TY - JOUR

T1 - Comparison of Different Regularization Parameter Estimates: An Application to 1D Joint Inversion of DC Resistivity and CSRMT Data

AU - Аграхари, Судха

AU - Сингх, Акарш

AU - Шлыков, Арсений Андреевич

AU - Сараев, Александр Карпович

AU - Трипатхи, Приянг Мани

PY - 2023/11/13

Y1 - 2023/11/13

N2 - The choice of an appropriate regularization parameterenables the correct estimation of model parameters andconvergence of an inversion routine. The selection of the regularizationparameter in different inversion methodsdetermines/controls the local convergence, global convergence, orboth local and global convergence of the algorithms. This indicatesthat the choice of regularization parameter estimation method playsa crucial role in geophysical inversion. In this article, a comparisonof the effects of different regularization parameter approximationtechniques on the inversion of electrical resistivity and controlledsourceradiomagnetotelluric (CSRMT) data is tested. The constrainingequation defines the property of an inversion method;therefore, different methods can have different constraining equations.At this juncture, regularization parameters are calculated byLASSO and elastic-net (a convex combination of L2 and L1 norm)regression analyses. Also, the damping parameter for the Levenberg–Marquardt method is computed using singular valuedecomposition (SVD). In addition, a new empirical approachdeveloped for the estimation of regularization parameters is presentedin this paper and compared along with the above-mentionedtechniques. This exercise is performed on synthetic and field datasets. The efficacy of different regularization parameter schemes isanalyzed for the isotropic and anisotropic joint inversion of electricalresistivity and CSRMT data. In general, the elastic-netregularization and the new empirical scheme work well. However,the elastic-net solutions are slightly dependent on the choice ofconvex combination regularization term. Additionally, the solutionsobtained with the damping parameter estimation using SVDare dependent on the starting model. Elastic-net uses a combinationof L1 and L2 norm constraining equations, which is why in someplaces it has shown better convergence and parameter reconstructionthan the Marquardt method. However, an appropriate ratio ofeach (L1 and L2) norm is required to achieve optimal results withthis method. Consequently, the new empirical approach proved tobe optimal compared to other regularization parameter estimationapproaches discussed in this work.

AB - The choice of an appropriate regularization parameterenables the correct estimation of model parameters andconvergence of an inversion routine. The selection of the regularizationparameter in different inversion methodsdetermines/controls the local convergence, global convergence, orboth local and global convergence of the algorithms. This indicatesthat the choice of regularization parameter estimation method playsa crucial role in geophysical inversion. In this article, a comparisonof the effects of different regularization parameter approximationtechniques on the inversion of electrical resistivity and controlledsourceradiomagnetotelluric (CSRMT) data is tested. The constrainingequation defines the property of an inversion method;therefore, different methods can have different constraining equations.At this juncture, regularization parameters are calculated byLASSO and elastic-net (a convex combination of L2 and L1 norm)regression analyses. Also, the damping parameter for the Levenberg–Marquardt method is computed using singular valuedecomposition (SVD). In addition, a new empirical approachdeveloped for the estimation of regularization parameters is presentedin this paper and compared along with the above-mentionedtechniques. This exercise is performed on synthetic and field datasets. The efficacy of different regularization parameter schemes isanalyzed for the isotropic and anisotropic joint inversion of electricalresistivity and CSRMT data. In general, the elastic-netregularization and the new empirical scheme work well. However,the elastic-net solutions are slightly dependent on the choice ofconvex combination regularization term. Additionally, the solutionsobtained with the damping parameter estimation using SVDare dependent on the starting model. Elastic-net uses a combinationof L1 and L2 norm constraining equations, which is why in someplaces it has shown better convergence and parameter reconstructionthan the Marquardt method. However, an appropriate ratio ofeach (L1 and L2) norm is required to achieve optimal results withthis method. Consequently, the new empirical approach proved tobe optimal compared to other regularization parameter estimationapproaches discussed in this work.

KW - CSRMT method

KW - Joint inversion

KW - anisotropy

KW - regularization parameter

UR - https://www.mendeley.com/catalogue/3be727dc-e49d-3746-bc36-4c466efce4df/

U2 - 10.1007/s00024-023-03362-3

DO - 10.1007/s00024-023-03362-3

M3 - Article

JO - Pure and Applied Geophysics

JF - Pure and Applied Geophysics

SN - 0033-4553

ER -