ORCID Profile
0000-0002-6813-5265
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Publisher: Informa UK Limited
Date: 09-2003
DOI: 10.1071/EG03217
Publisher: Springer Science and Business Media LLC
Date: 29-08-2019
Publisher: Elsevier BV
Date: 08-2003
Publisher: Society of Exploration Geophysicists
Date: 10-08-2019
Publisher: Informa UK Limited
Date: 12-2013
Publisher: Springer Science and Business Media LLC
Date: 04-2009
Publisher: Springer Science and Business Media LLC
Date: 24-03-2017
Publisher: Informa UK Limited
Date: 06-2005
DOI: 10.1071/EG05234
Publisher: Informa UK Limited
Date: 03-2002
DOI: 10.1071/EG02001
Publisher: Oxford University Press (OUP)
Date: 20-11-2014
Publisher: Wiley
Date: 16-08-2004
Publisher: Springer Science and Business Media LLC
Date: 07-2006
Publisher: Society of Exploration Geophysicists
Date: 27-08-2018
Publisher: Society of Exploration Geophysicists
Date: 2021
Abstract: In viscoelastic anisotropic media, the elastic moduli, slowness vector, phase, and ray velocity are all complex-valued quantities in the frequency domain. Solving the complex eikonal equation becomes computationally complex and time-consuming. We have developed two approximate methods to effectively calculate the ray velocity vector, attenuation, and quality factor in viscoelastic transversely isotropic media with a vertical symmetry axis (VTI) and in orthorhombic (ORT) anisotropy. The first method is based on the perturbation theory (PER) under the assumption of a homogeneous complex ray vector, which is obtained by applying the elastic background and viscoelastic perturbations to the real and imaginary components of the modulus tensor, respectively. The perturbations of the slowness vectors of the three wave modes (qP, qSV, and qSH) are determined through the vanishing Hamiltonian function. The second method is derived by applying a real slowness direction (RSD) to the inhomogeneous complex slowness vector and then approximately calculating the complex ray velocity vector with the condition of the homogeneous complex vector. The numerical results verify that the two approaches can produce accurate ray velocity vector, attenuation, and quality factors of the qP-wave in viscoelastic VTI and ORT media. The RSD method can yield high accuracies of ray velocity for the qSV- and qSH-wave in viscoelastic VTI models even at triplication of the qSV wavefronts, as well as qS1 and qS2 in a weak ORT medium ([Formula: see text] 20), except for near the cusp of the qS1 wavefronts (errors approximately 6%) where the PER has more than 10% error.
Publisher: Society of Exploration Geophysicists
Date: 03-2010
DOI: 10.1190/1.3339386
Abstract: We implement prestack reverse time migration (RTM) using frequency-domain extrapolation. We assume the observed data are the scattered field from the seismic experiment then we time reverse them and derive the corresponding multipoint virtual sources to place along the receiver line rather than treat them as boundary conditions, which are common in time-domain reverse time migration (TRTM). Because the number of virtual sources is equal to the number of independent true sources in prestack frequency-domain reverse-time migration (FRTM), wavefield extrapolation is efficient in the frequency domain using a direct lower/upper (LU) triangular solver for 2D solutions and is still feasible using a parallel iterative or hybrid direct/iterative solver for 3D solutions. Each frequency implicitly contains information for all times, so we can implement the excitation-time and crosscorrelation imaging conditions straightforwardly without disk storage or input/output (I/O). Comparing costs, prestack shot-record FRTM is competitive with prestack shot-record TRTM. In our tests, prestack acoustic-wave FRTM accurately recovers the correct images of subsurface reflectors using 2D synthetic data.
