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1-20 of 28

George McMechan

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Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the SEG/AAPG/SEPM First International Meeting for Applied Geoscience & Energy, September 26–October 1, 2021

Paper Number: SEG-2021-3567601

Abstract

One important requirement for least-squares imaging (LSM) is having an accurate migration velocity model. LSM with large velocity errors results in erroneous reflector locations, strong swing artifact and even non-convergence. To mitigate these issues, we develop a novel least-squares imaging framework in the subsurface reflection angle domain. Instead of using high-wavenumber velocity perturbations for the reflectivity model as is done in traditional LSM, we parameterize the wave equation with an angle-dependent reflectivity, and derive the corresponding linearized forward modeling and adjoint migration operators. Because Gaussian Beam migration naturally incorporates the propagation directions in wavefield extrapolation, we represent the Green’s function using the Gaussian beam summation method. To improve the common-image gather (CIG) quality for low fold and low SNR data, a shaping regularization over the incident angle direction is introduced into the conjugate gradient scheme to iteratively update the angle-dependent reflectivity model. A flattening-enhanced summation is used to compute the stacked images by accounting for the depth moveout of CIGs caused by velocity errors, and produces constructive stacking results. Numerical experiments for a land survey demonstrate that the proposed method can improve LSM convergence and produce high-quality angle-dependent and stacked images with inaccurate migration velocity models.

Proceedings Papers

Paper presented at the International Petroleum Technology Conference, January 13–15, 2020

Paper Number: IPTC-20120-ABSTRACT

Abstract

In areas of complicated near-surface structures, estimation of an accurate near-surface velocity is challenging and this usually results in a distorted image of deeper targets. Surface waves have strong energy and decay exponentially with the depth, but they usually have high signal-to-noise ratios. Surface waves are strongly depending on S-wave velocities and also include information of P-wave velocity, density and attenuation of both P- and S-waves. Conventional inversion based on dispersion curves can only produce 1D S-wave velocity model. Full waveform inversion of surface waves breaks this limitation and can provide 2D or 3D high resolution near surface S-wave velocity, and reasonable P-wave velocity and density as well. Envelope of seismogram contains effective lower frequencies information which usually is not available in the seismogram. Combined with a multi-frequency strategy, cascadeded inversion of envelope-based and waveform-based misfit functions of both Rayleigh and body waves can reduce cycle skipping for FWI and estimate models with high resolution. This is due to the broader frequency bandwidth and composite contributions from Rayleigh waves and body waves. We test this method on the Arid 2D model, a typical near surface structure designed to include challenges in land seismic processing. Due to the high sensitivity to S-wave velocity and strong energy of Rayleigh waves, concurrent FWI of Rayleigh and body waves using cascaded envelope and waveform inversion produces S-wave velocity model with highest resolution. The resolution of P-wave velocity and density is lower than that of S-wave velocity. The small low velocity anomalies and faults at very shallow depths in the P- and S-wave velocity models are clearly defined. The low velocity structures at greater depths are better inverted in the S-wave velocity than in the P-wave velocity.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017

Paper Number: SEG-2017-17747338

Abstract

ABSTRACT We have developed a novel Q compensation approach for adjoint-based seismic imaging by pseudodifferential scaling. The algorithm is stable, because it doesn’t involve amplitude amplification during wavefield extrapolations. We consider an image has correct amplitudes if, with the image as input, linearized Born modeling approximately produces the data. This can be achieved with the application of the inverse Hessian to the RTM image, to compensate propagation effects, including the Q effects. Pseudodifferential scaling (a dip and space dependent filter) is used to efficiently approximate the action of the inverse Hessian, and is applied to the viscoacoustic RTM image to compensate attenuation loss, and approximately recover the model perturbation. We evaluate the performance of the Q compensation using the Marmousi model. Numerical examples indicate that the adjoint RTM images with pseudodifferential scaling approximate the true model perturbation, and can be used as well-conditioned gradients for least-squares imaging. Presentation Date: Wednesday, September 27, 2017 Start Time: 2:15 PM Location: 371A Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017

