Christopher L. Liner

Application of GPR to a site investigation involving shallow faults

A series of ground‐penetrating radar (GPR) lines were acquired on a proposed multistory building site in Fayetteville, Arkansas, because engineering work implied the existence of a shallow fault. Building a heavy structure in the vicinity of this fault would involve risk due to differential settlement, solution cavities, and fault reactivation. In this case, the new radar surveys, combined with pre‐existing borehole data and regional geological knowledge, verified and mapped the fault.

Least-squares DMO and migration

Conventional processing, such as Kirchhoff dip moveout (DMO) and prestack full migration, are based on independent imaging of subsets of the data before stacking or amplitude variation with offset (AVO) analysis. Least‐squares DMO (LSDMO) and least‐squares migration (LSMig) are a family of developing processing methods which are based on inversion of reverse DMO and demigration operators. LSDMO and LSMig find the earth model that best fits the data and a priori assumptions which can be imposed as constraints. Such inversions are more computer intensive, but have significant advantages compared to conventional processing when applied to irregularly sampled data. Various conventional processes are approximations of the inversions in LSDMO and LSMig. Often, processing is equivalent to using the transpose of a matrix which LSDMO/LSMig inverts. Such transpose processing is accurate when the data sampling is adequate. In practice, costly survey design, real‐time coverage quality control, in‐fill acquisition, re...

General theory and comparative anatomy of dip moveout

It is possible to derive a general formula for constant‐velocity, two‐dimensional dip moveout (DMO). This serves to unify the many published forms of DMO. Known results for common‐offset and shot profile DMO are special cases of the general formula. The analysis is based on the dip‐corrected NMO equation, and thus is a kinematic DMO theory. Using a logarithmic stretch of the time axis, efficient fast Fourier transform (FFT) common‐offset DMO algorithms can be derived. In the published versions, log variables are introduced into the NMO equation. It can be shown that the resulting impulse response departs from the DMO ellipse, which means that some dips have been improperly handled. A new log‐stretch formulation (exact log DMO) which preserves the DMO ellipse can be derived by starting with the analytic impulse response, rather than the NMO equation. Tests on field data indicate that exact log DMO handles shallow, steeply dipping events in agreement with Hale’s DMO, while the other log‐stretch algorithms d...

Ground-penetrating radar; a near-face experience from Washington County, Arkansas

Digital ground‐penetrating radar (GPR) is an emerging technology for detecting, locating, and/or mapping features in the shallow subsurface. It has application to geology, civil engineering, environmental science/engineering, soil science, and many other fields. This case history describes a high‐quality GPR survey performed in very close proximity to a vertical limestone rock face at a roadcut site in northwest Arkansas. The configuration allowed interpretation of the GPR results with the maximum of amount of geologic control: the rock face itself. Our experience suggests that GPR has significant potential as a high resolution tool for mapping shallow structure and stratigraphy in carbonate rocks.

Hybrid Fourier finite-difference 3D depth migration for anisotropic media

When a subsurface is anisotropic, migration based on the assumption of isotropy will not produce accurate migration images. We develop a hybrid wave-equation migration algorithm for vertical transversely isotropic (VTI) media based on a one-way acoustic wave equation, using a combination of Fourier finite-difference (FFD) and finite-difference (FD) approaches. The hybrid method can suppress an additional solution that exists in the VTI acoustic wave equation, and it offers speed and other advantages over conventional FFD or FD methods alone. The algorithm is tested on a synthetic model involving log data from onshore eastern Saudi Arabia, including estimates of both intrinsic and layer-induced VTI parameters. Results indicate that VTI imaging in this region offers some improvement over isotropic imaging, primarily with respect to subtle structure and stratigraphy and to image continuity. These benefits probably will be overshadowed by perennial land seismic data issues such as near-surface distortions and multiples.

