128 | else 129 | errordlg('geometric factor function : array type is not defined '); 130 | end 131 | 132 | r1=1./((XYZ.MEAS.C1(ind3,1)-XYZ.MEAS.P1(ind3,1)).^2 +(XYZ.MEAS.C1(ind3,2)-XYZ.MEAS.P1(ind3,2)).^2).^.5; % C1-P1 133 | r11=1./((XYZ.MEAS.C1(ind3,1)-XYZ.MEAS.P1(ind3,1)).^2 +(-XYZ.MEAS.C1(ind3,2)-XYZ.MEAS.P1(ind3,2)).^2).^.5; % C1 mirror -P1 134 | 135 | K(ind3)=(2*pi)./(.5*(r1+r11)-r2-r21-.5*(r3+r31)+r4+r41); 136 | end 137 | 138 | if ~isempty(ind4) 139 | 140 | if ~isnan(XYZ.MEAS.C2(1,1)) && ~isnan(XYZ.MEAS.P2(1,1)) % dipole-dipole 141 | r2=1./((XYZ.MEAS.C2(ind4,1)-XYZ.MEAS.P1(ind4,1)).^2 +(XYZ.MEAS.C2(ind4,2)-XYZ.MEAS.P1(ind4,2)).^2).^.5; % C2-P1 142 | r3=1./((XYZ.MEAS.C1(ind4,1)-XYZ.MEAS.P2(ind4,1)).^2 +(XYZ.MEAS.C1(ind4,2)-XYZ.MEAS.P2(ind4,2)).^2).^.5; % C1-P2 143 | r4=1./((XYZ.MEAS.C2(ind4,1)-XYZ.MEAS.P2(ind4,1)).^2 +(XYZ.MEAS.C2(ind4,2)-XYZ.MEAS.P2(ind4,2)).^2).^.5; % C2-P2 144 | 145 | r21=1./((XYZ.MEAS.C2(ind4,1)-XYZ.MEAS.P1(ind4,1)).^2 +(-XYZ.MEAS.C2(ind4,2)-XYZ.MEAS.P1(ind4,2)).^2).^.5;%C2 mirror -P1 146 | r31=0; %C1 mirror -P2 147 | r41=1./((XYZ.MEAS.C2(ind4,1)-XYZ.MEAS.P2(ind4,1)).^2 +(-XYZ.MEAS.C2(ind4,2)-XYZ.MEAS.P2(ind4,2)).^2).^.5; %C2 mirror -P2 148 | else 149 | errordlg('geometric factor function : array type is not defined '); 150 | end 151 | 152 | r1=1./((XYZ.MEAS.C1(ind4,1)-XYZ.MEAS.P1(ind4,1)).^2 +(XYZ.MEAS.C1(ind4,2)-XYZ.MEAS.P1(ind4,2)).^2).^.5; % C1-P1 153 | r11=0; % C1 mirror -P1 154 | 155 | K(ind4)=(2*pi)./((r1+r11)-.5*(r2+r21)-(r3+r31)+.5*(r4+r41)); 156 | end 157 | 158 | end -------------------------------------------------------------------------------- /functions/getAperture.m: -------------------------------------------------------------------------------- 1 | function aperture = getAperture(quadril_points, linearArea_coef) 2 | 3 | %%========================================================================% 4 | % % 5 | % Gauss Newton inversion % 6 | % % 7 | %%========================================================================% 8 | % % 9 | % In : % 10 | % ----------- % 11 | % quadril_points: 4 points forming the quadrilateral of which we want % 12 | % to determine the surface. % 13 | % (row vector) -> 4 points, 8 coordinates % 14 | % [(xC1,zC1), (xC2,zC2), (xP1,zP1), (xP2,zP2)] % 15 | % linearArea_coef: coefficient applied on the inline quadrilateral % 16 | % to make its length comparable to a surface % 17 | % % 18 | % Out : % 19 | % ----------- % 20 | % aperture: area of the quadrilateral % 21 | % % 22 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 23 | %%========================================================================% 24 | % Copyright (C) 2019 Simon GERNEZ and Abderrezak BOUCHEDDA % 25 | %%========================================================================% 26 | % % 27 | % Contacts: % 28 | % % 29 | % Simon GERNEZ % 30 | % simon.gernez@ete.inrs.ca % 31 | % Institut National de la Recherche Scientifique % 32 | % Centre Eau-Terre-Environnement % 33 | % http://www.ete.inrs.ca/ % 34 | % % 35 | % Abderrezak BOUCHEDDA % 36 | % Abderrezak.Bouchedda@ete.inrs.ca % 37 | % Institut National de la Recherche Scientifique % 38 | % Centre Eau-Terre-Environnement % 39 | % http://www.ete.inrs.ca/ % 40 | % % 41 | % This program is free software; you can redistribute it and/or modify % 42 | % it under the terms of the GNU General Public License as published by % 43 | % the Free Software Foundation; either version 2 of the License, or % 44 | % (at your option) any later version. % 45 | % % 46 | % This program is distributed in the hope that it will be useful, % 47 | % but WITHOUT ANY WARRANTY; without even the implied warranty of % 48 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % 49 | % GNU General Public License for more details. % 50 | % % 51 | % You should have received a copy of the GNU General Public License % 52 | % along with this program; if not, write to the Free Software % 53 | % Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA% 54 | 55 | %%========================================================================% 56 | 57 | %% Calculation 58 | 59 | quadril_points = reshape(quadril_points,2,4)'; % 4x2 matrix : c1 : x coord ; c2 : z coord 60 | 61 | % Lengths 62 | 63 | % if length(unique(quadril_points(:,1))) == 1 || length(unique(quadril_points(:,2))) == 1 % Test colinearity vectors better 64 | % Inline electrodes: no proper area calculable 65 | if length(unique(quadril_points(:,1))) == 1 66 | Pmax = max(quadril_points(:,2)); 67 | Pmin = min(quadril_points(:,2)); 68 | aperture = (Pmax - Pmin)*linearArea_coef; 69 | return 70 | elseif length(unique(quadril_points(:,2))) == 1 71 | Pmax = max(quadril_points(:,1)); 72 | Pmin = min(quadril_points(:,1)); 73 | aperture = (Pmax - Pmin)*linearArea_coef; 74 | return 75 | end 76 | 77 | % Areas 78 | 79 | indP = convhull(quadril_points); 80 | 81 | quadril_points = quadril_points(indP(1:end-1),:); 82 | 83 | x = quadril_points(:,1); 84 | y = quadril_points(:,2); 85 | 86 | % area : http://www.mathopenref.com/coordpolygonarea.html 87 | 88 | x2 = circshift(x,-1); 89 | y2 = circshift(y,-1); 90 | 91 | aperture = abs(sum(x.*y2 - y.