Paper Number: SEG-2017-17790704

Abstract

ABSTRACT Elastic reverse time migration (E-RTM) has limitations when the migration velocities contain strong contrasts. First, the vector-based imaging condition needs to use the reflector-image normal, and also cannot give the correct polarity of the PP image in all possible polarization conditions. Second, the angle-domain common-image gathers (ADCIGs) obtained using Poynting vectors do not consider the wave interferences that occur at each reflector. Therefore, smooth models are often used for E-RTM. This paper relaxes this condition by proposing an improved data flow that has two new aspects. First, new elastic imaging conditions are proposed, which are based on multidirectional vectors. These imaging conditions can give the correct image polarity in all possible conditions without knowledge of the reflector-image normal. Second, multidirectional propagation vectors are calculated to give E-RTM images and ADCIGs. To make the vectors multidirectional, approximate wavefield decomposition (WD) in the frequency-wavenumber () domain is applied to the particle velocities; the approximate WD can also provide the sign of the / components to convert the particle velocities (the polarization vector) into the propagation vector. Numerical examples show the robustness of the improved data flow. Presentation Date: Wednesday, September 27, 2017 Start Time: 9:20 AM Location: 361A Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017

Paper Number: SEG-2017-17791370

Abstract

ABSTRACT The full waveform inversion (FWI) is based on a strongly approximate solution of a mathematical problem. To connect it with physical concepts, previously we used the classical reflectivity-to-velocity inversion to derive an FWI formula, which suggests that the relative velocity update is a phase-modified and deconvolved reverse-time-migration (RTM) image using the residual data. In this paper, we extend this method from P-velocity inversion into P-impedance inversion. During the extension, a difficult point is that the P-impedance is a product of P-velocity and density; updates of the two parameters have a trade-off during the inversion process. In our system, solving this trade-off is similar to an amplitude-versus-angle (AVA) inversion. However, the accurate AVA information is hard to obtain in practice; the AVA inversion also requires the angle-domain common-image gathers (ADCIGs) to be (nearly) flat, which poses a much stricter constraint on the accuracy of the background P-velocity than the half-wavelength condition for single-parameter (P-velocity) FWI. To proceed, we combine our formula with the rock physics in which the relation between the P-velocity and density can be approximated. Thus we can invert only the P-impedance and use it to approximate the P-velocity and density in each iteration. So we convert the multi-parameter inversion (P-velocity and density) into single-parameter inversion (P-impedance). Extension of this method into elastic media is also given. In the real world, the rock-physics relationship is complicated, probabilistic and condition-dependent; we suggest addressing this via Machine learning, by building and progressively modifying a database of statistical multi-parameter (P and S velocities, density, attenuation, etc.) relations that can be navigated with a search engine (e.g., like Google) to dynamically determine the solution with the highest probability and its nonuniqueness. This implies a major, multi-year effort. A stable amplitude-preserved RTM formula is also given as an approximation to the deconvolution imaging condition. Presentation Date: Tuesday, September 26, 2017 Start Time: 9:20 AM Location: Exhibit Hall C, E-P Station 3 Presentation Type: EPOSTER

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017

Paper Number: SEG-2017-17789761

Abstract

ABSTRACT The traditional scheme of P/S wave mode separation based on Helmholtz's equations ignores the conversion between P and S waves at the current separation time. Thus, it contains an implicit assumption of constant shear modulus and requires smoothing the heterogeneous model to satisfy a locally constant condition. A direct consequence is that, when there is a reflector in the shear-modulus model, the summation of P and S particle velocities obtained using Helmholtz’s equations is not equivalent to the total elastic particle velocity. We relax this condition by proposing an improved system of P/S wave mode separation. It considers the converted wave generated at the current separation time and thus does not require the assumption of constant shear modulus. We further apply this system to elastic reverse time migration to obtain PP and PS images. Presentation Date: Monday, September 25, 2017 Start Time: 3:30 PM Location: Exhibit Hall C/D Presentation Type: POSTER

