# Browsing by Author "McMechan, George A."

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Item 2d Frequency-Domain Elastic Full-Waveform Inversion Using Time-Domain Modeling and a Multistep-Length Gradient Approach(Soc Exploration Geophysicists, 2014-02-17) Xu, Kun; McMechan, George A.; McMechan, George A.Show more To decouple the parameters in elastic full-waveform inversion (FWI), we evaluated a new multistep-length gradient approach to assign individual weights separately for each parameter gradient and search for an optimal step length along the composite gradient direction. To perform wavefield extrapolations for the inversion, we used parallelized high-precision finite-element (FE) modeling in the time domain. The inversion was implemented in the frequency domain; the data were obtained at every subsurface grid point using the discrete Fourier transform at each time-domain extrapolation step. We also used frequency selection to reduce cycle skipping, time windowing to remove the artifacts associated with different source spatial patterns between the test and predicted data, and source wavelet estimation at the receivers over the full frequency spectrum by using a fast Fourier transform. In the inversion, the velocity and density re-constructions behaved differently; as a low-wavenumber tomography (for velocities) and as a high-wavenumber migration (for density). Because velocities and density were coupled to some extent, variations were usually underestimated (smoothed) for V_P and V_S and correspondingly overestimated (sharpened) for ρ. The impedances I_P and I_S from the products of the velocity and density results compensated for the under-or overestimations of their variations, so the recovered impedances were closer to the correct ones than V_P, V_S, and ρ were separately. Simultaneous reconstruction of V_P, V_S, and ρ was robust on the FE and finite-difference synthetic data (without surface waves) from the elastic Marmousi-2 model; satisfactory results are obtained for V_P, V_S, ρ, and the recovered I_P and I_S from their products. Convergence is fast, needing only a few tens of iterations, rather than a few hundreds of iterations that are typical in most other elastic FWI algorithms.Show more Item 3D, 9C Seismic Modeling and Inversion of Weyburn Field Data(2012-06-18) Rusmanugroho, H.; McMechan, George A.; McMechan, George A.Show more Inversion of 3D, 9C wide azimuth vertical seismic profiling (VSP) data from the Weyburn Field for 21 independent elastic tensor elements was performed based on the Christoffel equation, using slowness and polarization vectors measured from field data. To check the ability of the resulting elastic tensor to account for the observed data, simulation of the 3C particle velocity seismograms was done using eighth-order, staggered-grid, finite-differencing with the elastic tensor as input. The inversion and forward modeling results were consistent with the anisotropic symmetry of the Weyburn Field being orthorhombic. It was dominated by a very strong, tranverse isotropy with a vertical symmetry axis, superimposed with minor near-vertical fractures with azimuth ∼55° from the inline direction. The predicted synthetic seismograms were very similar to the field VSP data. The examples defined and provided a validation of a complete workflow to recover an elastic tensor from 9C data. The number and values of the nonzero tensor elements identified the anisotropic symmetry present in the neighborhood of a 3C borehole geophone. Computation of parameter correlation matrices allowed evaluation of solution quality through relative parameter independence. © 2012 Society of Exploration Geophysicists.Show more Item Characterization of a Coalesced, Collapsed Paleocave Reservoir Analog Using GPR and Well-Core Data(Society of Exploration Geophysicists, 2002-07) McMechan, George A.; Loucks, R. G.; Mescher, P.; Zeng, Xiaoxian; McMechan, George A.; Zeng, XiaoxianShow more The three-dimensional architecture, spatial complexity, and pore-type distribution are mapped in a near-surface analog of a coalesced, collapsed paleocave system in the Lower Ordovician Ellenburger Group near the city of Marble Falls in central Texas. The surface area of the site has dimensions of about 350 × 1000 m. The data collected include about 12 km of 50-MHz ground-penetrating radar (GPR) data arranged in a grid of orthogonal lines, 29 cores of about 15-m length, and detailed facies maps of an adjacent quarry face. Electrical property measurements along with detailed core descriptions were the basis of integrated interpretation of the GPR data. Three main GPR facies are defined on the basis of degree of brecciation in the corresponding cores: undisturbed host rock, disturbed host rock, and paleocave breccia. This GPR facies division defined the major paleocave trends and the distribution of porosity types, which correlate with reservoir quality. Highly brecciated zones are separated by disturbed and undisturbed host rock. The breccia bodies that outline the trend of collapsed cave passages are up to 300 m wide: the intervening intact areas between breccias are up to 200 m wide. Understanding