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An elastic isotropic medium is described with three parameters. In seismic migration the perturbation of one elastic parameter affects the images of all the three, which means that these parameters are coupled. For an effective quantitative reconstruction of the true elastic medium reflectivity one can apply an iterative linearized migration/inversion, where minimization of the misfit functional is done by the conjugate gradient method. The final result of the iterative approach can be obtained directly by Newton’s method, using the pseudo-inverse Hessian matrix. Calculation of this matrix for a realistic model is an extremely resource-intensive problem, but for a model of a scatterer in a homogeneous elastic medium it is quite feasible. This paper presents the numerical results of elastic linearized inversion for this simple model, calculated both with iterative approach and Newton’s method. Experiments show that in the both cases the elastic parameters have coupled weaker than in the case of migration. The iterative approach allows achieving acceptable quality of the inversion, but requires a large number of iterations. For faster convergence it is necessary to use the preconditioned conjugate gradient method. The optimal preconditioning will improve the convergence of the method as well as the quality of inversion.

An elastic isotropic medium is described with three parameters. In seismic migration the perturbation of one elastic parameter affects the images of all the three, which means that these parameters are coupled. For an effective quantitative reconstruction of the true elastic medium reflectivity one can apply an iterative linearized migration/inversion, where minimization of the misfit functional is done by the conjugate gradient method. The final result of the iterative approach can be obtained directly by Newton’s method, using the pseudo-inverse Hessian matrix. Calculation of this matrix for a realistic model is an extremely resource-intensive problem, but for a model of a scatterer in a homogeneous elastic medium it is quite feasible. This paper presents the numerical results of elastic linearized inversion for this simple model, calculated both with iterative approach and Newton’s method. Experiments show that in the both cases the elastic parameters have coupled weaker than in the case of migration. The iterative approach allows achieving acceptable quality of the inversion, but requires a large number of iterations. For faster convergence it is necessary to use the preconditioned conjugate gradient method. The optimal preconditioning will improve the convergence of the method as well as the quality of inversion.

Imaging the soil physical parameters with surface seismic recordings is a non linear inverse problem. The elastic full waveform inversion is a quantitative multiparameters imaging method of diffractors that requires beforehand the knowledge of an initial velocity model. The corresponding forward problem, the elastic waves propagation, is solved in the frequency domain, allowing to efficiently take into account multisources and multireceivers acquisitions, with a finite difference method that modelizes the propagation of all wave types (body waves, surface waves, diffrated waves, refracted waves ...). The chosen finite difference stencil precisely simulates the free surface and surface waves propagation. This linearized inversion is based on a gradient method that minimizes a misfit function containing the difference between observed and calculated data. Two seismic parameters are reconstructed from vertical and horizontal seismograms. The inversion is performed from low to high frequencies, allowing to progressively introduce higher wavelengths in the parameters images. The latter are sensitive to the choice of the physical approximations chosen to calculate the misfit function gradient (Born or Rytov approximation), to the acquisition geometry, to the data preconditionning and to the inverted parameters choice. This method is then applicated to media containing a free surface. The free surface is a very contrasted interface that generates very energetic surface waves in seismograms. Near-surface media are complex, propagating waves are reflected or diffrated several times. When the medium contains two anomalies whose velocity contrast is equal to $20 \%$, the inversion correctly localize them in a known backgound model. Images are improved and anomalies amplitudes are very well recovered when the number of inverted frequencies increases and the data are selected from low to high offset. With a strongly contrasted anomaly like an empty cavity, the inversion correctly recovers the object position, shape and size but its amplitude is underestimated.The application to subsurface real vertical data recorded in a complex medium containing a cavity shows that the inversion constructs a heterogeneous medium allowing to better fit data and allows to reproduce inverted waves. Nevertheless the cavity is not imaged., L'imagerie des paramètres physiques du sous-sol à partir d'enregistrements sismiques de surface constitue un problème inverse non linéaire. L'inversion des formes d'onde élastique est une méthode d'imagerie quantitative multiparamètres de diffractants, nécessitant au préalable la connaissance précise d'un macromodèle de vitesse. Le problème direct associé, la propagation des ondes élastiques, est résolu dans le domaine fréquentiel, permettant la prise en compte efficace d'acquisitions multisources et multirécepteurs, par une méthode numérique de différences finies modélisant la propagation de tous les types d'onde (ondes de volume, de surface, diffractées, réfractées ...). Le stencil de différences finies choisi permet simule précisément la surface libre et la propagation des ondes de surface. Cette inversion linéarisée s'appuie sur une méthode de gradient, qui minimise une fonction coût contenant les différences entre données observées et calculées. Deux paramètres sismiques sont reconstruits à partir de sismogrammes verticaux et horizontaux. L'inversion est effectuée des basses fréquences vers les hautes fréquences, introduisant des longueurs d'onde de plus en plus courtes dans les images des paramètres. Ces dernières sont sensibles au choix des approximations physiques effectuées pour calculer le gradient de la fonction coût (approximation de Born ou de Rytov), au dispositif d'acquisition, au préconditionnement des données et au choix des paramètres inversés. Cette méthode est ensuite appliquée à des milieux contenant une surface libre. La surface libre est une interface très contrastée qui donne lieu à des ondes de surface très énergétiques dans les sismogrammes. Les milieux de subsurface sont complexes, les ondes qui s'y propagent subissent des réflexions ou diffractions multiples. Lorsque le milieu contient deux anomalies dont le contraste en vitesse vaut $20 \%$, l'inversion les localise correctement dans un macromodèle connu. Les images sont améliorées et l'amplitude des anomalies est très bien reconstruite lorsque le nombre de fréquences inversées augmente et les données sont sélectionnées des faibles déports vers les grands déports. Avec une anomalie fortement contrastée comme une cavité vide, l'inversion retrouve correctement la position, la forme et la taille de l'objet mais son amplitude est sous-estimée.L'application à des données réelles verticales de subsurface acquises dans un milieu complexe contenant une cavité maçonnée montre que le milieu hétérogène issu de l'inversion ajuste mieux les données et permet de bien reproduire les ondes inversées. Néanmoins, la cavité n'est pas imagée.

