# McMechan, George A.

Permanent URI for this collectionhttps://hdl.handle.net/10735.1/2490

George McMechan is the Ida Green Professor of Geosciences and Director of the Center for Lithospheric Studies. He is considered an expert in seismology, geophysics, ground-penetrating radar, and wave fields. Learn more about Dr. McMechan from his profile and Research Explorer pages

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# Browsing McMechan, George A. by Author "103911551 (McMechan, GA)"

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Item Combining Multidirectional Source Vector with Antitruncation-Artifact Fourier Transform to Calculate Angle Gathers from Reverse Time Migration in Two Steps(Society of Exploration Geophysicists, 2017-08-11) Tang, Chen; McMechan, George A.; 103911551 (McMechan, GA); Tang, Chen; McMechan, George A.Because receiver wavefields reconstructed from observed data are not as stable as synthetic source wavefields, the source-propagation vector and the reflector normal have often been used to calculate angle-domain common-image gathers (ADCIGs) from reverse time migration. However, the existing data flows have three main limitations: (1) Calculating the propagation direction only at the wavefields with maximum amplitudes ignores multiarrivals; using the crosscorrelation imaging condition at each time step can include the multiarrivals but will result in backscattering artifacts. (2) Neither amplitude picking nor Poynting-vector calculations are accurate for overlapping wavefields. (3) Calculating the reflector normal in space is not accurate for a structurally complicated reflection image, and calculating it in the wavenumber (k) domain may give Fourier truncation artifacts. We address these three limitations in an improved data flow with two steps: During imaging, we use a multidirectional Poynting vector (MPV) to calculate the propagation vectors of the source wavefield at each time step and output intermediate source-angle-domain CIGs (SACIGs). After imaging, we use an antitruncation-artifact Fourier transform (ATFT) to convert SACIGs to ADCIGs in the k-domain. To achieve the new flow, another three innovative aspects are included. In the first step, we develop an angle-tapering scheme to remove the Fourier truncation artifacts during the wave decomposition (ofMPV) while preserving the amplitudes, and we use a wavefield decomposition plus angle-filter imaging condition to remove the backscattering artifacts in the SACIGs. In the second step, we compare two algorithms to remove the Fourier truncation artifacts that are caused by the plane-wave assumption. One uses an antileakage FT (ALFT) in local windows; the other uses an antitruncation-artifact FT, which relaxes the planewave assumption and thus can be done for the global space. The second algorithm is preferred. Numerical tests indicate that this new flow (source-side MPV plus ATFT) gives high-quality ADCIGs.Item Efficient Love Wave Modelling via Sobolev Gradient Steepest Descent(Oxford University Press, 2016-02-22) Browning, Matt; Ferguson, John; McMechan, George A.; 103911551 (McMechan, GA); McMechan, George A.A new method for finding solutions to ordinary differential equation boundary value problems is introduced, in which Sobolev gradient steepest descent is used to determine eigenfunctions and eigenvalues simultaneously in an iterative scheme. The technique is then applied to the 1-D Love wave problem. The algorithm has several advantages when computing dispersion curves. It avoids the problem of mode skipping, and can handle arbitrary Earth structure profiles in depth. For a given frequency range, computation times scale approximately as the square root of the number of frequencies, and the computation of dispersion curves can be implemented in a fully parallel manner over the modes involved. The steepest descent solutions are within a fraction of a per cent of the analytic solutions for the first 25 modes for a two-layer model. Since all corresponding eigenfunctions are computed along with the dispersion curves, the impact on group and phase velocity of the displacement behaviour with depth is thoroughly examined. The dispersion curves are used to compute synthetic Love wave seismograms that include many higher order modes. An example includes addition of attenuation to a model with a low-velocity zone, with values as low as Q = 20. Finally, a confirming comparison is made with a layer matrix method on the upper 700 km of a whole Earth model.Item P- and S-Decomposition in Anisotropic Media with Localized Low-Rank Approximations(Society of Exploration Geophysicists, 2017-11-13) Wang, W.; Hua, B.; McMechan, George A.; Duquet, B.; 103911551 (McMechan, GA); McMechan, George A.We have developed a P- and S-wave decomposition algorithm based on windowed Fourier transforms and a localized low-rank approximation with improved scalability and efficiency for anisotropic wavefields. The model and wavefield are divided into rectangular blocks that do not have to be geologically constrained; low-rank approximations and P- and S-decomposition are performed separately in each block. An overlap-add method reduces artifacts at block boundaries caused by Fourier transforms at wavefield truncations; limited communication is required between blocks. Localization allows a lower rank to be used than global lowrank approximations while maintaining the same quality of decomposition. The algorithm is scalable, making P- and S-decomposition possible in complicated 3D models. Tests with 2D and 3D synthetic data indicate good P- and S-decomposition results.Item Removing Smearing-Effect Artifacts in Angle-Domain Common-Image