the breccia distribution in a reservoir analog will help in defining strategies for efficient development of coalesced, collapsed paleocave reservoirs.Show more 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.Show more 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.Show more Item Common-Reflection-Point Migration Velocity Analysis of 2D P-Wave Data From TTI Media(Soc Exploration Geophysicists, 2014-05) Oropeza, Ernesto V.; McMechan, George A.; McMechan, George A.Show more We have developed a common-reflection-point (CRP)-based kinematic migration velocity analysis for 2D P-wave reflection data to estimate the four transversely isotropic (TI) parameters VPo, δ, and ε, and the tilt angle ϕ of the symmetry axis in a TI medium. In each iteration, the tomographic parameter was updated alternately with prestack anisotropic ray-based migration. Iterations initially used layer stripping to reduce the number of degrees of freedom; after convergence was reached, a couple of more iterations over all parameters and all CRPs ensured global interlayer coupling and parameter interaction. The TI symmetry axis orientation was constrained to be locally perpendicular to the reflectors. The VPo dominated the inversion, and so it was weighted less than δ and ε in the parameter updates. Estimates of δ and ε were influenced if the error in ϕ was >5⁰ estimates of VPo were also influenced if the error in ϕ was >10⁰. Examples included data for a simple model with a homogeneous TI layer whose dips allowed recovery of all anisotropy parameters from noise-free data, and a more realistic model (the BP tilted transversely isotropic (TTI) model) for which only VPo, delta, and ϕ were recoverable. The adequacy of the traveltimes predicted by the inverted anisotropic models was tested by comparing migrated images and common image gathers, with those produced using the known velocity models.Show more Item Comparison of Methods for Extracting ADCIGS from RTM(Soc Exploration Geophysicists, 2014-04-01) Jin, Hu; McMechan, George A.; Guan, Huimin; McMechan, George A.Show more Methods for extracting angle-domain common-image gathers (ADCIGs) during 2D reverse-time migration fall into three main categories; direction-vector-based methods, local-plane-wave decomposition methods, and local-shift imaging condition methods. The direction-vector-based methods, which use either amplitude gradients or phase gradients, cannot handle overlapping events because of an assumption of one propagation direction per imaging point per imaging time; however, the ADCIGs from the direction-vector-based methods have the highest angle resolution. A new direction-vector-based method using instantaneous phase gradients in space and time gives the same propagation directions and ADCIGs as those obtained by the Poynting vector or polarization vector based methods, where amplitudes are large. Angles calculated by the phase gradients have larger uncertainties at smaller amplitudes, but they do not significantly degrade the ADCIGs because they contribute only small amplitudes. The local-plane-wave decomposition and local-shift imaging condition methods, implemented either by a Fourier transform or by a slant stack transform, can handle overlapping events, and produce very similar angle gathers. ADCIGs from both methods depend on the local window size in which the transforms are done. In small local windows, both methods produce ADCIGs with low noise, but also with low angle resolution; in large windows, they have high angle resolution, but contain smeared artifacts.Show more Item Comparison of Two Algorithms for Isotropic Elastic P and S Vector Decomposition(Society of Exploration Geophysicists, 2015-06-10) Wang, Wenlong; McMechan, George A.; Zhang, Qunshan; Wang, Wenlong; McMechan, George A.Show more P- and S-wavefield separation is necessary to extract PP and PS images from prestack elastic reverse time migrations. Unlike traditional separation methods that use curl and divergence operators, which do not preserve the wavefield vector component information, we did P and S vector decomposition, which preserves the same vector components that exist in the input elastic wavefield. The amplitude and phase information was automatically preserved, so no amplitude or phase corrections were required. We considered two methods to realize P and S vector decomposition: selective attenuation and decoupled propagation. Selective attenuation uses viscoelastic extrapolation, in which the Q-values are used as processing parameters, to remove either the P-waves or the S-waves. Decoupled propagation rewrites the stress and particle velocity formulation of the elastic equations into separate P-and S-wave components. In both methods, the decomposition is realized during the extrapolation of an elastic wavefield. These algorithms could also perform P and S decomposition in x-t gather data by extrapolating the data downward from the receivers, during which the decomposition is performed, and then back upward to record the decomposed P-and S-waves at the receivers. Comparisons of the two methods in terms of efficiency, accuracy, and memory showed that both could