*x2)/2); 92 | 93 | 94 | end -------------------------------------------------------------------------------- /functions/gradient_product_anis.m: -------------------------------------------------------------------------------- 1 | function gpa = gradient_product_anis(G,u,h_x,h_z,k) 2 | 3 | %%========================================================================% 4 | % % 5 | % Calculation of the finite-differences gradient needed for sensitivity % 6 | % in anisotropic media using the adjoint equation approach % 7 | % for each discrete frequency % 8 | % % 9 | %%========================================================================% 10 | % % 11 | % In: % 12 | % ----------- % 13 | % G : adjoint Green's function. % 14 | % For the electrical resistivity problem, G is the reciprocal % 15 | % potentials % 16 | % u : potential data % 17 | % h_x : x step vector % 18 | % h_z : z step vector % 19 | % k : wave number vector % 20 | % % 21 | % Out: % 22 | % ----------- % 23 | % g : anisotropic gradient product % 24 | % % 25 | %%========================================================================% 26 | % Copyright (C) 2019 Simon GERNEZ and Abderrezak BOUCHEDDA % 27 | %%========================================================================% 28 | % % 29 | % Contacts: % 30 | % % 31 | % Simon GERNEZ % 32 | % simon.gernez@ete.inrs.ca % 33 | % Institut National de la Recherche Scientifique % 34 | % Centre Eau-Terre-Environnement % 35 | % http://www.ete.inrs.ca/ % 36 | % % 37 | % Abderrezak BOUCHEDDA % 38 | % Abderrezak.Bouchedda@ete.inrs.ca % 39 | % Institut National de la Recherche Scientifique % 40 | % Centre Eau-Terre-Environnement % 41 | % http://www.ete.inrs.ca/ % 42 | % % 43 | % This program is free software; you can redistribute it and/or modify % 44 | % it under the terms of the GNU General Public License as published by % 45 | % the Free Software Foundation; either version 2 of the License, or % 46 | % (at your option) any later version. % 47 | % % 48 | % This program is distributed in the hope that it will be useful, % 49 | % but WITHOUT ANY WARRANTY; without even the implied warranty of % 50 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % 51 | % GNU General Public License for more details. % 52 | % % 53 | % You should have received a copy of the GNU General Public License % 54 | % along with this program; if not, write to the Free Software % 55 | % Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA% 56 | 57 | %%========================================================================% 58 | 59 | %% Initialisation 60 | 61 | n = length(h_z)+1; 62 | m = length(h_x)+1; 63 | la = n*m; 64 | nb_k = length(k); 65 | gpa.xx = zeros(n*m,nb_k); %m-n ; phi : McGillivray's notation 66 | gpa.xz = zeros(n*m,nb_k); 67 | gpa.zz = zeros(n*m,nb_k); 68 | gpa.yy = zeros(n*m,nb_k); 69 | %A = zeros(n*m,nb_k); 70 | %Sk = zeros(n*m,nb_k); 71 | h_x = h_x(:); 72 | h_z = h_z(:); 73 | k = k(:)'; 74 | nb_k = length(k); 75 | 76 | % Index nodes for boundary condition (bc) 77 | ind_Rtc = sub2ind([n m],1,m); % index right top corner 78 | ind_Ltc = sub2ind([n m],1,1); % index left top corner 79 | ind_Rbc = sub2ind([n m],n,m); % index right bottom corner 80 | ind_Lbc = sub2ind([n m],n,1); % index left bottom corner 81 | %ind_T = sub2ind([n m],ones(1,m-2),[2:m-1]); % index top edge 82 | ind_B = sub2ind([n m],n*ones(1,m-2),2:m-1); % index bottom edge 83 | ind_R = sub2ind([n m],2:n-1,m*ones(1,n-2)); % index right edge 84 | ind_L = sub2ind([n m],2:n-1,ones(1,n-2)); % index left edge 85 | ind = 1:n*m; % index for all nodes 86 | ind_wbc = ind; 87 | ind_wbc ([ind_Ltc ind_Lbc ind_L ind_R ind_Rtc ind_Rbc ind_B]) = []; % index without bc 88 | 89 | dz = repmat([h_z;h_z(end)],m,1); 90 | dx = repmat([h_x' h_x(end)],n,1); 91 | dx = dx(:); 92 | 93 | dx = dx(ind_wbc,ones(1,nb_k)); 94 | dz = dz(ind_wbc,ones(1,nb_k)); 95 | 96 | U = zeros((n+2)*(m+1),nb_k); 97 | g = U; 98 | 99 | for i=1:nb_k 100 | u1 = reshape(u(:,i),n,m); 101 | u1 = [u1(2,:);u1;u1(end,:)]; 102 | u1 = [u1 u1(:,end)]; 103 | U(:,i) = u1(:); 104 | 105 | G1 = reshape(G(:,i),n,m); 106 | G1 = [G1(2,:) ; G1 ; G1(end,:)]; 107 | G1 = [G1 G1(:,end)]; 108 | g(:,i) = G1(:); 109 | end 110 | 111 | G = g; 112 | u = U; 113 | clear G1 u1 U g 114 | 115 | ind_wbc1 = ind_wbc; 116 | n = n+2; 117 | m = m+1; 118 | ind_wbc = 1:n*m; % index for all nodes 119 | ind_wbc = reshape(ind_wbc,n,m); 120 | ind_wbc = ind_wbc(2:end-2,2:end-2); 121 | ind_wbc = ind_wbc(:); 122 | 123 | %% Calculation 124 | 125 | gpa.xx(ind_wbc1,:) = ( ... 126 | (u(ind_wbc+n,:)-u(ind_wbc,:)) .* (G(ind_wbc+n,:)-G(ind_wbc,:)) ... 127 | + (u(ind_wbc+n+1,:)-u(ind_wbc+1,:)) .* (G(ind_wbc+n+1,:)-G(ind_wbc+1,:)) ... 128 | + ((u(ind_wbc+n,:)+u(ind_wbc+n+1,:)-u(ind_wbc-n,:)-u(ind_wbc-n+1,:))/4).*((G(ind_wbc+n,:)+G(ind_wbc+n+1,:)-G(ind_wbc-n,:)-G(ind_wbc-n+1,:))/4) ... 129 | + ((u(ind_wbc+2*n,:)+u(ind_wbc+2*n+1,:)-u(ind_wbc,:)-u(ind_wbc+1,:))/4).*((G(ind_wbc+2*n,:)+G(ind_wbc+2*n+1,:)-G(ind_wbc,:)-G(ind_wbc+1,:))/4) ... 130 | ).*dz./dx; 131 | 132 | gpa.zz(ind_wbc1,:) = ( ... 133 | (u(ind_wbc+1,:)-u(ind_wbc,:)).*(G(ind_wbc+1,:)-G(ind_wbc,:)) ... 134 | + (u(ind_wbc+n+1,:)-u(ind_wbc+n,:)).*(G(ind_wbc+n+1,:)-G(ind_wbc+n,:)) ... 135 | + ((u(ind_wbc+1,:)+u(ind_wbc+n+1,:)-u(ind_wbc-1,:)-u(ind_wbc+n-1,:))/4).*((G(ind_wbc+1,:)+G(ind_wbc+n+1,:)-G(ind_wbc-1,:)-G(ind_wbc+n-1,:))/4) ... 136 | + ((u(ind_wbc+2,:)+u(ind_wbc+n+2,:)-u(ind_wbc,:)-u(ind_wbc+n,:))/4).*((G(ind_wbc+2,:)+G(ind_wbc+n+2,:)-G(ind_wbc,:)-G(ind_wbc+n,:))/4) ... 137 | ).*dx./dz; 138 | 139 | gpa.xz(ind_wbc1,:) = ( ... 140 | + ((u(ind_wbc+n,:)-u(ind_wbc,:))).* ... 