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017

Paper Number: SEG-2017-17667669

Abstract

ABSTRACT We develop a localized low-rank approximation algorithm with (space) domain decomposition that significantly improves the scalability of P/S decomposition of anisotropic wavefields. The model and simulated wavefield are decomposed into rectangular blocks, which don’t have to be geologically constrained; low-rank approximations and P/S decomposition are performed separately and simultaneously in each block. An overlap-add method is used to reduce artifacts at block boundaries caused by Fourier transforms at wavefield truncations, and limited communication is required between blocks. Tests with synthetic data show good P/S decomposition results. Presentation Date: Tuesday, September 26, 2017 Start Time: 1:50 PM Location: 360D Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017

Paper Number: SEG-2017-17585000

Abstract

ABSTRACT We use the least-squares reverse-time migration for viscoelastic media (Q-LSRTM), to compensate the attenuation loss for both P and S images. A first-order viscoelastic formulations, based on the generalized standard linear solid (GSLS), is used as the forward modeling operator. Q-LSRTM solves the viscoelastic linearized modeling operator for generating synthetic data, and the adjoint operator for back propagating the data residual in each iteration. The viscoelastic adjoint operator, and the P and S imaging conditions are derived using the adjoint-state method. With the correct background velocity model, and with the merit of including Q in modeling and imaging, Q-LSRTM is capable of iteratively updating the amplitudes of seismic images, in the direction of minimizing data residual between the observed and synthetic data. With a few tens of iterations, the amplitude loss caused by Qp and Qs in the P and S images of modulus perturbation can be compensated. The P and S images from Q-LSRTM have more balanced (closer to the true modulus perturbation) and continuous amplitudes than those from elastic LSRTM. Presentation Date: Monday, September 25, 2017 Start Time: 2:15 PM Location: 361A Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2016 SEG International Exposition and Annual Meeting, October 16–21, 2016

Paper Number: SEG-2016-13879599

Abstract

ABSTRACT Because receiver wavefields from observed data are not as stable as source wavefields, the source direction and the reflector normal have been used to calculate angle-domain common-image gathers (ADCIGs) from reverse time migration (RTM), but has three limitations: 1) The existing method calculates only the direction at maximum wavefield amplitudes during propagation; thus each grid point is assumed to have only one arrival. 2) The velocity needs to be smoothed to avoid wavefield interferences at each reflector, because both amplitude picking and Poynting vector calculation do not work for overlapping wavefields. 3) Computing the reflector normal in space gives only one polarity direction for each point. We propose an improved flow, which includes two steps: a) During imaging, we use a multidirectional slowness vector to calculate the source wavefield directions at each time step, and output intermediate source direction angle CIGs (SACIGs). b) After imaging, we convert the SACIGs to ADCIGs in the wavenumber domain by using the reflector normal by anti-leakage Fourier transforms in local windows. To achieve the new flow, two innovative aspects are included. In the first step, we combine the wavefield decomposition and an angle filter imaging condition to remove the backscattering artifacts in the SACIGs and RTM image; in the second step, the ALFT is slow and produces Fourier artifacts when the images in local windows are not straight (especially for incorrect migration velocities); we revise the ALFT algorithm, in which we taper the amplitudes within a very small window that surrounds a selected point and transfer the data in the entire tapered window back to the space domain (rather than only transfer its central point back), and also use a new criterion to accelerate ALFT. Numerical tests show this new flow gives high-quality ADCIGs. Presentation Date: Thursday, October 20, 2016 Start Time: 10:10:00 AM Location: 171/173 Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2016 SEG International Exposition and Annual Meeting, October 16–21, 2016