separate P-and S-waves in the vector domain. The decoupled propagation is preferable in terms of speed and memory cost, but was applicable only to elastic propagation.Show more Item Conductivity and Scattering Q in GPR Data: Example from the Ellenburger Dolomite, Central Texas(2012-06-27) Harbi, H.; McMechan, George A.; McMechan, George A.Show more Total attenuation (Qt -1) in ground-penetrating radar (GPR) data is a composite of intrinsic and scattering attenuations (Qin -1 and Qsc -1). For nonmagnetic materials, Qin -1 is a combination of the effects of real conductivity and dielectric relaxation. The attenuation for real conductivity >1.0 mS/m in the GPR frequency band is a function of frequency while the dielectric relaxation is frequency-independent. These frequency behaviors allow separation of the attenuation types by attributing and fitting the Qt -1 decay shape with frequency to the conductivity, and by attributing the magnitude of Qt -1 to the sum of conductivity and dielectric relaxation attenuations at each frequency. Total attenuation is calculated from GPR data using spectral ratios, and Qin -1 is obtained by fitting a smooth lower bound to Qt -1; the difference between Qt -1 and Qin -1 estimates the scattering contribution Qsc -1. Scatterer size spectra are evaluated using KA=1 for 2D, and KA=1.5 for 3D, propagation (where K is wavenumber and A is the scatterer size). We illustrate with 2D synthetic data and three field 2D crosshole profiles from an outcrop of an Ellenburger collapsed paleocave environment in central Texas. Between the three pairs of holes, we estimate the breccia sizes from the scattering spectra Qsc -1. To image the anisotropic electrical conductivity distributions, we use simultaneous iterative reconstruction tomography. There is a correlation between the low wavenumber features of the results of the current conductivity tomography and those in previous velocity tomography, and with surface data results that are predicted and calculated from GPR data attributes. Low- and high-conductivity zones tend to follow either the GPR facies distributions, lithological boundaries, or the larger of the fractures. Correlations are not visible where the breccias are finer because these tend to be more randomly oriented, and/or below the resolution of the GPR data. © 2012 Society of Exploration Geophysicists.Show more 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.Show more 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.Show more Item Elastic and Acoustic Wavefield Decompositions and Application to Reverse Time Migrations(2016-12) Wang, Wenlong; McMechan, George A.; Aiken, Carlos L. V.; Brikowski, Thomas H.; Ferguson, John F.Show more P- and S-waves coexist in elastic wavefields, and separation between them is an essential step in elastic reverse-time migrations (RTMs). Unlike the traditional separation methods that use curl and divergence operators, which do not preserve the wavefield vector component information, we propose and compare two vector decomposition methods, which preserve the same vector components that exist in the input elastic wavefield. The amplitude and phase information is automatically preserved, so no amplitude or phase corrections are required. The decoupled propagation method is extended from elastic to viscoelastic wavefields To use the decomposed P and S vector wavefields and generate PP and PS images, we create a new 2D migration context for isotropic, elastic RTM which includes PS vector decomposition; the propagation directions of both incident and reflected P- and S-waves are calculated directly from the stress and particle velocity definitions of the decomposed P- and S-wave Poynting vectors. Then an excitation-amplitude image condition that scales the receiver wavelet by the source vector magnitude produces angle-dependent images of PP and PS reflection coefficients with the correct polarities, polarization, and amplitudes. It thus simplifies the process of obtaining PP and PS angle-domain common-image gathers (ADCIGs); it is less effort to generate ADCIGs from vector data than from scalar data. Besides P- and S-waves decomposition, separations of up- and down-going waves are also a part of processing of multi-component recorded data and propagating wavefields. A complex trace based up/down separation approach is extended from acoustic to elastic, and combined with P- and S-wave decomposition by decoupled propagation. This eliminates the need for a Fourier transform over time, thereby significantly reducing the storage cost and improving computational efficiency. Wavefield decomposition is applied to both 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. The up/down separation algorithm is also applicable in acoustic RTMs, where both (forward-time extrapolated) source and (reverse-time extrapolated) receiver wavefields are decomposed into up-going and down-going parts. Together with the crosscorrelation imaging condition, four images (down-up, up-down, up-up and down-down) are generated, which facilitate the analysis of artifacts and the imaging ability of the four images. Artifacts may exist in all the decomposed