Publisher: Oxford University Press (OUP)
Date: 04-1996
Publisher: Oxford University Press (OUP)
Date: 03-2009
Publisher: Informa UK Limited
Date: 12-2006
Publisher: Informa UK Limited
Date: 09-1998
DOI: 10.1071/EG998680
Publisher: Society of Exploration Geophysicists
Date: 07-2003
DOI: 10.1190/1.1598125
Abstract: We investigate a simple scheme for full‐waveform litude spectrum inversion of crosshole seismic data with an unknown source wavelet. The method is based on our 2D/2.5D finite‐element method of acoustic‐wave modeling. The normalized litude data, defined as the spectral ratio of the original trace litude to the average litude for the entire common shot gather, are used for full‐waveform inversion in the frequency domain. In essence, the normalization of litudes removes the source wavelet and is easily carried out in the time domain or frequency domain from crosshole seismic surveying. Two synthetic models, simulating, respectively, a dipping fracture model and a complicated sedimentary structure, are examined with the inversion scheme. The numerical results show that clear images of the targets can be obtained by using the single‐ and multiple‐frequency data. For comparison, two other litude inversion schemes in which the source signatures are known and estimated with an iterative procedure were carried out for the same models. The results show that the iteratively source‐estimated procedure also produces satisfactory images of the velocity structure and yields an approximate litude of the source wavelet. With the multifrequency data, three such schemes yield very competitive results.
Publisher: Wiley
Date: 26-11-2023
Abstract: The attenuation of seismic waves propagating in reservoirs can be obtained accurately from the data analysis of vertical seismic profile in terms of the quality‐factor Q . The common methods usually use the downgoing wavefields in vertical seismic profile data. However, the downgoing wavefields consist of more than 90% energy of the spectrum of the vertical seismic profile data, making it difficult to estimate the viscoacoustic parameters accurately. Thus, a joint viscoacoustic waveform inversion of velocity and quality‐factor is proposed based on the multi‐objective functions and analysis of the difference between the results inverted from the separated upgoing and downgoing wavefields. A simple separating step is accomplished by the reflectivity method to obtain the in idual wavefields in vertical seismic profile data, and then a joint inversion is carried out to make full use of the information of the in idual wavefields and improve the convergence of viscoacoustic full‐waveform inversion. The sensitivity analysis of the different wavefields to the velocity and quality‐factor shows that the upgoing and downgoing wavefields contribute differently to the viscoacoustic parameters. A numerical ex le validates our method can improve the accuracy of viscoacoustic parameters compared with the direct inversion using full wavefield and the separate inversion using upgoing or downgoing wavefield. The application on real field data indicates our method can recover a reliable viscoacoustic model, which helps reservoir appraisal.
Publisher: Wiley
Date: 12-02-2007
Publisher: European Association of Geoscientists & Engineers
Date: 2010
Publisher: Society of Exploration Geophysicists
Date: 05-2002
DOI: 10.1190/1.1484518
Abstract: We develop a method to obtain 2‐D/3‐D resistivity images for crosshole dc electric measurements. This imaging procedure consists of two steps: (1) an approximate resistivity image is obtained using a simple projection based on the analytic form of the sensitivity function for the specified electrode array and a modified version of an inversion formula (2) a final image may be obtained by nonlinear regularized inversion using the approximate resistivity image as the starting model. The imaging procedure is sufficiently flexible to handle different crosshole resistivity applications. Numerical experiments for 2‐D and 3‐D synthetic models show that the first step can give a satisfactory image of the target between the boreholes or underground when the background medium is uniform. For an inhomogeneous background, the approximate resistivity image is not as good but still conveys a reasonable outline of the resistivity structure. The procedure has no limitation on choice of electrode array (pole‐pole, pole‐bipole, bipole‐pole, bipole‐bipole) or field surveying configurations (surface‐to‐surface, surface‐to‐borehole, multiborehole crosshole). It may be applied in a routine way for processing crosshole electric data in various applications.