Paper Number: SEG-2016-13879906

Abstract

ABSTRACT Using Poynting vectors (PVs) is a relatively cheap way to calculate ADCIGs, but can be inaccurate and unstable because of the inability to calculate the propagation directions of overlapping wavefields. However, even if a multidirectional PV (MPV) is used, in which the wavefields have been separated before calculating PVs, the vector computation is still not stable because the PV is a product of the time and space derivatives of the pressure field. When the magnitude of the pressure field is at a peak, the magnitudes of both the time and space derivatives are zero, which means the direction is undefined. This leads to unstable points when pressure magnitudes are near peaks, and reduces the quality of ADCIGs and the subsequent velocity and reflectivity estimation. We propose two methods to increase the stability of MPVs. The first method defines and uses a variable "time-shift"; the direction vector is not computed simultaneously with its corresponding pressure field, but with a time shift. The time-shift is determined by picking the maximum magnitude of time derivatives of pressure fields within a time window, and there is a time-shift value at each grid point at each time step. The other method combines the existing optical flow (OF) method with the multidirectional scheme, to produce a multidirectional OF (MOF). The MOF needs iterations and thus is relatively expensive. Numerical examples show both the time-shift MPV (TMPV) and MOF can improve the MPV results, and give more accurate ADCIGs; the result obtained using T-MPV has similar quality as that of the MOF result, but T-MPV does not require iterations. Presentation Date: Thursday, October 20, 2016 Start Time: 11:00:00 AM Location: 171/173 Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2016 SEG International Exposition and Annual Meeting, October 16–21, 2016

Paper Number: SEG-2016-13879375

Abstract

ABSTRACT To obtain a physical understanding of the process of full waveform inversion (FWI), we find a connection between the FWI gradient and the image obtained using reverse time migration (RTM). The gradient uses the residual data as a virtual source and RTM uses the recorded data directly as the boundary condition, so the FWI gradient is similar to a time integration of the RTM image using the residual data, which physically converts the phase of the reflectivity to the phase of the velocity. Therefore, the steepest-descent FWI can be connected to the classical reflectivity-to-velocity inversion (RVI). We propose a new FWI scheme, the inversion formula of which is derived from RVI and has a clear physical meaning. In this scheme, the relative velocity update is a phase-modified and deconvolved RTM image, which is obtained with source wavelet and time-integrated residual data that are both deconvolved. Because of the deconvolution, spectral amplitudes within the frequency band are well balanced and thus we have a wider "effective" frequency bandwidth; a multi-scale approach with a gradually widening frequency band is applied. Presentation Date: Tuesday, October 18, 2016 Start Time: 8:25:00 AM Location: 162/164 Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2016 SEG International Exposition and Annual Meeting, October 16–21, 2016

Paper Number: SEG-2016-13512297

Abstract

ABSTRACT Elastic reverse time migration (ERTM) requires separation of PP and PS reflections before, or as part of, applying the image conditions. Traditional P- and S-waves separation methods based on divergence and curl operators don't preserve the elastic vector information, and the non-normalized cross-correlation image condition generates image amplitudes with no physical meaning. Thus a preferable workflow for isotropic ERTM should include a vector decomposition of the elastic wavefields and a vector-based image condition that directly uses the signed magnitudes of the decomposed vector wavefields to produce PP and PS images. The image condition involves the calculation of propagation directions of the decomposed P- and S-waves, which can be further utilized to efficiently generate PP and PS angle domain common image gathers (ADCIGs). Presentation Date: Monday, October 17, 2016 Start Time: 3:20:00 PM Location: 171/173 Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2016 SEG International Exposition and Annual Meeting, October 16–21, 2016

Paper Number: SEG-2016-13974653

Abstract

ABSTRACT Understanding the flow and deformation that occurs in a reservoir during fluid injection for enhanced oil and gas recovery is critical for maximizing the efficiency of production from unconventional reservoirs. A one-way coupled model for flow and deformation simulation is used for microseismic nucleation and subsequent wavefield modeling of the elastic emissions from the microseismic events. Presentation Date: Wednesday, October 19, 2016 Start Time: 11:10:00 AM Location: 144/145 Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015

