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Author

George A. McMechan

Other affiliations: United States Geological Survey, University of Victoria, ARCO  ...read more
Bio: George A. McMechan is an academic researcher from University of Texas at Dallas. The author has contributed to research in topics: Seismic migration & Extrapolation. The author has an hindex of 52, co-authored 403 publications receiving 9992 citations. Previous affiliations of George A. McMechan include United States Geological Survey & University of Victoria.


Papers
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Journal ArticleDOI
TL;DR: In this article, a finite-difference solution of the two-dimensional acoustic wave equation is proposed to migrate an observed zero-offset wavefield as the solution of a boundary value problem in which the data are extrapolated backward in time.
Abstract: Migration of an observed zero-offset wavefield can be performed as the solution of a boundary value problem in which the data are extrapolated backward in time. This concept is implemented through a finite-difference solution of the two-dimensional acoustic wave equation. All depths are imaged simultaneously at time 0 (the imaging condition), and all dips (right up to vertical) are correctly migrated. Numerical examples illustrate this technique in both constant and variable velocity media.

756 citations

Journal ArticleDOI
TL;DR: In this article, the dispersion curves for the mode overtones and fundamental are directly observed in the transformed wave field, where the data wave field is linearly transformed from the time-distance domain into the slowness-time intercept (p − τ) domain.
Abstract: The dispersive waves in a common‐shot wave field can be transformed into images of the dispersion curves of each mode in the data. The procedure consists of two linear transformations: a slant stack of the data produces a wave field in the phase slowness‐time intercept (p — τ) plane in which phase velocities are separated. The spectral peak of the one‐dimensional (1-D) Fourier transform of the p — τ wave field then gives the frequency associated with each phase velocity. Thus, the data wave field is linearly transformed from the time‐distance domain into the slowness‐frequency (p — ω) domain, where dispersion curves are imaged. All the data are present throughout the transformations. Dispersion curves for the mode overtones as well as the fundamental are directly observed in the transformed wave field. In the p — ω domain, each mode is separated from the others even when its presence is not visually detectable in the untransformed data. The resolution achieved in the result is indicated in the p — ω wave ...

517 citations

Journal ArticleDOI
TL;DR: In this paper, a 40-channel wide-aperture ground penetrating radar (GPR) data set was recorded in a complicated fluvial/aeolian environment in eastern Canada.
Abstract: A 40-channel wide‐aperture ground penetrating radar (GPR) data set was recorded in a complicated fluvial/aeolian environment in eastern Canada. The data were collected in the multichannel format usually associated with seismic reflection surveys and were input directly into a standard seismic processing sequence (filtering, static corrections, common‐midpoint gathering, velocity analysis, normal‐ and dip‐moveout corrections, stacking and depth migration). The results show significant improvements, over single‐channel recordings, in noise reduction and depth of penetration (by stacking), and in spatial positioning and reduction of diffraction artifacts (by migration). These characteristics increase the potential for reliable interpretation of structural and stratigraphic details. Thus, without having to develop any new software, GPR data processing technology is brought to the same level of capability, flexibility, and accessibility that is current in seismic exploration.

283 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed an excitation-time imaging condition, in which each point is imaged at the one-way traveltime from the source to that point, which is applicable to all source-receiver geometries and variable-velocity media.
Abstract: To apply reverse-time migration to prestack, finite-offset data from variable-velocity media, the standard (time zero) imaging condition must be generalized because each point in the image space has a different image time (or times). This generalization is the excitation-time imaging condition, in which each point is imaged at the one-way traveltime from the source to that point.Reverse-time migration with the excitation-time imaging condition consists of three elements: (1) computation of the imaging condition; (2) extrapolation of the recorder wave field; and (3) application of the imaging condition. Computation of the imaging condition for each point in the image is done by ray tracing from the source point; this is equivalent to extrapolation of the source wave field through the medium. Extrapolation of the recorded wave field is done by an acoustic finite-difference algorithm. Imaging is performed at each step of the finite-difference extrapolation by extracting, from the propagating wave field, the amplitude at each mesh point that is imaged at that time and adding these into the image space at the same spatial locations. The locus of all points imaged at one time step is a wavefront [a constant time (or phase) trajectory]. This prestack migration algorithm is very general. The excitation-time imaging condition is applicable to all source-receiver geometries and variable-velocity media and reduces exactly to the usual time-zero imaging condition when used with zero-offset surface data. The algorithm is illustrated by application to both synthetic and real VSP data. The most interesting and potentially useful result in the processing of the synthetic data is imaging of the horizontal fluid interfaces within a reservoir even when the surrounding reservoir boundaries are not well imaged.

