3‐D forward modeling and inversion of IP data based on quasi‐linear approximation

2001 ◽  
Author(s):  
Ken Yoshioka ◽  
Michael Zhdanov
Keyword(s):  
Linear Approximation ◽  
Forward Modeling ◽  
And Inversion

2.5-D forward modeling and inversion of time domain IP method

2017 ◽  
Vol 70 (0) ◽  
pp. 69-79
Author(s):  
Hideki Mizunaga ◽  
Kiyotaka Ishinaga
Keyword(s):  
Time Domain ◽  
Forward Modeling ◽  
And Inversion

Enabling isotropic reflectivity modeling and inversion in anisotropic media

2021 ◽  
Vol 40 (4) ◽  
pp. 267-276
Author(s):  
Peter Mesdag ◽  
Leonardo Quevedo ◽  
Cătălin Tănase
Keyword(s):  
Synthetic Data ◽  
Anisotropic Media ◽  
Forward Modeling ◽  
Seismic Inversion ◽  
Stratified Medium ◽  
Effective Parameters ◽  
Elastic Parameters ◽  
Pp Wave ◽  
Anisotropic Elastic ◽  
And Inversion

Exploration and development of unconventional reservoirs, where fractures and in-situ stresses play a key role, call for improved characterization workflows. Here, we expand on a previously proposed method that makes use of standard isotropic modeling and inversion techniques in anisotropic media. Based on approximations for PP-wave reflection coefficients in orthorhombic media, we build a set of transforms that map the isotropic elastic parameters used in prestack inversion into effective anisotropic elastic parameters. When used in isotropic forward modeling and inversion, these effective parameters accurately mimic the anisotropic reflectivity behavior of the seismic data, thus closing the loop between well-log data and seismic inversion results in the anisotropic case. We show that modeling and inversion of orthorhombic anisotropic media can be achieved by superimposing effective elastic parameters describing the behavior of a horizontally stratified medium and a set of parallel vertical fractures. The process of sequential forward modeling and postinversion analysis is exemplified using synthetic data.

Three-dimensional magnetotelluric axial anisotropic forward modeling and inversion

2018 ◽  
Vol 153 ◽  
pp. 75-89 ◽  
Author(s):  
Hui Cao ◽  
Kunpeng Wang ◽  
Tao Wang ◽  
Boguang Hua
Keyword(s):  
Three Dimensional ◽  
Forward Modeling ◽  
And Inversion

Frequency‐domain acoustic‐wave modeling and inversion of crosshole data: Part II—Inversion method, synthetic experiments and real‐data results

Geophysics ◽  
1995 ◽  
Vol 60 (3) ◽  
pp. 796-809 ◽  
Author(s):  
Zhong‐Min Song ◽  
Paul R. Williamson ◽  
R. Gerhard Pratt
Keyword(s):  
Frequency Domain ◽  
Real Data ◽  
Forward Modeling ◽  
Two Dimensions ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Data Set ◽  
Wave Inversion ◽  
Full Wave ◽  
And Inversion

In full‐wave inversion of seismic data in complex media it is desirable to use finite differences or finite elements for the forward modeling, but such methods are still prohibitively expensive when implemented in 3-D. Full‐wave 2-D inversion schemes are of limited utility even in 2-D media because they do not model 3-D dynamics correctly. Many seismic experiments effectively assume that the geology varies in two dimensions only but generate 3-D (point source) wavefields; that is, they are “two‐and‐one‐half‐dimensional” (2.5-D), and this configuration can be exploited to model 3-D propagation efficiently in such media. We propose a frequency domain full‐wave inversion algorithm which uses a 2.5-D finite difference forward modeling method. The calculated seismogram can be compared directly with real data, which allows the inversion to be iterated. We use a descents‐related method to minimize a least‐squares measure of the wavefield mismatch at the receivers. The acute nonlinearity caused by phase‐wrapping, which corresponds to time‐domain cycle‐skipping, is avoided by the strategy of either starting the inversion using a low frequency component of the data or constructing a starting model using traveltime tomography. The inversion proceeds by stages at successively higher frequencies across the observed bandwidth. The frequency domain is particularly efficient for crosshole configurations and also allows easy incorporation of attenuation, via complex velocities, in both forward modeling and inversion. This also requires the introduction of complex source amplitudes into the inversion as additional unknowns. Synthetic studies show that the iterative scheme enables us to achieve the theoretical maximum resolution for the velocity reconstruction and that strongly attenuative zones can be recovered with reasonable accuracy. Preliminary results from the application of the method to a real data set are also encouraging.