Publisher: Wiley
Date: 09-2000
Publisher: Informa UK Limited
Date: 03-1992
DOI: 10.1071/EG992459
Publisher: Society of Exploration Geophysicists
Date: 17-08-2017
Publisher: Wiley
Date: 07-1999
Publisher: Informa UK Limited
Date: 12-2006
Publisher: Oxford University Press (OUP)
Date: 19-08-2004
Publisher: Society of Exploration Geophysicists and Chinese Petroleum Society
Date: 11-12-2018
DOI: 10.1190/IGC2018-232
Publisher: Wiley
Date: 11-2005
Publisher: Elsevier BV
Date: 07-2014
Publisher: Elsevier BV
Date: 07-2017
Publisher: Oxford University Press (OUP)
Date: 04-1998
Publisher: Society of Exploration Geophysicists
Date: 09-11-2021
Abstract: The real ray-tracing approach leads to an effective solution in the real space domain using a homogeneous ray velocity vector. However, it fails to yield solutions for quasi-S-waves, which suffer from triplications of the wavefronts. To address this challenging problem, a new real ray-tracing method and its two approximations are developed to solve the complex ray equation. The numerical results indicate that the new real ray-tracing method is superior to the common real ray-tracing method in the presence of triplications of the quasi-S-waves in the computation of ray velocity, ray attenuation, and ray quality factors, as well as the reflection and transmission coefficients in viscoelastic anisotropic media. Based on the assumptions of the real slowness direction and real polarization vectors, two new approximations of the new real ray-tracing method are developed for directly computing the homogeneous complex ray velocity vectors of three wave modes (qP, qS1, and qS2). These approximations significantly improve computational efficiency by avoiding the iterative process required by the new real ray-tracing method that is inherited from the common real ray-tracing method. The computational accuracies are verified through transversely isotropic and orthorhombic models with different strengths of attenuation and anisotropy. Incorporation of the new approximation into the shortest-path method turned out to be efficient and accurate for seismic ray tracing in heterogeneous viscoelastic and transversely isotropic media with a vertical axis of symmetry, even in the presence of strong attenuation and anisotropy.
Publisher: Informa UK Limited
Date: 08-2003
Publisher: Elsevier BV
Date: 02-2012
Publisher: Informa UK Limited
Date: 12-2012
Publisher: Oxford University Press (OUP)
Date: 23-05-2008
Publisher: Oxford University Press (OUP)
Date: 13-06-2011
Publisher: Society of Exploration Geophysicists
Date: 07-2008
DOI: 10.1190/1.2910827
Abstract: Crosshole seismic tomography often is applied to image the velocity structure of an interwell medium. If the rocks are anisotropic, the tomographic technique must be adapted to the complex situation otherwise, it leads to a false interpretation. We propose a nonlinear kinematic inversion method for crosshole seismic tomography in composite transversely isotropic media with known dipping symmetry axes. This method is based on a new version of the first-order traveltime perturbation equation. It directly uses the derivative of the phase velocity rather than the eigenvectors of the body-wave modes to overcome the singularity problem for application to the two quasi-shear waves. We applied an iterative nonlinear solver incorporating our kinematic ray-tracing scheme and directly compute the Jacobian matrix in an arbitrary reference medium. This reconstructs the five elastic moduli or Thomsen parameters from the first-arrival traveltimes of the three seismic body waves (qP, qSV, qSH) in strongly and weakly anisotropic media. We conducted three synthetic experiments that involve determining anisotropic parameters for a homogeneous rock, reconstructing a fault embedded in a strongly anisotropic background, and imaging a complicated four-layer model containing a small channel and a buried dipping interface. We compared results of our nonlinear inversion method with isotropic tomography and the traditional linear anisotropic inversion scheme, which showed the capability and superiority of the new scheme for crosshole tomographic imaging.
Publisher: Oxford University Press (OUP)
Date: 21-03-2006
Publisher: Society of Exploration Geophysicists
Date: 09-1998
DOI: 10.1190/1.1444475
Abstract: Theoretically, the Green’s function can be used to calculate the wavefield response of a specified source and the Fréchet derivative with respect to the model parameters for crosshole seismic full‐waveform inversion. In this paper, we apply the finite‐element method to numerically compute the 2.5-D Green’s function for an arbitrary acoustic medium by solving a composite boundary‐valued problem in the wavenumber‐frequency domain. The composite boundary condition consists of a 2.5-D absorbing boundary condition for the propagating wave field and a mixed boundary condition for the evanescent field in inhomogeneous media modeling. A numerical experiment performed for a uniform earth (having a known exact solution) shows the accuracy of the computation in the frequency and time domain. An inhomogeneous medium test, involving an embedded low‐velocity layer, demonstrates that the permissible range of [Formula: see text] at each frequency can be determined rationally from the critical wavenumber value of the medium around the source. Furthermore, it shows that the frequency‐domain solution is not improved continuously by increasing the number of [Formula: see text] s les because of the complicated nature of the wavefield. Both experiments show that the proposed method is effective and flexible for computing the 2.5-D Green’s function for arbitrary acoustic media.