3-D seismic survey design as an optimization problem

There are many trade‐offs in the design of a land 3-D seismic survey. The aim is to achieve certain goals subject to physical and economic constraints. Concentrating on the physical aspects, this can be set up as an optimization problem to find the “best” set of acquisition parameters to meet the desired goals.

Wavelet-based detection of singularities in acoustic impedances from surface seismic reflection data

Although the passage of singularity information from acoustic impedance to seismic traces is now well understood, it remains unanswered how routine seismic processing, mode conversions, and multiple reflections can affect the singularity analysis of surface seismic data. We make theoretical investigations on the transition of singularity behaviors from acoustic impedances to surface seismic data. We also perform numerical, wavelet-based singularity analysis on an elastic synthetic data set that is processed through routine seismic processing steps (such as stacking and migration) and that contains mode conversions, multiple reflections, and other wave-equation effects. Theoretically, seismic traces can be approximated as proportional to a smoothed version of the (N+1) th derivative of acoustic impedance,where N is the vanishing moment of the seismic wavelet. This theoretical approach forms the basis of linking singularity exponents (Holder exponents) in acoustic impedance with those computable from seismi...

Born theory of wave‐equation dip moveout

Wave‐equation dip moveout (DMO) addresses the DMO amplitude problem of finding an algorithm which faithfully preserves angular reflectivity while processing data to zero offset. Only three fundamentally different theoretical approaches to the DMO amplitude problem have been proposed: (1) mathematical decomposition of a prestack migration operator; (2) intuitively accounting for specific amplitude factors; and (3) cascading operators for prestack migration (or inversion) and zero‐offset forward modeling. Pursuing the cascaded operator method, wave‐equation DMO for shot profiles has been developed. In this approach, a prestack common‐shot inversion operator is combined with a zero‐offset modeling operator. Both integral operators are theoretically based on the Born asymptotic solution to the point‐source, scalar wave equation. This total process, termed Born DMO, simultaneously accomplishes geometric spreading corrections, NMO, and DMO in an amplitude‐preserving manner. The theory is for constant velocity a...

Elements of Seismic Dispersion: A Somewhat Practical Guide to Frequency-Dependent Phenomena

Elements of Seismic Dispersion: A Somewhat Practical Guide to Frequency-dependent Phenomena (SEG Distinguished Instructor Series No. 15) covers selected effects encountered in the acquisition, processing, and interpretation of reflectionseismic data. The material, based on the 2012 SEG Distinguished Instructor Short Course, shows how those phenomena arise, how they can be characterized, and the important information they contain. The text shows how spectral decomposition and time-frequency methods have led to improved understanding and use of nonlinear harmonics, near-surface guided waves, layer-induced anisotropy, velocity dispersion and attenuation, interference, and Biot reflection. Accessible discussion is augmented by examples, figures, and references to primary literature for further study. This book will interest technical managers and those who work in acquisition, processing, and interpretation of seismic data. (DISC on DVD, 761A, is also available.)

Layer-induced seismic anisotropy from full-wave sonic logs : Theory, application, and validation

Thin isotropic elastic layering in the earth is one cause of seismic VTI anisotropy, along with intrinsic anisotropy and fractures. An important issue related to the routine use of VTI seismic data processing is the estimation of the necessary parameters. The full set of layer-induced VTI anisotropy parameters can be computed from full-wave sonic and density log data using Backus averaging. Intrinsic anisotropy can be incorporated if it is known from laboratory analysis. The isotropic layering method is applied to six wells in eastern Saudi Arabia, and the estimated anisotropy parameters are persistent across distances of many kilometers. This leads to the possibility of parameter estimation at sparse well locations for use in seismic data processing. Validation is demonstrated by direct numerical simulation of elastic wavefields in original and Backus-averaged earth models with various window lengths. We observe precise equivalence of the full wavefield when the averaging length is less than or equal to one-third of the minimum dominant wavelength. First arrival information, used in depth migration, is preserved with much longer averaging windows, up to twice the minimum dominant wavelength.