240 citations

Journal ArticleDOI
TL;DR: In this paper, the authors use the coupled elastic wave equation for variable velocity solved with a second-order, explicit finite-difference scheme to extrapolate two-component seismic surface data.
Abstract: Elastic, prestack, reverse-time, finite-difference migration of two-component seismic surface data requires data extrapolation and application of an imaging condition. Data extrapolation involves synchronous driving of the vertical-component and horizontal-component finite-difference meshes with the time reverse of the recorded vertical and horizontal traces, respectively. Extrapolation uses the coupled elastic wave equation for variable velocity solved with a second-order, explicit finite-difference scheme. The imaging condition at any point in the grid is the one-way traveltime from the source to that point.Elastic migrations of both synthetic test data and real two-component common-source gathers produce simpler images than acoustic migrations because of the coalescing of double reflections (compressional waves and shear waves) into single loci.

220 citations


Cited by
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Journal ArticleDOI
TL;DR: This review attempts to illuminate the state of the art of FWI by building accurate starting models with automatic procedures and/or recording low frequencies, and improving computational efficiency by data-compression techniquestomake3DelasticFWIfeasible.
Abstract: Full-waveform inversion FWI is a challenging data-fitting procedure based on full-wavefield modeling to extract quantitative information from seismograms. High-resolution imaging at half the propagated wavelength is expected. Recent advances in high-performance computing and multifold/multicomponent wide-aperture and wide-azimuth acquisitions make 3D acoustic FWI feasible today. Key ingredients of FWI are an efficient forward-modeling engine and a local differential approach, in which the gradient and the Hessian operators are efficiently estimated. Local optimization does not, however, prevent convergence of the misfit function toward local minima because of the limited accuracy of the starting model, the lack of low frequencies, the presence of noise, and the approximate modeling of the wave-physics complexity. Different hierarchical multiscale strategiesaredesignedtomitigatethenonlinearityandill-posedness of FWI by incorporating progressively shorter wavelengths in the parameter space. Synthetic and real-data case studies address reconstructing various parameters, from VP and VS velocities to density, anisotropy, and attenuation. This review attempts to illuminate the state of the art of FWI. Crucial jumps, however, remain necessary to make it as popular as migration techniques. The challenges can be categorized as 1 building accurate starting models with automatic procedures and/or recording low frequencies, 2 defining new minimization criteria to mitigate the sensitivity of FWI to amplitude errors and increasing the robustness of FWI when multiple parameter classes are estimated, and 3 improving computational efficiency by data-compression techniquestomake3DelasticFWIfeasible.

2,981 citations

Journal ArticleDOI
TL;DR: In this article, a three-layer crust consisting of upper, middle, and lower crust is divided into type sections associated with different tectonic provinces, in which P wave velocities increase progressively with depth and there is a large variation in average P wave velocity of the lower crust between different type sections.
Abstract: Geophysical, petrological, and geochemical data provide important clues about the composition of the deep continental crust. On the basis of seismic refraction data, we divide the crust into type sections associated with different tectonic provinces. Each shows a three-layer crust consisting of upper, middle, and lower crust, in which P wave velocities increase progressively with depth. There is large variation in average P wave velocity of the lower crust between different type sections, but in general, lower crustal velocities are high (>6.9 km s−1) and average middle crustal velocities range between 6.3 and 6.7 km s−1. Heat-producing elements decrease with depth in the crust owing to their depletion in felsic rocks caused by granulite facies metamorphism and an increase in the proportion of mafic rocks with depth. Studies of crustal cross sections show that in Archean regions, 50–85% of the heat flowing from the surface of the Earth is generated within the crust. Granulite terrains that experienced isobaric cooling are representative of middle or lower crust and have higher proportions of mafic rocks than do granulite terrains that experienced isothermal decompression. The latter are probably not representative of the deep crust but are merely upper crustal rocks that have been through an orogenic cycle. Granulite xenoliths provide some of the deepest samples of the continental crust and are composed largely of mafic rock types. Ultrasonic velocity measurements for a wide variety of deep crustal rocks provide a link between crustal velocity and lithology. Meta-igneous felsic, intermediate and mafic granulite, and amphibolite facies rocks are distinguishable on the basis of P and S wave velocities, but metamorphosed shales (metapelites) have velocities that overlap the complete velocity range displayed by the meta-igneous lithologies. The high heat production of metapelites, coupled with their generally limited volumetric extent in granulite terrains and xenoliths, suggests they constitute only a small proportion of the lower crust. Using average P wave velocities derived from the crustal type sections, the estimated areal extent of each type of crust, and the average compositions of different types of granulites, we estimate the average lower and middle crust composition. The lower crust is composed of rocks in the granulite facies and is lithologically heterogeneous. Its average composition is mafic, approaching that of a primitive mantle-derived basalt, but it may range to intermediate bulk compositions in some regions. The middle crust is composed of rocks in the amphibolite facies and is intermediate in bulk composition, containing significant K, Th, and U contents. Average continental crust is intermediate in composition and contains a significant proportion of the bulk silicate Earth's incompatible trace element budget (35–55% of Rb, Ba, K, Pb, Th, and U).