images, but their positions and types are different. The causes of artifacts in different images are explained and illustrated with sketches and numerical tests.Show more Item Estimation of Gas Hydrate and Free Gas Saturation, Concentration, and Distribution from Seismic Data(Society of Exploration Geophysicists, 2018-08-24) Lu, Shaoming; McMechan, George A.; Lu, Shaoming; McMechan, George A.Show more Gas hydrates contain a major untapped source of energy and are of potential economic importance. The theoretical models to estimate gas hydrate saturation from seismic data predict significantly different acoustic/ elastic properties of sediments containing gas hydrate; we do not know which to use. Thus, we develop a new approach based on empirical relations. The water-filled porosity is calibrated (using well-log data) to acoustic impedance twice: one calibration where gas hydrate is present and the other where free gas is present. The water-filled porosity is used in a combination of Archie equations (with corresponding parameters for either gas hydrate or free gas) to estimate gas hydrate or free gas saturations. The method is applied to single-channel seismic data and well logs from Ocean Drilling Program leg 164 from the Blake Ridge area off the east coast of North America. The gas hydrate above the bottom simulating reflector (BSR) is estimated to occupy Ο3-8% of the pore space (Ο2-6% by volume). Free gas is interpreted to be present in three main layers beneath the BSR, with average gas saturations of 11-14%, 7-11%, and 1-5% of the pore space (6-8%, 4-6%, and 1-3% by volume), respectively. The estimated saturations of gas hydrate are very similar to those estimated from vertical seismic profile data and generally agree with those from independent, indirect estimates obtained from resistivity and chloride measurements. The estimated free gas saturations agree with measurements from a pressure core sampler. These results suggest that locally derived empirical relations between porosity and acoustic impedance can provide cost-effective estimates of the saturations, concentration, and distribution of gas hydrate and free gas away from control wells.Show more Item Extraction of Seismic Properties and Models From, and Full Waveform Inversion of, Dispersed Seismic Waves(2022-12-01T06:00:00.000Z) Ren, Li; Zhu, Hejun; Ferraris, John P.; McMechan, George A.; Ferguson, John F.; Stern, Robert J.Show more Surface waves, which propagate along boundaries between two different media, play an important role in resolving geological structures of different scales targeted from global seismology, exploration seismology, geotechnical engineering, to nondestructive testing. Over the past half century or so, different methods have been explored to process and invert surface waves for underground model properties, especially the shear wave velocity. However, there are still many problems waiting to be solved. Conventional dispersion curve inversion (DCI) is limited to 1-D model assumption and has increased uncertainty when the structure is complicated. It also requires picking of dispersion curves from field data, which is often a labor intensive process. Although, methods in the framework of full waveform inversion of surface waves yield models with good resolution, both laterally and vertically when carefully implemented and applied, they are computationally intensive and can easily suffer from the cycle skipping problem. Wave-equation based dispersion curve inversion method combine some of the advantages of those in conventional dispersion curve inversion and full waveform inversion, but also requires picking of dispersion curves from both field and synthetic data. This dissertation focuses to partially solve some of the above issues and leads to more work that can be done in the future. To automate the picking of dispersion curves from surface waves, which is required for many approaches for shallow-subsurface characterization using surface waves, my first project presents a convolutional-neural-network (CNN) based machine learning approach to automatically pick the curves for the fundamental and higher modes along the two azimuths of any 2D seismic profile. Various attributes such as amplitudes, coherency, and local phase velocity as well as frequency and wavenumber of dispersion curves are derived; different sub-sets of these are tested in the CNN training process to assess the best combinations. We use a U-net architecture that is modified to convert the conventional 2D image segmentation problem in the (f,k) domain into direct multi-mode curve fitting and a subsequent picking process. To make the automatic picking algorithm more practical, we (1) introduce a second loss function that combines conventional wavenumber residuals and curve slope residuals; (2) use the transfer learning strategy, in which the network is pre-trained with synthetic data and then with a relatively small portion of the field data, to improve the efficiency of the algorithm; (3) evaluate two categories of uncertainty, the epistemic uncertainty from the method itself and input data, and uncertainty from non-deterministic factors such