Paper Number: SEG-2015-5807889

Abstract

Summary Seismic exploration is increasingly challenged to image complex subsuface targets, such as subalt and overburden velocity inversion based on reverse-time migration. A yet unsolved problem is direct exploration of multipathing that exists within complex structures. When using the cross-correlation image condition in 2D prestack migration for each source, the contributions are summed over all the time steps to give one migrated image. The stacked image includes contributions from all primary and prismatic waves, multiples, converted waves and artifacts. Thus the final image summation contains a variety of wavefield distortions. However, if the image time slices are saved for each image time, and are sorted (across sources) into a three-parameter (incident angle, depth, image time) volume for which separate images can be constructed using any desired subset of the migrated data in the three data dimensions, much valuable information from multipath arrivals can be obtained. The separate partial images can by displayed for the primary contributions, or any combination of different types of waves (with or without artifacts). A numerical example for a simple model with two sets of source-to-reflector paths show how primary and prismatic contributions merge into a single incident angle vs image time trajectory. A second example using synthetic data from the Sigsbee2 model shows that the relative contributions of multipath arrivals to subsalt images are different. Introduction Prestack reverse-time migration (RTM) is effective for generation of prestack depth migrated images from common-source data. Combining the migrated depths with incident (or reflection) angle information produces angle-domain commonimage gathers (ADCIGs) from any prestack migration. Raybased prestack migration velocity analysis (Stork, 1992), is efficient, and the propagation angle information is already inherently available as part of the ray paths, but it based on high frequency assumption and often fails when we image complex structures. Wave-based prestack ADCIG algorithms have one of three different forms to extract angle information; directionvector- based methods (e.g., Yoon and Marfurt (2006); Zhang and McMechan (2011); Dickens and Winbow (2011); Vyas et al. (2011)), local plane-wave decomposition methods (e.g., Xu et al. (2011); Rui and Xie (2012)), and local-shift imaging condition methods (Sava and Fomel (2003)). Calculating the propagation angles from the wavefronts is a substantial extra computational effort. Xu et al. (2001) show that ADCIGS are ’cleaner’ than offset domain CIGs as the offset domain contains triplications, whereas ordering the image contributions by angle does not. However, the amplitudes in ADCIGS can still have data gaps, or rapid variations, discontinuities discontinuities and biases if both the source and receiver wavefields are not adequately corrected for all propagations effects (Deng and McMechan (2008)). Wave-based ADCIGs usually use the crosscorrelation (or source-normalized crosscorrelation) image condition, so all possible wave types and paths automatically contribute to the image. A prismatic path also satisfies an image time, but for it’s unique path; Cavalca and Lailly (2005) show that RTM images with multipaths provide more complete target information in complex geology, as multipaths usually have different incident angles, and amplitudes, from the primary reflections.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015

Paper Number: SEG-2015-5766697

Abstract

Summary P and S decomposition is an essential step in isotropic viscoelastic reverse time migration (VRTM). Separation using divergence and curl operators doesn’t preserve the phase or amplitude of the input viscoelastic wavefield, so an alternative decomposition that preserves the vector components of the P- and S-waves in the input wavefield is desired. With a decoupled assumption, we rearrange the memory variables in the elastodynamic equations based on the standard linear solid. The vector components of the propagating P- and S-wave can be can be decomposed in isotropic viscoelastic media without losing accuracy. Synthetic tests show that the P- and S-waves can be decomposed with no distortion of the amplitude or phase, and have the same vector components of particle velocity that exist in the viscoelastic wavefield before decomposition. Introduction Anelastic effects have been widely observed in wave propagation in the Earth (Carcione et al., 1988b). To simulate viscoelastic wave propagation, the theory of linear viscoelasticity based on Boltzmann’s superposition principle has been proposed and shown to be effective (Liu et al., 1976). Carcione et al. (1988a; 1988b; 1993) replace the time convolution in the viscoelastic constitutive equation by introducing memory variables, which allow the simulation of wavefields for models with arbitrary quality factor (Q) distributions, thus making viscoelastic computations practical and affordable in the time domain. This approach was extended to the stressparticle velocity formulation by Robertsson et al. (1994), that is used in this paper. Earth materials have been shown to have a nearly constant Q over the exploration seismic frequency range (McDonal et al., 1958; Bourbie et al., 1987). To achieve realistic simulation, Blanch et al. (1995) proposed a quick procedure for modeling constant Q behavior; Hestholm et al. (2006) combined the method of Blanch et al. (1995) and the Nelder - Mead algorithm (Powell, 1973) and improved Q estimation. Xu and McMechan (1995) improved the efficiency of the viscoelastic stress-particle velocity formulation by using composite memory variables, where the shear and compressional memory variables are combined by vector components to reduce RAM storage. With the linear viscoelastic formulation, attenuation loss can be compensated during both forward (source) and backward (receiver) wavefield extrapolations, which is used in true-amplitude migrations (Deng and McMechan, 2008).