2,909 citations

Journal ArticleDOI
TL;DR: In this article, a multichannel shot gather is decomposed into a swept-frequency record, allowing the fast generation of an accurate dispersion curve, which can then be examined and its effects appraised in both frequency and offset space.
Abstract: The frequency-dependent properties of Rayleigh-type surface waves can be utilized for imaging and characterizing the shallow subsurface. Most surface-wave analysis relies on the accurate calculation of phase velocities for the horizontally traveling fundamental-mode Rayleigh wave acquired by stepping out a pair of receivers at intervals based on calculated ground roll wavelengths. Interference by coherent source-generated noise inhibits the reliability of shear-wave velocities determined through inversion of the whole wave field. Among these nonplanar, nonfundamental-mode Rayleigh waves (noise) are body waves, scattered and nonsource-generated surface waves, and higher-mode surface waves. The degree to which each of these types of noise contaminates the dispersion curve and, ultimately, the inverted shear-wave velocity profile is dependent on frequency as well as distance from the source. Multichannel recording permits effective identification and isolation of noise according to distinctive traceto-trace coherency in arrival time and amplitude. An added advantage is the speed and redundancy of the measurement process. Decomposition of a multichannel record into a time variable-frequency format, similar to an uncorrelated Vibroseis record, permits analysis and display of each frequency component in a unique and continuous format. Coherent noise contamination can then be examined and its effects appraised in both frequency and offset space. Separation of frequency components permits real-time maximization of the S/N ratio during acquisition and subsequent processing steps. Linear separation of each ground roll frequency component allows calculation of phase velocities by simply measuring the linear slope of each frequency component. Breaks in coherent surface-wave arrivals, observable on the decomposed record, can be compensated for during acquisition and processing. Multichannel recording permits single-measurement surveying of a broad depth range, high levels of redundancy with a single field configuration, and the ability to adjust the offset, effectively reducing random or nonlinear noise introduced during recording. A multichannel shot gather decomposed into a sweptfrequency record allows the fast generation of an accurate dispersion curve. The accuracy of dispersion curves determined using this method is proven through field comparisons of the inverted shear-wave velocity (vs) profile with a downholevs profile.

2,131 citations

Book
01 Jan 2011
TL;DR: In this article, the authors present basic tools for elasticity and Hooke's law, effective media, granular media, flow and diffusion, and fluid effects on wave propagation for wave propagation.
Abstract: Preface 1. Basic tools 2. Elasticity and Hooke's law 3. Seismic wave propagation 4. Effective media 5. Granular media 6. Fluid effects on wave propagation 7. Empirical relations 8. Flow and diffusion 9. Electrical properties Appendices.

2,007 citations

Journal ArticleDOI
TL;DR: In this article, a method of seismic traveltime inversion for simultaneous determination of 2-D velocity and interface structure is presented that is applicable to any type of body-wave seismic data, as opposed to trial-and-error forward modelling, is that it provides estimates of model parameter resolution, uncertainty and non-uniqueness, and an assurance that the data have been fit according to a specified norm.
Abstract: SUMMARY A method of seismic traveltime inversion for simultaneous determination of 2-D velocity and interface structure is presented that is applicable to any type of body-wave seismic data. The advantage of inversion, as opposed to trial-and-error forward modelling, is that it provides estimates of model parameter resolution, uncertainty and non-uniqueness, and an assurance that the data have been fit according to a specified norm. In addition, the time required to interpret data is significantly reduced. The inversion scheme is iterative and is based on a model parametrization and a method of ray tracing suited to the forward step of an inverse approach. The number and position of velocity and boundary nodes can be adapted to the shot-receiver geometry and subsurface ray coverage, and to the complexity of the near-surface. The model parametrization also allows ancillary amplitude information to be used to constrain model features not adequately resolved by the traveltime data alone. The method of ray tracing uses an efficient numerical solution of the ray tracing equations, an automatic determination of take-off angles, and a simulation of smooth layer boundaries that yields more stable inversion results. The partial derivatives of traveltime with respect to velocity and the depth of boundary nodes are calculated analytically during ray tracing and a damped least-squares technique is used to determine the updated parameter values, both velocities and boundary depths simultaneously. The stopping criteria and optimum number of velocity and boundary nodes are based on the trade-off between RMS traveltime residual and parameter resolution, as well as the ability to trace rays to all observations. Methods for estimating spatial resolution and absolute parameter uncertainty are presented. An example using synthetic data demonstrates the algorithm's accuracy, rapid convergence and sensitivity to realistic noise levels. An inversion of refraction and wide-angle reflection traveltimes from the 1986 IRISPASSCAL Nevada, USA (Basin and Range province) seismic experiment illustrates the methodology and practical considerations necessary for handling real data. A comparison of our final 2-D velocity model with results from studies using other 1-D and 2-D forward and inverse methods serves as a check on the validity of the inversion scheme and provides estimates of parameter uncertainties that account for the bias introduced by the modelling approach and the interpreter.

1,465 citations