141 | ((G(ind_wbc+1,:)+G(ind_wbc+n+1,:)-G(ind_wbc-1,:)-G(ind_wbc+n-1,:))/4) ... 142 | + ((u(ind_wbc+n+1,:)-u(ind_wbc+1,:))).* ... 143 | ((G(ind_wbc+2,:)+G(ind_wbc+n+2,:)-G(ind_wbc,:)-G(ind_wbc+n,:))/4) ... 144 | + (u(ind_wbc+1,:)-u(ind_wbc,:)).* ... 145 | ((G(ind_wbc+n,:)+G(ind_wbc+n+1,:)-G(ind_wbc-n,:)-G(ind_wbc-n+1,:))/4) ... 146 | + (u(ind_wbc+n+1,:)-u(ind_wbc+1,:)).* ... 147 | ((G(ind_wbc+n,:)+G(ind_wbc+n+1,:)-G(ind_wbc-n,:)-G(ind_wbc-n+1,:))/4) ... 148 | + ((G(ind_wbc+n,:)-G(ind_wbc,:))).* ... 149 | ((u(ind_wbc+1,:)+u(ind_wbc+n+1,:)-u(ind_wbc-1,:)-u(ind_wbc+n-1,:))/4) ... 150 | + ((G(ind_wbc+n+1,:)-G(ind_wbc+1,:))).* ... 151 | ((u(ind_wbc+2,:)+u(ind_wbc+n+2,:)-u(ind_wbc,:)-u(ind_wbc+n,:))/4) ... 152 | + (G(ind_wbc+1,:)-G(ind_wbc,:)).* ... 153 | ((u(ind_wbc+n,:)+u(ind_wbc+n+1,:)-u(ind_wbc-n,:)-u(ind_wbc-n+1,:))/4) ... 154 | + (G(ind_wbc+n+1,:)-G(ind_wbc+1,:)).* ... 155 | ((u(ind_wbc+n,:)+u(ind_wbc+n+1,:)-u(ind_wbc-n,:)-u(ind_wbc-n+1,:))/4) ... 156 | ); 157 | 158 | k1 = (k.^2)/4; 159 | gpa.yy(ind_wbc1,:) = 2*( G(ind_wbc,:).*u(ind_wbc,:) + G(ind_wbc+n,:).*u(ind_wbc+n,:) +... 160 | G(ind_wbc+1,:).*u(ind_wbc+1,:) + G(ind_wbc+n+1,:).*u(ind_wbc+n+1,:) ... 161 | ).*dx.*dz; 162 | gpa.yy = k1(ones(la,1),:).*gpa.yy; 163 | 164 | return 165 | 166 | end -------------------------------------------------------------------------------- /functions/grille2d_elect.m: -------------------------------------------------------------------------------- 1 | function [grille,h_x,h_z] =grille2d_elect(hx,hz,fact,nb_pad_bloc,nb_raff,nb_surr,grid_plot) 2 | 3 | %%========================================================================% 4 | % % 5 | % % In: % 6 | % ----------- % 7 | % hx : bloc thick in x direction of interesting region % 8 | % hz : bloc thick in z direction of interesting region % 9 | % fact : pad factor % 10 | % nb_pad_bloc : nb of padded blocs % 11 | % nb_raff : refine the blocs in the intersting region by nb_aff(1) % 12 | % nb_aff(2) in z direction % 13 | % nb_surr : number of surrounding blocs % 14 | % % 15 | % such as: % 16 | % % 17 | % nb_pad_bloc nb_surr hx1 hx2 hx1 nb_surr nb_pad_bloc % 18 | % _____________________x0________________________________________ % 19 | % | | |surr b | | | |surr b | | | % 20 | % |_____|______|______ |____|____|____|_______|_______|_______|hz1 % 21 | % | | |surr b | | | |surr b | | | % 22 | % |_____|______|_______|____|____|____|_______|_______|_______|hz2 % 23 | % | | |surr b | | | |surr b | | | % 24 | % |_____|______|_______|____|____|____|_______|_______|_______|hz3 % 25 | % | | |surr |surr|surr|surr| surr | | | % 26 | % |padded blocs| b | b | b | b | b |padded blocs | % 27 | % |_____|______|_______|____|____|____|_______|_______|_______| % 28 | % | | | |padded blocs | | | | % 29 | % |_____|______|_______|____|____|____|_______|_______|_______| % 30 | % | | | | | | | | | | % 31 | % |_____|______|_______|____|____|____|_______|_______|_______| % 32 | % % 33 | % % Out: % 34 | % ----------- % 35 | % grille : grid ( ordered column by column % 36 | % h_x : mesh bloc thick in x direction % 37 | % h_z : mesh bloc thick in z direction % 38 | % % 39 | % % test: % 40 | % ----------- % 41 | % hz=ones(10,1); % 42 | % hx=ones(10,1); % 43 | % [X,Y] = meshgrid(0:9,0:9); % 44 | % x=X(:); % 45 | % y=Y(:);grille=[]; % 46 | % grille(:,1)=x; % 47 | % grille(:,2)=y; % 48 | % sigma=ones(10,10); % 49 | % [grille,h_x,h_z] = grille2d_elect(hx,hz,1.3,10,[1;1],0,1); % 50 | % % 51 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 52 | % Copyright (C) 2007 Abderrezak BOUCHEDDA 53 | %=====oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo====% 54 | % contact: \\\//// % 55 | % |_ _| % 56 | % (@ @) % 57 | % **********oooO***(_)***Oooo********** % 58 | % * -----> Abderrezak BOUCHEDDA<----- * % 59 | % * Abderrezak.Bouchedda@ete.inrs.ca * % 60 | % * INRS-ETE * % 61 | % * http://www.ete.inrs.ca/ete * % 62 | % ************************************* % 63 | % |_______| % 64 | % |__|__| % 65 | % () () % 66 | % ooO Ooo % 67 | % This program is free software; you can redistribute it and/or modify % 68 | % it under the terms of the GNU General Public License as published by % 69 | % the Free Software Foundation; either version 2 of the License, or % 70 | % (at your option) any later version. % 71 | % % 72 | % This program is distributed in the hope that it will be useful, % 73 | % but WITHOUT ANY WARRANTY; without even the implied warranty of % 74 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % 75 | % GNU General Public License for more details. % 76 | % % 77 | % You should have received a copy of the GNU General Public License % 78 | % along with this program; if not, write to the Free Software % 79 | % Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA% 80 | % % 81 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 82 | %%========================================================================% 83 | 84 | %% Calculation 85 | 86 | ind_x0 = nb_raff(1)*(nb_surr) + nb_pad_bloc + 1; % first electrode position in grid 87 | hx=hx(:); 88 | hz=hz(:); 89 | pwr = 1:nb_pad_bloc; 90 | factor = fact.