Publisher: Oxford University Press (OUP)
Date: 2008
Publisher: Informa UK Limited
Date: 12-2007
DOI: 10.1071/EG07025
Publisher: Society of Exploration Geophysicists
Date: 09-2009
DOI: 10.1190/1.3123766
Abstract: We present a perturbation method and a matrix method for formulating the explicit Fréchet derivatives for seismic body-wave waveform inversion in 3D general anisotropic, heterogeneous media. Theoretically, the two methods yield the same explicit formula valid for any class of anisotropy and are completely equivalent if the model parameterization in the inversion is the same as that used in the discretization scheme (unstructured or structured mesh) for forward modeling. Explicit formulas allow various model parameterization schemes that try to match the resolution capability of the data and possibly reduce the dimensions of the Jacobian matrix. Based on the general expressions, relevant formulas for isotropic and 2.5D and 3D tilted transversely isotropic (TTI) media are derived. Two computational schemes, constant-point and constant-block parameterization, offer effective and efficient means of forming the Jacobian matrix from the explicit Fréchet derivatives. The sensitivity patterns of the displacement vector to the independent model parameters in a weakly anisotropic medium clearly convey the imaging capability possible with seismic waveform inversion in such an anisotropic medium.
Publisher: Oxford University Press (OUP)
Date: 03-11-2011
Publisher: Informa UK Limited
Date: 03-1997
DOI: 10.1071/EG997001
Publisher: Wiley
Date: 24-06-2005
Publisher: Informa UK Limited
Date: 2009
Publisher: Wiley
Date: 11-2005
Publisher: European Association of Geoscientists & Engineers
Date: 2019
Publisher: Oxford University Press (OUP)
Date: 04-2010
Publisher: Informa UK Limited
Date: 12-2013
Publisher: Society of Exploration Geophysicists
Date: 05-2006
DOI: 10.1190/1.2198217
Abstract: Repeated resistivity measurement is a potentially powerful method for monitoring development of internal erosion and anomalous seepage in earth embankment dams. This study is part of a project to improve current longterm monitoring routines and data interpretation and increasing the understanding when interpreting existing data. This is accomplished by modeling various occurrences typical of embankment structures using properties from two rockfill embankment dams with central till cores in the north of Sweden. The study evaluates the influence from 3D effects created by specific dam geometry and effects of water level fluctuations in the reservoir. Moreover, a comparison between different layout locations is carried out, and detectability of internal erosion scenarios is estimated through modeling of simulated damage situations. Software was especially developed to model apparent resistivity for geometries and material distributions for embankment dams. The model shows that the 3D effect from the embankment geometry is clearly significant when measuring along dam crests. For dams constructed with a conductive core of fine-grained soil and high-resistive rockfill, the effect becomes greatly enhanced. Also, water level fluctuations have a clear effect on apparent resistivities. Only small differences were found between the investigated arrays. A layout along the top of the crest is optimal for monitoring on existing dams, where intrusive investigations are normally avoided, because it is important to pass the current through the conductive core, which is often the main target of investigation. The investigation technique has proven beneficial for improving monitoring routines and increasing the understanding of results from the ongoing monitoring programs. Although the technique and software are developed for dam modeling, it could be used for estimation of 3D influence on any elongated structure with a 2D cross section.
Publisher: Oxford University Press (OUP)
Date: 22-11-2019
DOI: 10.1093/GJI/GGZ529
Abstract: In seismic wave modelling, the boundary reflections caused by the computational grid edges should be reduced to produce accurate simulation results. The perfectly matched layer (PML) method is one of the popular techniques to suppress such artificial reflections, because it can be easily applied to the first-order wave equation in many numerical methods. However, one issue of the PML method is that the stability condition might be violated in complex elastic anisotropic media. In these cases, the PML method will not attenuate the boundary reflections but rather introduce strong artefacts in the simulation results. To tackle this problem, we propose a generalized stiffness reduction method (GSRM) as a substitute for the PML method. We first derive the stability conditions of the PML method and analyse the suitable conditions for their application to time- and frequency-domain seismic wave modelling. Then, we develop a simple and effective numerical implementation of the GSRM to attenuate the boundary reflections and apply it to seismic wave modelling in elastic anisotropic media. We give some numerical experiments to demonstrate the feasibility and advantages of the GSRM compared to the PML method. Numerical ex les show the GSRM is conceptually simpler, more computationally efficient and more straightforward in terms of numerical implementation than the PML method for seismic modelling using either first- or second-order time- and frequency-domain wave equations.