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2013 SEG Annual Meeting, September 22–27, 2013

Paper Number: SEG-2013-0189

Abstract

Summary Prestack migration has angle-dependent wavelet stretch effects, which lowers the image resolution at large reflection angles. Most current stretch correction methods operate on the migrated images. We develop a new stretch-free imaging condition, which does a shrink-and-shift operation on the extracted propagation wavelet after extrapolation, but before the imaging condition is applied. The algorithm is illustrated with the excitation amplitude imaging condition; the new images show successful stretch corrections over wide angle apertures, and preserve both amplitude and phase.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2012 SEG Annual Meeting, November 4–9, 2012

Paper Number: SEG-2012-0160

Abstract

SUMMARY In the past, various approximations to the Zoeppritz equations have been derived and used in conventional AVO inversion. These approximations have accuracy limited to small angles, and the number of invertible elastic parameters is limited to two or three (the so-called two- or three-term AVO). Although inapplicable near the critical angle, plane-wave reflection coefficients (RCs) given by Zoeppritz equations are closed form and accurate for models without critical angles. We propose using the "exact" elastic Zoeppritz equations to do AVO inversion for reflections without critical angles. We compare the PP RCs calculated by finite differencing (FD), the Zoeppritz equation, and some classical approximations. For inversion, the Fréchet derivatives can be calculated analytically, and least-squares amplitude fitting is able to invert for the density ratio and three velocity ratios at the reflector. This algorithm is useful for inversion of long-offset PP reflections.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2012 SEG Annual Meeting, November 4–9, 2012

Paper Number: SEG-2012-0161

Abstract

SUMMARY The residual moveout in an angle-domain common-image gather (ADCIG) can be used for migration velocity analysis. ADCIGs also have potential for amplitude variation with angle (AVA) analysis. However, previous AVA analyses are not very successful, especially for deeper layers, because transmission losses are not properly compensated, and phase shifts occur at near- and post-critical reflections. Phase is less affected than amplitude by transmission losses in prestack images from reverse-time migration. We consider amplitude and phase analysis of a target reflector in an ADCIG. Tests on a modified Marmousi2 elastic model show that the phase variation with angle (PVA) is better preserved than the AVA. This is significant for target-oriented inversion because distortions in the overburden are minimized in PVA. ADCIGs potentially extend AVA/PVA analysis to 2D/3D models.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2012 SEG Annual Meeting, November 4–9, 2012

Paper Number: SEG-2012-1061

Abstract

SUMMARY In the presence of critical angles, plane-wave reflection coefficients (PRCs) are not applicable to spherical-wave reflections. As a plane-wave decomposition method, the t- p transform provides a way of applying PRCs to wide-angle sphericalwave reflections in the t- p domain. Previous studies have focused on amplitude analysis. We analyze phase variation with ray parameter (PVP) in the t- p domain. Numerical tests confirm that PRCs are accurate (both in amplitude and phase) in the t- p domain, even near the critical ray parameter. Forward t- p modeling from common-source gathers show that PVP is less affected by the edge effects than is the amplitude variation with ray parameter (AVP). PVP is more reliable in the postcritical range than AVP, which makes it useful for inversion of wide-angle reflections in the t- p domain. The main limitation of this t- p method is the assumption of lateral homogeneity.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2011 SEG Annual Meeting, September 18–23, 2011

Paper Number: SEG-2011-2565

Abstract

ABSTRACT Seismic reflection data from near- to post-critical angles provide the potential of both velocity and density inversion. It is known that plane wave solutions are inapplicable near the critical angle. Spherical-wave solutions have recently been considered to study the amplitude variation with offset (AVO). However, amplitude is difficult to extract reliably due to transmission losses. To overcome this, we propose to use the phase variation with angle (PVA) information for elastic parameter inversion. The modeling is by spherical-wave reflection coefficients (SRCs). A linearized least-squares scheme is used to invert the modeled PVA for density and three velocities across the reflector. Numerical tests indicate that a correct solution can be reached only when the models are consistent for both observed and predicted phases. A spherical-wave model can produce a more accurate solution for real (spherical-wave) data than a plane-wave model can.

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