^pwr; 91 | factor=factor(:); 92 | 93 | if isempty(nb_raff) 94 | nb_raff=[1;1]; 95 | end 96 | 97 | hx1 = hx(1); 98 | hx2 = hx(end); 99 | hz1 = hz(end); 100 | % ind_x0 = ind_x0-3; 101 | hx=[hx1*ones(nb_surr,1); 102 | hx; 103 | hx2*ones(nb_surr,1)]; 104 | hz=[hz;hz1*ones(nb_surr,1)]; 105 | 106 | hx=repmat(hx',nb_raff(1),1); 107 | hx=hx(:)/nb_raff(1); 108 | hz=repmat(hz',nb_raff(2),1); 109 | hz=hz(:)/nb_raff(2); 110 | 111 | h_x = [hx1*factor(end:-1:1);hx;hx2*factor]; 112 | h_z = [hz;hz1*factor]; 113 | hx = [0;h_x]; 114 | hz = [0;h_z]; 115 | 116 | hx=cumsum(hx); 117 | hz=cumsum(hz); 118 | 119 | [X,Z]=meshgrid(hx,hz); 120 | x0=X(1,ind_x0); 121 | grille(:,1)=X(:)-x0; % x=0 position of first electrode (on the left) 122 | grille(:,2)=Z(:); 123 | 124 | if grid_plot==1 125 | plot(grille(:,1),-grille(:,2),'s','MarkerFaceColor','g','MarkerSize',2); 126 | gridxy(hx-x0,-hz); 127 | axis([min(grille(:,1)) max(grille(:,1)) min(-grille(:,2)) max(-grille(:,2))]) 128 | end 129 | end 130 | -------------------------------------------------------------------------------- /functions/integration_U.m: -------------------------------------------------------------------------------- 1 | function u = integration_U(U,wk,k,nbk1) 2 | 3 | %%========================================================================% 4 | % % 5 | % Integration of potential u, inverse Fourier transform % 6 | % % 7 | % ======================================================================= % 8 | % % 9 | % In: % 10 | % ----------- % 11 | % U : potential in wave number domain (matrix or vector) % 12 | % % 13 | % for one current electrode % 14 | % U = [U1_k1 U1_k2 ..... U1_kn] % 15 | % [U2_k1 U2_k2 ..... U2_kn] % 16 | % [. . . ] % 17 | % [. . . ] % 18 | % [Um_k1 U2_k2 ..... Um_kn] % 19 | % % 20 | % for nb current electrodes % 21 | % U = [U11_k1 U12_k1 ...U1nb_k1 U11_k2 U12_k2 ..... U1nb_kn] % 22 | % [U21_k1 U22_k1 ...U2nb_k1 U21_k2 U22_k2 ..... U2nb_kn] % 23 | % [. . . ] % 24 | % [. . . ] % 25 | % [Um1_k1 Um2_k1 ...Umnb_k1 Um1_k2 Um2_k2 ..... Umnb_kn] % 26 | % % 27 | % k : wave number % 28 | % k = [k1 k2 .... kn] % 29 | % % 30 | % Out: % 31 | % ----------- % 32 | % u : integrated potential into the spatial domain % 33 | % % 34 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 35 | % Copyright (C) 2007 Abderrezak BOUCHEDDA % 36 | %=====oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo====% 37 | % contact: ---------->\\\//// % 38 | % |_ _| % 39 | % (@ @) % 40 | % **********oooO***(_)***Oooo********** % 41 | % * -----> Abderrezak BOUCHEDDA<----- * % 42 | % * Abderrezak.Bouchedda@ete.inrs.ca * % 43 | % * INRS-ETE * % 44 | % * http://www.ete.inrs.ca/ete * % 45 | % ************************************* % 46 | % |_______| % 47 | % |__|__| % 48 | % () () % 49 | % ooO Ooo % 50 | % This program is free software; you can redistribute it and/or modify % 51 | % it under the terms of the GNU General Public License as published by % 52 | % the Free Software Foundation; either version 2 of the License, or % 53 | % (at your option) any later version. % 54 | % % 55 | % This program is distributed in the hope that it will be useful, % 56 | % but WITHOUT ANY WARRANTY; without even the implied warranty of % 57 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % 58 | % GNU General Public License for more details. % 59 | % % 60 | % You should have received a copy of the GNU General Public License % 61 | % along with this program; if not, write to the Free Software % 62 | % Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA% 63 | % % 64 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 65 | %%========================================================================% 66 | 67 | %% Calculation 68 | 69 | [h,l]=size(U); 70 | k1=sqrt(k(1:nbk1)); 71 | k1=k1(:)'; 72 | 73 | % potential integration using gauss quadrature 74 | u = (4/pi) * ( wk(1:nbk1) * (U(:,1:nbk1).*k1(ones(h,1),:))' ) ... 75 | + (2/pi) * ( wk(nbk1+1:end) * U(:,1+nbk1:end)' ); 76 | 77 | end 78 | 79 | 80 | -------------------------------------------------------------------------------- /functions/matrix_coeff_anis.m: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Simoger/AIM4RES/940b771bc74b5e8bb41aadf90db59591a5dfc957/functions/matrix_coeff_anis.m -------------------------------------------------------------------------------- /functions/tri_electr_pos.m: -------------------------------------------------------------------------------- 1 | function [pos,ind,L,sign]= tri_electr_pos(meas_posC1 , meas_posC2 , elect_bh1 , elect_bh2 , elect_sur , meas_posP1 , meas_posP2 , grille) 2 | 3 | %%========================================================================% 4 | % % 5 | % Electrode sorting function % 6 | % % 7 | %%========================================================================% 8 | % % 9 | % Sorts electrodes in order to model with a pole-pole, which allows for % 10 | % potential recombination in order to obtain the potential of a dipolar % 11 | % device % 12 | % % 13 | % In: % 14 | % ----------- % 15 | % meas_posC1: C1 measurement position % 16 | % meas_posC2: C2 measurement position % 17 | % elect_bh1 : borehole 1 electrodes position % 18 | % elect_bh2 : borehole 2 electrodes position % 19 | % elect_sur : surface electrodes position % 20 | % grille : grid nodes position % 21 | % % 22 | % Out: % 23 | % ----------- % 24 | % pos.C : current electrodes position for forward problem % 25 | % pos.P : potential electrodes position used as current electrodes % 26 | % for the calculation of reciprocal potential % 27 | % (sensit. calculation) % 28 | % ind.C1C2: index of current electrodes (pos.C) in meas_posC1 and % 29 | % meas_posC2 % 30 | % L : Contains