as random initialization of model weights and random shuffle of samples in training in the CNN, and in GPU parallelism. The epistemic uncertainty is an important indicator of the picking quality and can be used as a weighting of data in subsequent inversion; (4) perform post-processing to determine the effective dispersive frequency range of the picked curves by using different criteria, such as long/short moving average ratios (MAR) of squared picked wavenumbers, posterior uncertainty etc. The effectiveness of the automatic picking process is demonstrated in this study through applications to a field OBN dataset where different modes of Scholte waves were recorded. To reduce cycle skipping in FWI and to increase resolution of the estimated model, my second project develops and illustrates concurrent elastic full-waveform inversion (FWI) of P and S body waves and Rayleigh waves using interleaved envelope- and waveform- based misfit functions, in a gradually-increasing frequency, multi-scale, inversion strategy, to estimated both lateral and horizontal variations of models, which breaks the 1D assumption of conventional DCI. Computing correlation coefficients between the observed and predicted data, and between the inverted and correct models, provides quantitative measures of the composite contributions, of the starting model, the chosen data flow, and the depth extent of the solution space, to the fits of the corresponding solutions. Treating the whole wavefield as a single data set means that it is not necessary to separate, or even to identify, different types of body and surface waves.Show more Item From Multidirectional-Vector-Based Seismic Reverse Time Migration and Angle-Domain Common-Image Gathers to Full Waveform Inversion Using Phase-Modified and Deconvolved Images in Acoustic and Elastic Media(2018-05) Tang, Chen; McMechan, George A.Show more Angle-domain common-image gathers (ADCIGs) are an important product from reverse time migration (RTM). Using the Poynting vector (PV) to calculate propagation angles is efficient but suffers from instability problems. First, the PV can give only a single direction per grid point per time step, and thus it fails to give the multiple directions at wavefield overlaps. Second, the current PV formula is only kinematically correct, which leads to an undefined propagation angle at the magnitude peak of the wavefield. Third, the receiver wavefield reconstructed from the observed data is often not as stable as the source wavefield simulated from the synthetic source. We address the first two issues by proposing a dynamically-correct multidirectional PV (MPV) that decomposes the wavefield into several vector bins in the frequency-wavenumber (ω-k) domain and then uses PV to calculate the propagation directions of each decomposed wavefield in the time-space (t-x) domain. We also provide an improved flow to calculate the ADCIGs by using the source wavefield propagation direction and the reflector normal in the k domain. We propose an improved system for the elastic RTM, which involves three parts. For the P/S wave mode separation, we put forward a scheme to relax the assumption of the (locally) constant shear modulus caused by the Helmholtz theorem. We also give the elastic imaging conditions based on multidirectional vectors, which can give the correct polarities for PP, PS, SP, and SS images without using the reflector normal. For the ADCIG calculation, we give two methods to calculate the multiple propagation directions. For full waveform inversion (FWI), we propose a new scheme that provides a self-contained and physically-intuitive derivation which establishes a natural connection between the amplitude-preserved RTM, the Zoeppritz equations (the amplitude versus [reflection] angle [AVA] inversion) and the reflectivity-to-impedance inversion and combines them into a single framework to produce a preconditioned inversion formula. The formula also works for inverting only the velocity. For impedance inversion, we propose using rock-physics information to separate the impedance into velocity and density for wavefield extrapolation. Because of the complexity of the rock-physics relationship in the real world, we also suggest combining Machine Learning with this scheme for future development.Show more Item Gas hydrate and free gas petroleum system in 3D seismic data, offshore Angola(Society of Exploration Geophysicists, 2012-09-26) Nyamapfumba, Martin; McMechan, George C.; McMechan, George A.Show more Evidence of gas hydrate and free gas occurrences in a 3D seismic volume from the West-Central Coastal Province of the Congo Fan, offshore Angola, illustrates all the components of a complete petroleum system. Analysis and interpretation are based on the information in attributes calculated from three 3D time-migrated common-angle seismic volumes; the attributes include seismic amplitude, spectral components, dip magnitude, amplitude variation with angle, and instantaneous frequency. The source is organic-rich muds associated with late Cretaceous to early Tertiary channels, the migration paths are along growth faults, and the traps are partly defined by