Publisher: Springer Science and Business Media LLC
Date: 04-09-2010
Publisher: Oxford University Press (OUP)
Date: 2009
Publisher: Oxford University Press (OUP)
Date: 10-08-2013
DOI: 10.1093/GJI/GGT267
Publisher: Society of Exploration Geophysicists
Date: 11-2020
Abstract: In frequency-domain seismic wave modeling, absorbing artificial reflections is crucial to obtain accurate numerical solutions. We have determined that, in viscoelastic anisotropic media (VEAM), the most popular absorbing boundary techniques, such as the perfectly matched layer and the generalized stiffness reduction method (GSRM), fail. Then, we develop a new version of the GSRM and incorporate it into a 2D/2.5D spectral element method. We find with extensive nontrivial numerical experiments that the new GSRM exhibits excellent features of simple and efficient implementation, while handling free-surface and subsurface interface topography. Furthermore, we find that s ling the positive wavenumber range is an efficient strategy to compute the 3D wavefield in arbitrary 2D VEAM, and the new version takes full advantage of the symmetry/antisymmetry of the wavefield. The new GSRM removes artificial reflections by d ing the real and imaginary viscoelastic moduli in different ways. The wavefields in two vertically transverse isotropic and one orthorhombic viscoelastic homogeneous models are compared with the corresponding analytical solutions to show the high accuracy performance of the new GSRM. Finally, a complex 2D geologic model with irregular free-surface and subinterface is considered to present the modeling technique and its adaptation capacity for complex 2D VEAM.
Publisher: Wiley
Date: 09-2005
Publisher: Oxford University Press (OUP)
Date: 24-10-2017
DOI: 10.1093/GJI/GGX460
Publisher: Society of Exploration Geophysicists
Date: 31-12-2021
Abstract: We have developed a simple yet effective transform function to convert 3D point-source seismic data to equivalent 2D line-source data, which is required when applying efficient 2D migration and full-waveform inversion to field data collected along a line. By numerically comparing the 3D and corresponding 2D Green’s tensors in various media, the phase shift approximately 45° and the offset litude compensation factor, as well as small fluctuations of the litude ratios, are observed in all nonzero components of the wave-equation solutions. Based on these observations, we derive a transform function consisting of (1) a simple filter for compensating litude and phase shift and (2) stretching scalars for scaling litude differences for different components. We use the 3D and 2D analytical wave solutions in various homogeneous media to demonstrate the accuracy of our transform function, and then apply it to a heterogeneous viscoelastic anisotropic model and a modified Marmousi model. All of these results indicate that our transform function is applicable for the conversion of point-source data to equivalent line-source data for imaging 2D subsurface structure.
Publisher: Society of Exploration Geophysicists
Date: 11-2020
Abstract: In a viscoelastic anisotropic medium, velocity anisotropy and wave energy attenuation occur and are often observed in seismic data applications. Numerical investigation of seismic wave propagation in complex viscoelastic anisotropic media is very helpful in understanding seismic data and reconstructing subsurface structures. Seismic ray tracing is an effective means to study the propagation characteristics of high-frequency seismic waves. Unfortunately, most seismic ray-tracing methods and traveltime tomographic inversion algorithms only deal with elastic media and ignore the effect of viscoelasticity on the seismic raypath. We have developed a method to find the complex ray velocity that gives the seismic ray speed and attenuation in an arbitrary viscoelastic anisotropic medium, and we incorporate them with the modified shortest-path method to determine the raypath and calculate the real and imaginary traveltime (wave energy attenuation) simultaneously. We determine that the complex ray-tracing method is applicable to arbitrary 2D/3D viscoelastic anisotropic media in a complex geologic model and the computational errors of the real and imaginary traveltime are less than 0.36% and 0.59%, respectively. The numerical ex les verify that the new method is an effective and powerful tool for accomplishing seismic complex ray tracing in heterogeneous viscoelastic anisotropic media.
Publisher: Oxford University Press (OUP)
Date: 03-2005
Publisher: Scientific Research Publishing, Inc.