the number of measures identified in 'ind' for % 31 | % each 'pos' position % 32 | % sign : +1 for a C1 electrode and -1 for a C2 electrode % 33 | % flag : 1 for borehole electrodes and 2 for surface electrodes % 34 | % % 35 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 36 | % Copyright (C) 2007 Abderrezak BOUCHEDDA % 37 | %=====oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo====% 38 | % contact: ---------->\\\//// % 39 | % |_ _| % 40 | % (@ @) % 41 | % **********oooO***(_)***Oooo********** % 42 | % * -----> Abderrezak BOUCHEDDA<----- * % 43 | % * Abderrezak.Bouchedda@ete.inrs.ca * % 44 | % * INRS-ETE * % 45 | % * http://www.ete.inrs.ca/ete * % 46 | % ************************************* % 47 | % |_______| % 48 | % |__|__| % 49 | % () () % 50 | % ooO Ooo % 51 | % This program is free software; you can redistribute it and/or modify % 52 | % it under the terms of the GNU General Public License as published by % 53 | % the Free Software Foundation; either version 2 of the License, or % 54 | % (at your option) any later version. % 55 | % % 56 | % This program is distributed in the hope that it will be useful, % 57 | % but WITHOUT ANY WARRANTY; without even the implied warranty of % 58 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % 59 | % GNU General Public License for more details. % 60 | % % 61 | % You should have received a copy of the GNU General Public License % 62 | % along with this program; if not, write to the Free Software % 63 | % Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA% 64 | % % 65 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 66 | %%========================================================================% 67 | 68 | %% Initialisation 69 | 70 | eps=.0001; 71 | [nh1,~]=size(elect_bh1); 72 | [nh2,~]=size(elect_bh2); 73 | [nsr,~]=size(elect_sur); 74 | 75 | ind=[]; 76 | L=[]; 77 | sign=[]; 78 | I=[]; 79 | pos1=[]; 80 | flag=[]; 81 | 82 | %% Calculation 83 | 84 | % find first borehole electrodes that are used in the measurements 85 | for i=1:nh1 86 | ind11 = find(meas_posC1(:,1) == elect_bh1(i,1) & meas_posC1(:,2) == elect_bh1(i,2)); 87 | l1=length(ind11); 88 | ind12 = find(meas_posC2(:,1) == elect_bh1(i,1) & meas_posC2(:,2) == elect_bh1(i,2)); 89 | l2=length(ind12); 90 | 91 | if (l1==0 && l2==0) 92 | I=[I,i]; % indices to throw electrodes that do not contribute to the measurements 93 | end 94 | 95 | L11=length(ind11); sign1= 1*ones(size(ind11)); % times that electrode elect_bh1(i,1) is used in meas.PosC1 96 | L12=length(ind12); sign2=-1*ones(size(ind12)); % times that electrode elect_bh1(i,1) is used in meas.PosC2 97 | 98 | L1=L11+L12; 99 | if L1==0 100 | L1=[]; 101 | end 102 | 103 | ind=[ind;ind11;ind12]; 104 | L=[L;L1]; 105 | sign=[sign;sign1;sign2]; 106 | end 107 | 108 | pos1=elect_bh1(I,:);flagg=ones(length(pos1),1); 109 | elect_bh1(I,:)=[]; I=[]; 110 | flag=ones(length(elect_bh1),1); 111 | 112 | % find second borehole electrodes that are used in the measurement (C1 ou C2) 113 | for i=1:nh2 114 | 115 | ind11 = find(meas_posC1(:,1) == elect_bh2(i,1) & meas_posC1(:,2) == elect_bh2(i,2)); 116 | l1=length(ind11); 117 | ind12 = find(meas_posC2(:,1) == elect_bh2(i,1) & meas_posC2(:,2) == elect_bh2(i,2)); 118 | l2=length(ind12); 119 | 120 | if (l1==0 && l2==0) 121 | I=[I,i]; 122 | end 123 | 124 | L11=length(ind11); sign1=1*ones(size(ind11)); 125 | L12=length(ind12); sign2=-1*ones(size(ind12)); 126 | 127 | L1=L11+L12; 128 | if L1==0 129 | L1=[]; 130 | end 131 | 132 | ind=[ind;ind11;ind12]; 133 | L=[L;L1]; 134 | sign=[sign;sign1;sign2]; 135 | 136 | end 137 | pos1=[pos1;elect_bh2(I,:)]; 138 | flagg=[flagg;ones(length(elect_bh2(I,1)),1)]; 139 | elect_bh2(I,:)=[]; 140 | I=[]; 141 | flag=[flag;ones(length(elect_bh2),1)]; 142 | 143 | % find surface electrodes that are used in the measurement (C1 ou C2) 144 | for i=1:nsr 145 | 146 | ind11 = find(elect_sur(i,1) == meas_posC1(:,1) & elect_sur(i,2) == meas_posC1(:,2)); 147 | l1=length(ind11); 148 | ind12 = find(elect_sur(i,1) == meas_posC2(:,1) & elect_sur(i,2) == meas_posC2(:,2)); 149 | l2=length(ind12); 150 | 151 | if (l1==0 && l2==0) 152 | I=[I,i]; 153 | end 154 | 155 | L11=length(ind11); 156 | sign1=1*ones(size(ind11)); 157 | L12=length(ind12); 158 | sign2=-1*ones(size(ind12)); 159 | 160 | L1=L11+L12; 161 | if L1==0 162 | L1=[]; 163 | end 164 | 165 | ind=[ind;ind11;ind12]; 166 | L=[L;L1]; 167 | sign=[sign;sign1;sign2]; 168 | 169 | end 170 | 171 | pos1=[pos1;elect_sur(I,:)]; 172 | flagg=[flagg;2*ones(length(elect_sur(I,1)),1)]; 173 | elect_sur(I,:)=[]; 174 | I=[]; 175 | flag=[flag;2*ones(length(elect_sur),1)]; 176 | pos=[elect_bh1;elect_bh2;elect_sur]; 177 | 178 | warning off 179 | ind_tmp = ind; 180 | clear ind 181 | ind.C1C2 = ind_tmp; 182 | 183 | % Search for nodes corresponding to potential electrodes (P1 & P2) 184 | n=length(ind.C1C2); 185 | ind_P1=[]; 186 | ind_P2=[]; 187 | 188 | if isnan(meas_posP2) 189 | for i=1:n 190 | k=ind.C1C2(i); 191 | ind11 = find( abs(grille(:,1)- meas_posP1(k,1)) < eps & abs(grille(:,2)- meas_posP1(k,2))< eps); 192 | ind_P1=[ind_P1;ind11]; 193 | ind_P2=[]; 194 | end 195 | 196 | else 197 | for i=1:n 198 | k=ind.C1C2(i); 199 | ind11 = find( abs(grille(:,1) - meas_posP1(k,1)) < eps & abs(grille(:,2) - meas_posP1(k,2)) < eps); 200 | ind12 = find( abs(grille(:,1) - meas_posP2(k,1)) < eps & abs(grille(:,2) - meas_posP2(k,2)) < eps); 201 | 202 | ind_P1=[ind_P1;ind11]; 203 | ind_P2=[ind_P2;ind12]; 204 | end 205 | end 206 | 207 | ind.P1 = ind_P1; 208 | if isempty(ind_P2) 209 | ind.P2=ones(size(ind_P1)); % P2 dummy values for pole-pole 210 | else 211 | ind.P2 = ind_P2; 212 | end 213 | 214 | % Search for P1 & P2 electrodes position for sensitivity calculation 215 | n_ele=size(pos1); 216 | n_ele=n_ele(1,1); 217 | 218 | if n_ele ~=0 219 | for i=1:n_ele 220 | ind11 = find(meas_posP1(:,1) == pos1(i,1) & meas_posP1(:,2) == pos1(i,2));l1=length(ind11); 221 | ind12 = find(meas_posP2(:,1) == pos1(i,1) & meas_posP2(:,2) == pos1(i,2));l2=length(ind12); 222 | if (l1==0 && l2==0) 223 | I=[I,i]; 224 | end 225 | end 226 | pos1(I,:) = []; 227 | flagg(I) = []; 228 | end 229 | 230 | nb_meas=size(meas_posC1,1); 231 | position = [pos;pos1]; 232 | 233 | pos_tmp = pos; 234 | clear pos 235 | pos.C = pos_tmp; 236 | pos.P = pos1; 237 | pos.flag = [flag;flagg]; 238 | warning on 239 | 240 | % Take electrodes indices in position touse them in order to rebuild 241 | % the data (for the sensitivity calculation) 242 | if isnan(meas_posP2(1,1)) && isnan(meas_posC2(1,1)) % pole-pole 243 | ind_meas = zeros(nb_meas,2); 244 | for i=1:nb_meas 245 | ind1 = find(position(:,1) == meas_posC1(i,1) & position(:,2)== meas_posC1(i,2)); 246 | ind3 = find(position(:,1) == meas_posP1(i,1) & position(:,2)== meas_posP1(i,2)); 247 | ind_meas(i,:) = [ind1 ind3]; 248 | end 249 | 250 | elseif isnan(meas_posC2(1,1)) && ~isnan(meas_posP2(1,1)) % pole-dipole 251 | ind_meas=zeros(nb_meas,3); 252 | for i=1:nb_meas 253 | ind1 = find(position(:,1) == meas_posC1(i,1) & position(:,2) == meas_posC1(i,2)); 254 | ind3 = find(position(:,1) == meas_posP1(i,1) & position(:,2) == meas_posP1(i,2)); 255 | ind4 = find(position(:,1) == meas_posP2(i,1) & position(:,2) == meas_posP2(i,2)); 256 | ind_meas(i,:)=[ind1 ind3 ind4]; 257 | end 258 | 259 | else % dipole-dipole (default) 260 | ind_meas=zeros(nb_meas,4); 261 | for i=1:nb_meas 262 | ind1 = find(position(:,1) == meas_posC1(i,1) & position(:,2) == meas_posC1(i,2)); 263 | ind2 = find(position(:,1) == meas_posC2(i,1) & position(:,2) == meas_posC2(i,2)); 264 | ind3 = find(position(:,1) == meas_posP1(i,1) & position(:,2) == meas_posP1(i,2)); 265 | ind4 = find(position(:,1) == meas_posP2(i,1) & position(:,2) == meas_posP2(i,2)); 266 | ind_meas(i,:) = [ind1 ind2 ind3 ind4]; 267 | end 268 | 269 | end 270 | 271 | ind.meas = ind_meas; 272 | 273 | end -------------------------------------------------------------------------------- /functions/vec2model.m: -------------------------------------------------------------------------------- 1 | function [rho]= vec2model(solution_vector,nb_ligne,nb_col,flag) 2 | 3 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 4 | % 5 | % Convert the resistivity solution vector to a structure which elements are 6 | % s.xx, s.zz and s.xz 7 | % 8 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 9 | 10 | 11 | % flag == 2 rhoxx rhozz 12 | % flag == 3 rhoxx rhozz rhoxz 13 | 14 | if flag == 2 15 | n = length(solution_vector)/2; 16 | rho.xx = reshape(solution_vector(1:n),nb_col,nb_ligne)'; 17 | % rho.xx(rho.xx < 1)=1; 18 | rho.yy = rho.xx; 19 | rho.zz = reshape(solution_vector(1+n:n*2),nb_col,nb_ligne)'; 20 | % rho.zz(rho.zz < 1)=1; 21 | rho.xz = zeros(nb_ligne,nb_col); 22 | rho.angle = zeros(nb_ligne,nb_col); 23 | rho.rho_1 = rho.xx; 24 | rho.rho_2 = rho.zz; 25 | elseif flag == 3 26 | n = length(solution_vector)/3; 27 | rho.rho_1 = reshape(solution_vector(1:n),nb_col,nb_ligne)'; 28 | rho.rho_2 = reshape(solution_vector(1+n:n*2),nb_col,nb_ligne)'; 29 | rho.rho_1(rho.rho_1 < 1) = 1; 30 | rho.rho_2(rho.rho_2 < 1) = 1; 31 | rho.angle = reshape(solution_vector(1+2*n:end),nb_col,nb_ligne)'; 32 | rho.xx = rho.rho_1.*cosd(rho.angle).^2 + rho.rho_2.*sind(rho.angle).^2; 33 | rho.zz = rho.rho_1.*sind(rho.angle).^2 + rho.rho_2.*cosd(rho.angle).^2; 34 | rho.xz = (rho.rho_2-rho.rho_1).*cosd(rho.angle).*sind(rho.angle); 35 | rho.yy = rho.rho_1; 36 | 37 | end 38 | end -------------------------------------------------------------------------------- /scripts/drawing/script_drawing_aniso.m: -------------------------------------------------------------------------------- 1 | %% Inversion plots for anisotropic models 2 | 3 | graphFontSize = 20; 4 | 5 | param.cell_size = [4 4]; 6 | 7 | disp('Ki2 and rms values :') 8 | Ki2_rms = [(1:length(Inv.rho))' Inv.Ki2 cell2mat(Inv.rms)'] 9 | 10 | n = length(Inv.rho); 11 | 12 | x = param.nb_raff(1)*param.cell_size(1); % cell number in 1m 13 | z = param.nb_raff(2)*param.cell_size(2); % cell number in 1m 14 | dist_from_xborders = 15; 15 | dist_from_surface1 = 0; % should be = 0 to run the whole script, else you'll have an error 16 | dist_from_surface2 = 15; 17 | margin_h = (dist_from_xborders+param.nb_surr./param.cell_size(1))*x; 18 | depth1 = (dist_from_surface1)*z+1; 19 | depth2 = (dist_from_surface2)*z; 20 | inv_xx = Inv.rho{1,n}.rho_1(param.h_z==1/param.cell_size(2), param.h_x==1/param.cell_size(1)); 21 | inv_zz = Inv.rho{1,n}.rho_2(param.h_z==1/param.cell_size(2), param.h_x==1/param.cell_size(1)); 22 | inv_xx = inv_xx(depth1:depth2, margin_h+1:(size(inv_xx,2)-margin_h+1)); 23 | inv_zz = inv_zz(depth1:depth2, margin_h+1:(size(inv_zz,2)-margin_h+1)); 24 | coef_anis = sqrt(inv_zz./inv_xx); 25 | 26 | 27 | % figure 28 | figure('units','normalized','outerposition',[0 0 1 1]); 