the gas hydrate stability zone (for the gas hydrate), partly by the bottom-simulating reflector (for the subhydrate free gas), and partly by faults (for both). The spatial distribution of free gas is further supported by the associated seismic bright spots, and also by the attenuation of high frequencies of P-waves that traverse the gas-saturated zone. Locally higher temperatures, associated with upward fluid circulation along fault zones, facilitate gas transmission through the gas hydrate and forms gas chimneys that extend to the sea floor.Show more 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.Show more 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.Show more 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.Show more 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.Show more Item Reverse Time Migrations in Transversely Isotropic Media: A Comparison between Acoustic and Elastic Wave Equations with Two Wave Mode Separation Algorithms(Society of Exploration Geophysicists) Wang, W.; Hua, B.; McMechan, George A.; Williamson, P.; McMechan, George A.Show more Anisotropic reverse time migrations (RTMs) using pseudoacoustic or elastic wave equations are tested, and the migrated PP images, obtained using the same data set as input, are compared. In anisotropic elastic RTMs, both divergence operators, and localized low-rank approximations (LLA), are tested and compared for P/S separation. Tests with synthetic data indicate that elastic RTMs have better illumination apertures than pseudoacoustic RTMs in subsalt areas because of the involvement of converted S-waves in the former. Pseudoacoustic RTMs have diamond-shaped S-wave artifacts, which do not exist in elastic RTM images, provided that the P- and S-waves are separated in the elastic wavefields. LLAs provide affordable, accurate P/S separations in anisotropic media, and the separation results are better than those obtained using divergence operators. Anisotropic elastic RTMs with LLA give the best quality images. ©2019 Society of Exploration Geophysicists.Show more Item Sensitivity of Estimated Elastic Moduli to Completeness of Wave Type, Measurement Type, and Illumination Apertures at a Receiver in Multicomponent VSP Data(2012-02-01) Rusmanugroho, Herurisa; McMechan, George A.; McMechan, George A.Show more Inversion of phase slowness and polarization vectors measured from multicomponent vertical seismic profile data can yield estimates of all 21 density-normalized elastic moduli for anisotropic elastic media in the neighborhood of each 3C geophone. Synthetic test data are produced by direct evaluation of the Christoffel equation, and by finite-difference solution of the elastodynamic equations. Incompleteness of the data, with respect to illumination (polar and azimuth angle) apertures (qP and/or qS) wave types, wave-propagation directions, and the amount of data (e.g., with or without horizontal slowness components), produces solutions with variations in quality, as revealed by the distribution of model parameter correlations. In a good solution, with all parameters well constrained by the data, the correlation matrix is diagonally dominant. qP-only and qS-only solutions typically produce complementary distributions in their correlation matrices, as they are orthogonal in their sampling of the medium with respect to polarization. The elastic moduli become less independent as the data apertures decrease. If the other input data are relatively complete, the horizontal components of the slowness vector are not needed as the information they contain is redundant. The main consequence of omitting horizontal slowness components is slower convergence. When modest amounts of random noise are added to the slowness and polarization data, in otherwise adequately sampled apertures, the solution is still very close to the correct model, but with larger residual variance. © 2012 Society of Exploration Geophysicists.Show more 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.Show more 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.Show more Item Tomography of Diffraction-Based Focusing Operators(2012-08-24) Santos, Luiz Alberto; Mansur, Webe Joao; McMechan, George A.; McMechan, George A.Show more Diffractions carry the same kinematic information provided by common focus point operators (CFPOs). Thus CFPO and diffraction time trajectories may be used separately, or combined into a single unified tomography for velocity analysis. Velocity estimation by tomography of CFPOs reduces the depth-velocity ambiguity compared to two-way time tomography. CFPO estimation is complicated where there are event discontinuities and diffractions. This problem is overcome by using the kinematic information in diffractions in near-offset common-offset gathers. The procedure is illustrated using synthetic data, and a single-channel field seismic profile from the Blake Ridge (off the east coast of the United States). The results show the effectiveness of the proposed method for estimation of velocity from single channel seismic data, and for refinement of the velocity field from multichannel data. Both applications are cost-competitive.Show more