Date: 2015
Publisher: Wiley
Date: 02-09-2023
DOI: 10.1002/NSG.12265
Abstract: Derivatives of the displacement tensor with respect to the independent model parameters of the subsurface, also called Fréchet derivatives (or sensitivity kernels), are a key ingredient for seismic full‐waveform inversion with a local‐search optimization algorithm. They provide a quantitative measure of the expected changes in the seismograms due to perturbations of the subsurface model parameters for a given survey geometry. Since 2.5‐D wavefield modeling involves a real point source in a 2‐D geological model with 3D (spherical) wave properties, it yields synthetic data much closer to the actual practical field data than the commonly used 2‐D wave simulation does, which uses an unrealistic line source in which the waves spread cylindrically. Based on our recently developed general 2.5‐D wavefield modeling scheme, we apply the perturbation method to obtain explicit analytic expressions for the derivatives of the displacement tensor for 2.5‐D/2‐D frequency‐domain seismic full‐waveform inversion in general viscoelastic anisotropic media. We then demonstrate the numerical calculations of all these derivatives in two common cases: (i) viscoelastic isotropic and (ii) viscoelastic tilted transversely isotropic (TTI) solids. Ex les of the differing sensitivity patterns for the various derivatives are investigated and compared for four different homogeneous models involving 2‐D and 2.5‐D modeling. Also, the numerical results are verified against the analytic solutions for homogeneous models. We further validate the numerical derivatives in a 2‐D heterogeneous viscoelastic TTI case by conducting a synthetic data experiment of frequency‐domain full‐waveform inversion to in idually recover the twelve independent model parameters (density, dip angle, five elastic moduli, and five corresponding Q‐factors) in a simple model comprising an anomalous square box target embedded in a uniform background. Another 2.5‐D multi‐target model experiment presenting impacts from four common seismic surveying geometries validates the Fréchet derivatives again. This article is protected by copyright. All rights reserved
Publisher: Informa UK Limited
Date: 06-1992
DOI: 10.1071/EG992497
Publisher: Scientific Research Publishing, Inc.
Date: 2015
Publisher: Informa UK Limited
Date: 12-2004
Publisher: Society of Exploration Geophysicists
Date: 07-2007
DOI: 10.1190/1.2732549
Abstract: We present an accurate 3D ray-tracing algorithm based on a modified (more flexible and economical) shortest-path method (SPM). Unlike the regular SPM in the 3D case, which uses only primary nodes at the corners of each cell and whose accuracy depends on actual cell size, the new method can work with much larger cell sizes by introducing secondary nodes along all bounding surfaces of the cell. This increases the ray angular coverage and permits detailed specification of the velocity field. The modified SPM simultaneously calculates first-arrival times and gradually locates the related raypaths on all grid nodes as the wave field evolves. Its advantages over the regular SPM are its ability to handle high-contrast velocity models more easily, lower memory requirements and less CPU time, and the capability to calculate a relatively large 3D model without losing accuracy. The maximum relative error bound in the computed traveltimes of the modified SPM is established for a uniform velocity field, which may be considered an upper error bound for the whole model in real problems. The modified method in this study is compared with the regular SPM theoretically and on two specific velocity models. The Marmousi model is used to further test the performance of the new approach for both accuracy and flexibility in a complex velocity field. The study shows that the modified SPM is preferable to regular SPM for real 3D problems.
Publisher: Springer Science and Business Media LLC
Date: 18-01-2008
Publisher: Elsevier BV
Date: 04-2002
Publisher: Oxford University Press (OUP)
Date: 27-01-2005
Publisher: Society of Exploration Geophysicists
Date: 10-08-2019
Publisher: Informa UK Limited
Date: 2009
Publisher: Wiley
Date: 06-2003
Publisher: Wiley
Date: 09-2011
Publisher: Informa UK Limited
Date: 12-2006
Publisher: Springer Science and Business Media LLC
Date: 17-06-2021
Publisher: Society of Exploration Geophysicists
Date: 07-2018
Abstract: Kinematic ray tracing is an effective way to simulate the seismic wave propagation in isotropic and anisotropic media. It is essential to know the ray velocity when tracing seismic rays. But in anisotropic media, the ray velocity is a function of the direction of the slowness vector instead of the ray direction and it often deviates from the phase velocity. In this case, it causes a critical problem for ray tracing, which is how to calculate the ray velocity from a known ray direction. If we could calculate the phase slowness vector from ray directions, the ray velocity could be computed. We have evaluated a previous method in the first place. Then, we developed two new methods to solve two existing problems of the previous method: (1) It leads to complex and multiple solutions of the slowness vector and (2) it mixes up the qP- and qSV-wave modes. Our first method solves the two problems by applying eigenvalues to separate the wave modes and decrease the two unknowns ([Formula: see text] and [Formula: see text]) to only one unknown in two equations. Our second method is based on the general relationship between the slowness and ray-velocity vectors and shows that only one unknown is involved in one equation for tilted transversely isotropic (TTI) media. After obtaining the slowness vector, the ray velocity can be computed easily. A 2D model is designed to test the feasibility of the new methods. Using the results for the model, we found that the presented approaches were applicable for ray tracing in TTI media.