The inversion of vertical electrical sounding (VES) is normally performed considering a stratified medium formed by homogeneous, isotropic and horizontal layers. The simplicity of this geophysical model makes the inversion simple and computationally fast, and together with the main characteristics of the electroresistivity method, it was greatly responsible to make VES one of the most popular geophysical method for groundwater exploration and engineering geophysics. However, even in a sedimentary basin where the geology is more conform, the assumption of horizontal and homogeneous layers is not necessarily valid, limiting the reliability of the inversion results. In this paper we present a fast and robust 2D resistivity modeling and inversion algorithm for the interpretation of sets of VES. We consider three inversion algorithms: the Gauss-Newton method of linearized inversion (LI), the genetic algorithm (GA), and a hybrid approach (GA-LI) that uses LI to improve the best model at the end of each step of the GA. The medium parametrization consists of the partition of the domain into fixed homogeneous rectangular blocks such that their resistivities are the only free parameters. The apparent resistivity is evaluated by an iterative scheme that is derived from a finite-difference discretization of the potential differential equation. We enhance the convergence rate of the scheme by adopting an incomplete Cholesky preconditioner. Numerical results using synthetic and real 2D apparent resistivity data formed by sets of VES for the Schlumberger configuration illustrate the performance of the hybrid GA-LI algorithm. The VES field data were acquired near Conceição do Coité, state of Bahia, Brazil. We compare the performance of the LI, GA and GA-LI algorithms. A inversão de uma sondagem elétrica vertical (SEV) normalmente assume que o meio é estratifcado e formado por camadas horizontais homogêneas e isotrópicas. A simplicidade deste modelo geofísico torna a inversão simples e com reduzido custo computacional. Esta simplicidade, junto às principais qualidades do método de eletroresistividade, foi responsável por tornar a SEV um dos métodos geofísicos mais populares nos trabalhos de exploração de águas subterrâneas e geofísica aplicada à engenharia. Porém, mesmo em bacias sedimentares, onde a geologia é mais conforme, a hipótese de camadas planas e homogêneas não é válida, o que limita a confiabilidade dos resultados da inversão. Apresentamos neste artigo um algoritmo rápido e robusto de modelagem e inversão eletroresistiva para a interpretação de conjuntos de SEVs. Consideramos três algoritmos de inversão: o método de inversão linearizada de Gauss-Newton (LI), o algorítmo genético (GA), e uma abordagem híbrida (GA-LI) que usa a inversão linearizada para aprimorar o melhor modelo obtido ao final de cada geração do algoritmo genético. A parametrização do meio consiste na partição do dommínio em blocos retangulares e homogêneos, de modo que a resistividade de cada bloco é um parâmetro do modelo. A resistividade aparente é calculada com um método iterativo baseado numa aproximação por diferenças finitas da equação do potencial elétrico. Um precondicionamento do tipo Cholesky incompleto é utilizado para acelerar a convergência do método. Avaliamos a performance do método híbrido por meio de experimentos numéricos com perfis de eletroresistividades reais e sintéticos, formados por conjuntos de SEVs obtidas com o arranjo Schlumberger. Os dados de campo foram coletados nas proximidades de Conceição do Coité, estado da Bahia, Brasil.

Submitted by Santiago Fabio (fabio.ssantiago@hotmail.com) on 2011-10-13T18:31:06Z No. of bitstreams: 1 55555.pdf: 878136 bytes, checksum: 9687a521def08ade280c32b51afe7a01 (MD5) Made available in DSpace on 2011-10-13T18:31:06Z (GMT). No. of bitstreams: 1 55555.pdf: 878136 bytes, checksum: 9687a521def08ade280c32b51afe7a01 (MD5) Previous issue date: 2003 The inversion of vertical electrical sounding (VES) is normally performed considering a stratified medium formed by homogeneous, isotropic and horizontal layers. The simplicity of this geophysical model makes the inversion simple and computationally fast, and together with the main characteristics of the electroresistivity method, it was greatly responsible to make VES one of the most popular geophysical method for groundwater exploration and engineering geophysics. However, even in a sedimentary basin where the geology is more conform, the assumption of horizontal and homogeneous layers is not necessarily valid, limiting the reliability of the inversion results. In this paper we present a fast and robust 2D resistivity modeling and inversion algorithm for the interpretation of sets of VES. We consider three inversion algorithms: the Gauss-Newton method of linearized inversion (LI), the genetic algorithm (GA), and a hybrid approach (GA-LI) that uses LI to improve the best model at the end of each step of the GA. The medium parametrization consists of the partition of the domain into fixed homogeneous rectangular blocks such that their resistivities are the only free parameters. The apparent resistivity is evaluated by an iterative scheme that is derived from a finite-difference discretization of the potential differential equation. We enhance the convergence rate of the scheme by adopting an incomplete Cholesky preconditioner. Numerical results using synthetic and real 2D apparent resistivity data formed by sets of VES for the Schlumberger configuration illustrate the performance of the hybrid GA-LI algorithm. The VES field data were acquired near Conceição do Coité, state of Bahia, Brazil. We compare the performance of the LI, GA and GA-LI algorithms. São Paulo