29 | 30 | subplot(2,3,1) 31 | % subplot(222) 32 | imagesc(0:10:50, 0:15, param.rho.xx(1:(15*param.cell_size(1)),1:(50*param.cell_size(2)))) 33 | xticks(0:10:50) 34 | title('Synthetic anisotropic model') 35 | colormap jet(64) 36 | set(gca,'fontsize',graphFontSize) 37 | ylabel('z (m)') 38 | xlabel('x (m)') 39 | text(2,2,'\rho_H = 400 \Omega.m','FontSize',graphFontSize,'FontWeight','bold','Color','w') 40 | text(28,2,'\rho_V = 100 \Omega.m','FontSize',graphFontSize,'FontWeight','bold','Color','w') 41 | text(2,10,'\rho_H = 40 \Omega.m','FontSize',graphFontSize,'FontWeight','bold','Color','w') 42 | text(28,10,'\rho_V = 10 \Omega.m','FontSize',graphFontSize,'FontWeight','bold','Color','w') 43 | xm = [25*ones(1,15) 0:2:50]; 44 | ym = [1:15 zeros(1,length(0:2:50))]; 45 | hold on 46 | plot(xm,ym,'ok','MarkerFaceColor','w','MarkerSize',7); 47 | axis tight 48 | 49 | subplot(2,3,2) 50 | minv = log(ceil(min(inv_xx(:)))); 51 | maxv = log(floor(max(inv_xx(:)))); 52 | imagesc(dist_from_xborders:size(inv_xx,2)/x+dist_from_xborders, 0:dist_from_surface2, log(inv_xx)) 53 | title('\rho_H') 54 | colormap jet(128) 55 | h = colorbar('FontSize',16,'YTick',linspace(minv,maxv,8)... 56 | ,'YTickLabel',round(exp(linspace(minv,maxv,8)))); 57 | title(h, '\Omega/m') 58 | set(gca,'fontsize',graphFontSize) 59 | ylabel('z (m)') 60 | xlabel('x (m)') 61 | axis tight 62 | 63 | subplot(2,3,3) 64 | minv = log(ceil(min(inv_zz(:)))); 65 | maxv = log(floor(max(inv_zz(:)))); 66 | imagesc(dist_from_xborders:size(inv_zz,2)/x+dist_from_xborders, 0:dist_from_surface2, log(inv_zz)) 67 | title('\rho_V') 68 | colormap jet(128) 69 | h = colorbar('FontSize',16,'YTick',linspace(minv,maxv,8),'YTickLabel',round(exp(linspace(minv,maxv,8)))); 70 | title(h, '\Omega/m') 71 | set(gca,'fontsize',graphFontSize) 72 | ylabel('z (m)') 73 | xlabel('x (m)') 74 | axis tight 75 | 76 | subplot(2,3,4) 77 | imagesc(dist_from_xborders:size(inv_zz,2)/x+dist_from_xborders, 0:.25:(dist_from_surface2-0.25), (coef_anis)) 78 | colorbar 79 | colormap jet(128) 80 | title('\lambda') 81 | set(gca, 'fontsize',graphFontSize) 82 | h = colorbar; 83 | title(h, '[-]') 84 | xlabel('x (m)') 85 | ylabel('z (m)') 86 | caxis([0 4]) 87 | axis tight 88 | 89 | subplot(2,3,5) 90 | his = histogram(coef_anis,10); 91 | title('\lambda distribution') 92 | xlabel('\lambda') 93 | ylabel('# cells') 94 | set(gca,'fontsize',graphFontSize) 95 | axis([0 max(his.Data(:))+.5 0 max(his.Values)+10]) 96 | box off 97 | 98 | %% Data fit plots 99 | 100 | [K] = geometric_factor(XYZ,param.flag.geo_factor); 101 | param.K = K; 102 | res_num = Inv.d_cal{n}; 103 | res_obs = log(param.K.*param.MEAS.Res); 104 | res_obs = res_obs(Inv.rho_app_pos_index{n}); 105 | 106 | subplot(2,3,6) 107 | his = histogram(2*(res_obs-res_num)./(abs(res_obs)+abs(res_num))*100,10); 108 | title('Relative error') 109 | xlabel('error (%)') 110 | ylabel('# cells') 111 | box off 112 | ylim([0 max(his.Values)+10]) 113 | set(gca,'FontSize',graphFontSize) -------------------------------------------------------------------------------- /scripts/drawing/script_drawing_iso.m: -------------------------------------------------------------------------------- 1 | %% Inversion plots for isotropic models 2 | 3 | graphFontSize = 20; 4 | 5 | param.cell_size = [4 4]; 6 | 7 | disp('Ki2 and rms values :') 8 | Ki2_rms = [(1:length(Inv.rho))' Inv.Ki2 cell2mat(Inv.rms)'] 9 | 10 | n = length(Inv.rho); 11 | 12 | res_num = Inv.d_cal{n}; 13 | res_obs = log(param.K.*param.MEAS.Res); 14 | 15 | x = param.nb_raff(1)*param.cell_size(1); 16 | z = param.nb_raff(2)*param.cell_size(2); 17 | dist_from_xborders = 15; 18 | dist_from_surface1 = 0; % should be = 0 to run the whole script, else you'll have an error 19 | dist_from_surface2 = 15; 20 | margin_h = (dist_from_xborders+param.nb_surr./param.cell_size(1))*x; 21 | depth1 = (dist_from_surface1)*z+1; 22 | depth2 = (dist_from_surface2)*z; 23 | inv = Inv.rho{1,n}(param.h_z==1/param.cell_size(2), param.h_x==1/param.cell_size(1)); 24 | inv = inv(depth1:depth2, margin_h+1:(size(inv,2)-margin_h+1)); 25 | 26 | % figure 27 | figure('units','normalized','outerposition',[0 0 1 1]); 28 | 29 | subplot(1,3,1) 30 | imagesc(0:10:50, 0:15, param.rho.xx(1:(15*param.cell_size(1)),1:(50*param.cell_size(2)))) 31 | xticks(0:10:50) 32 | title('Synthetic anisotropic model') 33 | colormap jet(64) 34 | set(gca,'fontsize',graphFontSize) 35 | ylabel('z (m)') 36 | xlabel('x (m)') 37 | text(2,2,'\rho = 200 \Omega.m','FontSize',graphFontSize,'FontWeight','bold','Color','w') 38 | text(2,10,'\rho = 20 \Omega.m','FontSize',graphFontSize,'FontWeight','bold','Color','w') 39 | xm = [25*ones(1,15) 0:2:50]; 40 | ym = [1:15 zeros(1,length(0:2:50))]; 41 | hold on 42 | plot(xm,ym,'ok','MarkerFaceColor','w','MarkerSize',7); 43 | axis square 44 | 45 | subplot(1,3,2) 46 | minv = log(10); 47 | maxv = log(300); 48 | imagesc(dist_from_xborders:size(inv_xx,2)/x+dist_from_xborders, 0:dist_from_surface2, log(inv)) 49 | title('\rho_H') 50 | colormap jet(128) 51 | h = colorbar('FontSize',16,'YTick',linspace(minv,maxv,8)... 