2D modeling and inversion of gravity data using density contrast varying with depth and source–basement geometry described by the Fourier series

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 1909-1916 ◽  
Author(s):  
Juan García‐Abdeslem
Keyword(s):  
Fourier Series ◽  
Gravity Data ◽  
Forward Modeling ◽  
Density Contrast ◽  
Nonlinear Inversion ◽  
Bouguer Gravity ◽  
Data Set ◽  
Cubic Polynomial ◽  
Broad Variety ◽  
And Inversion

A method is developed for 2D forward modeling and nonlinear inversion of gravity data. The forward modeling calculates the gravity anomaly caused by a 2D source body with an assumed depth‐dependent density contrast given by a cubic polynomial. The source body is bounded at depth by a smooth, curvilinear surface given by the Fourier series, which represents the basement. The weighted and damped discrete nonlinear inverse method presented here can invert gravity data to infer the geometry of the source body. The use of the Fourier series to define the basement geometry allows the interpreter to reconstruct a broad variety of geometries for the geologic structures using a small number of free parameters. Both modeling and inversion methods are illustrated with examples using field gravity data across the San Jacinto graben in southern California and across the Sayula basin in Jalisco, Mexico. The inversion of the San Jacinto graben residual Bouguer gravity data yields results compatible with those from previous interpretations of the same data set, suggesting that this geologic structure accommodates about 2.5 km of sediments. The inversion of the residual Bouguer gravity data across the Sayula basin suggests a maximum of 1‐km‐thick sedimentary infill.

Quasi‐analytical approximations and series in electromagnetic modeling

Geophysics ◽  
2000 ◽  
Vol 65 (6) ◽  
pp. 1746-1757 ◽  
Author(s):  
Michael S. Zhdanov ◽  
Vladimir I. Dmitriev ◽  
Sheng Fang ◽  
Gábor Hursán
Keyword(s):  
Integral Equation ◽  
Linear Approximation ◽  
Linear Equations ◽  
Integral Equation Method ◽  
Forward Modeling ◽  
Computational Effort ◽  
Correct Result ◽  
Electromagnetic Modeling ◽  
Analytical Approximations ◽  
Analytical Series

The quasi‐linear approximation for electromagnetic forward modeling is based on the assumption that the anomalous electrical field within an inhomogeneous domain is linearly proportional to the background (normal) field through an electrical reflectivity tensor λ⁁. In the original formulation of the quasi‐linear approximation, λ⁁ was determined by solving a minimization problem based on an integral equation for the scattering currents. This approach is much less time‐consuming than the full integral equation method; however, it still requires solution of the corresponding system of linear equations. In this paper, we present a new approach to the approximate solution of the integral equation using λ⁁ through construction of quasi‐analytical expressions for the anomalous electromagnetic field for 3-D and 2-D models. Quasi‐analytical solutions reduce dramatically the computational effort related to forward electromagnetic modeling of inhomogeneous geoelectrical structures. In the last sections of this paper, we extend the quasi‐analytical method using iterations and develop higher order approximations resulting in quasi‐analytical series which provide improved accuracy. Computation of these series is based on repetitive application of the given integral contraction operator, which insures rapid convergence to the correct result. Numerical studies demonstrate that quasi‐analytical series can be treated as a new powerful method of fast but rigorous forward modeling solution.

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