Publisher: Oxford University Press (OUP)
Date: 06-2001
Publisher: Oxford University Press (OUP)
Date: 03-10-2018
DOI: 10.1093/GJI/GGY410
Publisher: Informa UK Limited
Date: 06-2006
DOI: 10.1071/EG06150
Publisher: Springer Science and Business Media LLC
Date: 11-02-2011
Publisher: Oxford University Press (OUP)
Date: 07-2009
Publisher: Elsevier BV
Date: 11-2016
Publisher: Oxford University Press (OUP)
Date: 30-11-2010
Publisher: Society of Exploration Geophysicists
Date: 05-2009
DOI: 10.1190/1.3111114
Abstract: We have developed explicit expressions for the Fréchet derivatives or sensitivity functions in resistivity imaging of a heterogeneous and fully anisotropic earth. The formulation involves the Green’s functions and their gradients, and it is developed from a formal perturbation analysis and by means of a numerical (finite-element) method. A critical factor in the equations is the derivative of the electrical conductivity tensor with respect to the principal conductivity values and the angles defining the axes of symmetry. The Fréchet derivative expressions were derived for the 2.5D and 3D problems using constant-point and constant-block model parameterizations. Special cases such as an isotropic earth and tilted transversely isotropic (TTI) media emerge from the general solutions. Numerical ex les were investigated for various sensitivities as functions of dip angle and strike of the plane of stratification in uniform TTI media.
Publisher: Informa UK Limited
Date: 03-2000
DOI: 10.1071/EG00315
Publisher: Wiley
Date: 06-2013
Publisher: Springer Science and Business Media LLC
Date: 05-1993
DOI: 10.1007/BF02650939
Publisher: Wiley
Date: 14-10-2020
DOI: 10.1002/NSG.12125
Publisher: Oxford University Press (OUP)
Date: 18-12-2019
DOI: 10.1093/JGE/GXZ106
Abstract: We derive explicit expressions for the dissipation factors of inhomogeneous P and SV-waves in isotropic viscoelastic media. The Q−1 values are given as concise and simple functions of material parameters and the wave inhomogeneity parameter using two different definitions. Unlike homogenous waves, inhomogeneous waves may have significant differences in the values of dissipation factors because of different definitions. For ex le, under one of the three dissipation factor definitions that Q−1 is equal to the time-averaged dissipated-energy density ided by twice the time-averaged strain-energy density, it is found and proved that the dissipation factor of SV-waves is totally independent of the inhomogeneity parameter. For materials in which P-waves are normally more dissipative than S-waves (e.g. a porous reservoir), the dissipation factors of P-waves tend to decrease with increasing degree of inhomogeneity. Based on Buchan's classic real value energy balance equation, a parallel investigation is conducted for each step similar to that based on the Carcione equations, including derivation of explicit formulas (with inhomogeneity angle representing the degree of inhomogeneity of a plane wave), and dissipation curves calculations. We also obtain an inhomogeneity independent formula of $Q_{\\, SV}^{ - 1}$, and exactly the same phase velocity and attenuation dispersion results for the ex le material.
Publisher: Oxford University Press (OUP)
Date: 15-09-2016
DOI: 10.1093/GJI/GGW345
Publisher: Wiley
Date: 05-2015
DOI: 10.1002/CJG2.220175
Publisher: Thomas Telford Ltd.
Date: 26-06-2020
Publisher: Oxford University Press (OUP)
Date: 17-02-2015
DOI: 10.1093/GJI/GGV012
Location: Saudi Arabia
Start Date: 2017
End Date: 2021
Funder: Khalifa University of Science, Technology and Research
View Funded Activity