52 | ,'YTickLabel',round(exp(linspace(minv,maxv,8)))); 53 | title(h, '\Omega/m') 54 | set(gca,'fontsize',graphFontSize) 55 | ylabel('z (m)') 56 | xlabel('x (m)') 57 | caxis([minv maxv]) 58 | axis square 59 | ax = gca; 60 | axpos = ax.Position; 61 | ax.Position = axpos; 62 | 63 | subplot(1,3,3) 64 | his = histogram(2*(res_obs-res_num)./(abs(res_obs)+abs(res_num))*100); 65 | title('Relative error') 66 | xlabel('error (%)') 67 | ylabel('# cells') 68 | box off 69 | xlim([-10 10]) 70 | ylim([0 max(his.Values)+10]) 71 | set(gca,'FontSize',graphFontSize) -------------------------------------------------------------------------------- /scripts/forward/script_analytical_anis_2layers.m: -------------------------------------------------------------------------------- 1 | %% 2 layer model analytical solution (Telford) 2 | 3 | rhoX = param.rho.xx; 4 | rho_calc = param.K(:).*u_num(:); 5 | 6 | nb_points = 50; 7 | nb_images = 100; 8 | 9 | rho_h1 = 100; 10 | rho_v1 = 400; 11 | rho_n1 = sqrt(rho_v1*rho_h1); 12 | rho_h2 = 10; 13 | rho_v2 = 40; 14 | rho_n2 = sqrt(rho_v2*rho_h2); 15 | kn = (rho_n2-rho_n1)/(rho_n2+rho_n1); 16 | f = sqrt(rho_v1/rho_h1); 17 | z = 4; 18 | n = 2; % dipole-dipole separation 19 | 20 | rho_aa = zeros(nb_points,1); 21 | summ = zeros(nb_points,1); 22 | p = zeros(nb_points,1); 23 | r1 = zeros(nb_points,1); 24 | r2 = zeros(nb_points,1); 25 | r3 = zeros(nb_points,1); 26 | r4 = zeros(nb_points,1); 27 | 28 | for i = 1:nb_points 29 | % Wenner 30 | j = i; 31 | r1(i) = j; 32 | r2(i) = 2*j; 33 | r3(i) = 2*j; 34 | r4(i) = j; 35 | ABs2(i) = 3*j/2; 36 | 37 | p(i) = (1/r1(i)-1/r2(i)-1/r3(i)+1/r4(i))^(-1); 38 | summ(i) = 0; 39 | operande = 0; 40 | for m = 1:nb_images 41 | operande = 1/sqrt(r1(i)^2+4*m^2*f^2*z^2) - 1/sqrt(r2(i)^2+4*m^2*f^2*z^2)... 42 | -1/sqrt(r3(i)^2+4*m^2*f^2*z^2) + 1/sqrt(r4(i)^2+4*m^2*f^2*z^2); 43 | operande = kn^m*operande; 44 | summ(i) = summ(i) + operande; 45 | end 46 | rho_aa(i) = rho_n1*(1+2*p(i)*summ(i)); 47 | 48 | end 49 | 50 | ABs2 = ABs2(2:end)'; 51 | rho_aa = rho_aa(2:end); 52 | rho_calc = rho_calc(2:end); 53 | 54 | %% Plots 55 | 56 | figure 57 | subplot(4,3,[1 4 7]) 58 | imagesc(0:25:150,0:5:15,rhoX(1:60,:)) 59 | colormap jet 60 | hold on 61 | xm = 0:10:150; 62 | ym = -.1*ones(1,16); 63 | plot(xm,ym,'ok','MarkerFaceColor','w','MarkerSize',10); 64 | xlabel('x (m)') 65 | ylabel('z (m)') 66 | set(gca,'FontSize',20) 67 | title('Resistivity model') 68 | text(10,2,'\rho_H = 100 \Omega.m','FontSize',20,'FontWeight','bold','Color','w') 69 | text(80,2,'\rho_V = 400 \Omega.m','FontSize',20,'FontWeight','bold','Color','w') 70 | text(10,10,'\rho_H = 10 \Omega.m','FontSize',20,'FontWeight','bold','Color','w') 71 | text(80,10,'\rho_V = 40 \Omega.m','FontSize',20,'FontWeight','bold','Color','w') 72 | subplot(4,3,[2 3 5 6]) 73 | semilogx(ABs2,rho_aa,'ok') 74 | set(gca,'FontSize',20,'YTick',0:50:220) 75 | xticklabels({}) 76 | ylabel('\rho_a (\Omega.m)') 77 | ylim([0 220]) 78 | hold on 79 | x = (6:3:150)/2; 80 | semilogx(x,rho_calc,'LineWidth',4) 81 | legend('Analytical','Numerical') 82 | subplot(4,3,[8 9]) 83 | semilogx(ABs2,(rho_calc-rho_aa)./rho_aa*100,'.-') 84 | set(gca,'FontSize',20,'YTick',-1:2) 85 | xlabel('AB/2 (m)') 86 | ylabel('error (%)') 87 | ylim([-1 2]) -------------------------------------------------------------------------------- /scripts/forward/script_analytical_anis_semiInfiniteSpace.m: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Simoger/AIM4RES/940b771bc74b5e8bb41aadf90db59591a5dfc957/scripts/forward/script_analytical_anis_semiInfiniteSpace.m -------------------------------------------------------------------------------- /scripts/inversion/script_preparation_inversion.m: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Simoger/AIM4RES/940b771bc74b5e8bb41aadf90db59591a5dfc957/scripts/inversion/script_preparation_inversion.m -------------------------------------------------------------------------------- /scripts/script_drawing.m: -------------------------------------------------------------------------------- 1 | %% Script that calls the suitable drawing script for the inverted results graphic representation 2 | 3 | close all 4 | clear 5 | 6 | disp('Drawing inverted results:') 7 | disp('1. Load anisotropic inversion of anisotropic model') 8 | disp('2. Load anisotropic inversion of isotropic model') 9 | disp('3. Load isotropic inversion of isotropic model') 10 | prompt = ''; 11 | 12 | val = input(prompt); 13 | 14 | if val == 1 15 | load inv_aniso_model_aniso 16 | script_drawing_aniso 17 | elseif val == 2 18 | load inv_aniso_model_iso 19 | script_drawing_aniso 20 | elseif val == 3 21 | load inv_iso_model_iso 22 | script_drawing_iso 23 | else 24 | error('Please enter 1, 2 or 3') 25 | end -------------------------------------------------------------------------------- /scripts/script_forward_validation.m: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Simoger/AIM4RES/940b771bc74b5e8bb41aadf90db59591a5dfc957/scripts/script_forward_validation.m -------------------------------------------------------------------------------- /scripts/script_inversion.m: -------------------------------------------------------------------------------- 1 | %% Anisotropic inversion 2 | 3 | clear 4 | close all 5 | 6 | disp('Input data already existing ?') 7 | disp('1. No: launch script_preparation_inversion.m to create synthetic data') 8 | disp('2. Yes: import existing input data') 9 | val = input(''); 10 | 11 | if val == 1 12 | script_preparation_inversion 13 | elseif val == 2 14 | load synt_data_for_inversion 15 | end 16 | 17 | tic 18 | 19 | gauss_newton_inversion_anis(param, XYZ) --------------------------------------------------------------------------------