Gathers from Reverse Time Migration(Soc Exploration Geophysicists, 2015-03-17) Jin, Hu; McMechan, George A.; 103911551 (McMechan, GA); Jin, Hu; McMechan, George A.Local plane-wave decomposition (LPWD) and local shift imaging condition (LSIC) methods for extracting angle-domain common-image gathers (ADCIGs) from prestack reverse time migration are based on the local plane-wave assumption, and both suffer from a trade-off in choosing the local window size. Small windows produce clean ADCIGs, but with low angle resolution, whereas large windows produce noisy ADCIGs, which include smearing-effect artifacts, but with high angle resolution. The cause of the smearing-effect artifacts in LPWD is the crosscorrelation of plane waves obtained by decomposition of the source and receiver wavefronts, at points that do not lie on the source wavefront excitation time trajectory. The cause of the smearing-effect artifacts in LSIC is the decomposition of curved events of offset-domain common-image gathers (ODCIGs) at incorrect depth points at zero offset. These artifacts can occur even if the migration velocity model is correct. Two methods were proposed to remove the artifacts. In the LPWD method, the smearing-effect artifacts were removed by decomposing and crosscorrelating the resulting source and receiver plane waves only at image points and excitation (image) times. In the LSIC method, the artifacts were removed by decomposing curved events in ODCIGs into planar events only at zero-offset target image points. Numerical tests with synthetic data revealed the success of the proposed methods.Item Time-Domain Least-Squares Migration Using the Gaussian Beam Summation Method(Oxford University Press) Yang, Jidong; Zhu, Hejun; McMechan, George A.; Yue, Yubo; 0000-0002-7452-075X (Zhu, H); 103911551 (McMechan, GA); Yang, Jidong; Zhu, Hejun; McMechan, George A.With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modelling rather than the inverse operator.We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modelling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a pre-conditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration. © The Author(s) 2018. Published by Oxford University Press on behalf of The Royal Astronomical Society.Item Up/Down and P/S Decompositions of Elastic Wavefields Using Complex Seismic Traces with Applications to Calculating Poynting Vectors and Angle-Domain Common-Image Gathers from Reverse Time Migrations(Society of Exploration Geophysicists, 2018-06-01) Wang, Wenlong; McMechan, George A.; Tang, Chen; Xie, F.; 0000-0002-0255-6147 (Wang, W); 103911551 (McMechan, GA); Wang, Wenlong; McMechan, George A.; Tang, ChenSeparations of up- and down-going as well as of P- and S-waves are often a part of processing of multicomponent recorded data and propagating wavefields. Most previous methods for separating up/down propagating wavefields are expensive because of the requirement to save time steps to perform Fourier transforms over time. An alternate approach for separation of up-and down-going waves, based on extrapolation of complex data traces is extended from acoustic to elastic, and combined with P- and S-wave decomposition by decoupled propagation. This preserves all the information in the original data and eliminates the need for a Fourier transform over time, thereby significantly reducing the storage cost and improving computational efficiency. Wavefield decomposition is applied to synthetic elastic VSP data and propagating wavefield snapshots. Poynting vectors obtained from the particle velocity and stress fields after P/S and up/down decompositions are much more accurate than those without because interference between the corresponding wavefronts is significantly reduced. Elastic reverse time migration with the P/S and up/down decompositions indicated significant improvement compared with those without decompositions, when applied to elastic data from a portion of the Marmousi2 model.Item Vector-Based Elastic Reverse Time Migration(Society of Exploration Geophysicists, 2015-10-15) Wang, Wenlong; McMechan, George A.; 103911551 (McMechan, GA); Wang, Wenlong; McMechan, George A.Prestack elastic reverse time migration (RTM) of multicomponent seismic data requires separating PP and PS reflections before, or as part of, applying the image condition, and using image conditions that preserve the angle and amplitude information. Both of these requirements are best achieved when all operations are on vectors.We have created a new 2D migration context for isotropic, elastic RTM, which included decomposition of the elastic source and receiver wavefields into P- and S-wave vectors by decoupled elastodynamic extrapolation, which retained the same stress and particle velocity components as the input data. Then, the propagation directions of the incident and reflected P- and S-waves were calculated directly from the stress and particle velocity definitions of the P- and S-wave Poynting vectors. An excitation- amplitude image condition that scaled the receiver wavelet by the source vector magnitude produced angle-dependent images of PP and PS reflection coefficients with the correct polarities, polarization, and amplitudes. It thus simplified the process of obtaining PP and PS angle-domain common-image gathers (ADCIGs); it was less effort to generate ADCIGs from vector data than from scalar data. We found that the resulting prestack elastic images were nearly identical to the corresponding source-normalized crosscorrelation images and had improved resolution because the wavelet broadening that resulted from the crosscorrelation was not present. © 2015 Society of Exploration Geophysicists.