George A. McMechan

Scalar reverse-time depth migration of prestack elastic seismic data

Reflected P‐to‐P and P‐to‐S converted seismic waves in a two‐component elastic common‐source gather generated with a P‐wave source in a two‐dimensional model can be imaged by two independent scalar reverse‐time depth migrations. The inputs to migration are pure P‐ and S‐waves that are extracted by divergence and curl calculations during (shallow) extrapolation of the elastic data recorded at the earth’s surface. For both P‐to‐P and P‐to‐S converted reflected waves, the imaging time at each point is the P‐wave traveltime from the source to that point. The extracted P‐wave is reverse‐time extrapolated and imaged with a P‐velocity model, using a finite difference solution of the scalar wave equation. The extracted S‐wave is reverse‐time extrapolated and imaged similarly, but with an S‐velocity model. Converted S‐wave data requires a polarity correction prior to migration to ensure constructive interference between data from adjacent sources. Synthetic examples show that the algorithm gives satisfactory resul...

Finite-difference modeling of borehole ground penetrating radar data

Abstract In the fall of 1996, borehole ground penetrating radar (BGPR) data were acquired as part of a comprehensive characterization of a clastic reservoir analog in the Ferron Sandstone in east central Utah. BGPR data were collected in and between three 15-m-deep holes as well as surface profiles that connect each pair of holes. Two-dimensional finite-difference modeling of the data provides estimates of the distributions of velocity and attenuation, and the geometry of the reflectors. Depth control on the interfaces in the model is provided by the core logs from the three holes. Average estimated relative dielectric permittivity generally increases with depth from ∼4 to ∼17 in the sandy units, and is larger (as high as ∼30) in the clays. The corresponding estimated electrical conductivities are from 10 −8 S/m for the most sandy layers to 10 −2 S/m for the most clay-rich layers. Comparing the velocities for vertical and horizontal electric field propagations shows a 20–25% anisotropy in the upper 6–7xa0m; vertical propagation (with horizontal polarization) is faster than horizontal propagation (with vertical polarization). This anisotropy is interpreted as being caused by the pervasive vertically oriented conjugate fractures that are visible at the site. At greater depths, the anisotropy is not seen, which we interpret as smaller fracture widths below the depths affected by surface weathering.

Imaging of earthquake sources

Elastic waves, produced by temporally and spatially finite fault ruptures during earthquakes, propagate through the Earth. Recordings of these waves at the Earths surface provide the data for reconstruction of the source properties, including location, spatial and temporal extents, and rupture velocities. A 2D finite‐difference solution of the elastic wave equation is used to numerically extrapolate synthetic observations backward in time to create images of the energy release during an earthquake.

Nonlinear reverse‐time inversion of elastic offset vertical seismic profile data

An iterative nonlinear inversion algorithm for two‐dimensional elastic media gives estimates of P-velocity and S-velocity distributions from synthetic offset vertical seismic profiles. The algorithm is a hybrid of inversion and principles borrowed from reverse‐time migration. Gradients of the misfit function are dynamically determined by crosscorrelations of the computed incident wave fields with the scattered compressional and shear wave fields. Model perturbations are defined in the steepest descent direction. In order to optimize the sensitivity of the inversion to both compressional and shear velocity distributions, two data collection experiments are required, one with a compressional wave source and the other with a shear wave source. Inversion iterations alternate between the compressional and shear source data sets. In test examples, the new algorithm converges successfully to the correct solution when the starting model’s compressional and shear velocities deviated by as much as 20 percent from t...

3D modeling of fracture-induced shear-wave splitting in the southern California basin

Splitting of shear waves, generated by local earthquakes in the Southern California basin, and their polarization changes during propagation through layers with different orientations of anisotropy, are investigated from multicomponent seismograms and their hodograms. Synthetic data for earthquakes in the Southern California basin illustrate the effects on polarization caused by dry vertical microcracks with a crack density of ∼0.04 at the source and receiver locations. Hodograms for observed and synthetic data show that the polarization at the receiver depends only on the orientation of the anisotropy within two wavelengths of the receiver, which qualitatively explains the frequency dependence of anisotropy in previous studies.nnSeismograms are simulated for a model with a range of station azimuths and distances. If the anisotropy-producing crack orientations do not change between the source and a receiver, and the source motion is parallel to the cracks, there is no shear-wave splitting. Splitting occurs when the anisotropy orientation at the receiver (or between the source and receiver) is different from the source orientation.

Phase variation with angle inversion using plane and spherical waves

Seismic reflection data from nearto 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.

Petro‐seismic inversion for sandstone properties

We use empirical relations derived from laboratory and log data for sandstones to estimate unknown parameters from given parameters. The known and unknown parameters may be any of the following: compressional and shear wave velocities (Vp and Vs), density (ρ), compressional and shear wave quality factors (Qp and Qs), effective pressure (P), frequency (f), water saturation (S), porosity (φ), clay content (C), fluid permeability (k), and Vp/Vs and Qs/Qp ratios. The goal is to obtain estimates of all thirteen of these petro‐seismic variables from subsets of these as input; whether this is achievable depends on the particular combination of input variables.The inversion typically proceeds through a hierarchy of three levels of parameter estimation, in order of the expected reliability of the estimates. First, we solve for the parameters that can be obtained directly from the fitted empirical equations. Then, a grid search is performed to simultanously fit more than one unknown parameter by finding values that...

Inversion and interpretation of a 3D seismic data set from the Ouachita Mountains, Oklahoma

Acoustic impedance inversion (AI) and simultaneous angle-dependent inversion (SADI) of a 3D seismic data set characterize reservoirs of Mississippian Morrowan age in the triangle zone of the frontal Ouachita Mountains, Oklahoma. Acoustic impedance of the near-angle seismic data images the 3D spatial distributions of Wapanucka limestone and Cromwell sandstone. Lame parameters×density ( λρ and μρ ) and λ∕μ sections are derived from the P-wave and S-wave impedance ( IP and IS ) sections produced by the SADI. Lithology is identified from the gamma logs and μρ . The VP ∕ VS , λρ , and λ∕μ are interpreted in terms of a hydrocarbon distribution pattern. The IP is used to identify high IP regions that are consistent with high sand/shale ratio. The estimated impedances and derived Lame parameter sections are consistent with the interpretation that parts of the Wapanucka limestone and Cromwell sandstone contain potential gas reservoirs in fault-bounded compartments. The Cromwell sandstone contains the main inferred...

Simulation and Imaging of GPR Data Scattered by Reinforcing Bars in a Concrete Bridge Deck

Ground Penetrating Radar (GPR) is a non‐destructive method that can be used to locate reinforcing bars in concrete structures such as bridge decks. Provided that the frequency used is sufficiently high, and the antenna radiation pattern adequately illuminates the features of interest, reliable images can be obtained. Both 2‐D and 3‐D GPR data were collected over a bridge deck before and after resurfacing with a layer of reinforced concrete. Numerical simulation of the 2‐D data shows the best results that can be expected. Migration of both the 2‐D and 3‐D data enhances and focuses image details by collapsing diffractions, and moving reflectors to their correct spatial positions.Migrated images provide a realistic picture for interpretation. Comparing the images with photographs and blueprints shows good correspondence; some minor deviations (e.g., in spacing of reinforcing bars) of the actual configuration as produced by the contractors, from the specifications, are detected.

Wavenumber Correction For the Recording Group Effects In the Seismic Data

Numerically defined filters deconvolve the recording group response from the data as a function of wavenumber, to correct for the effect of the recording group. The correction for the recording group effect is feasible for uniform and variable group response with variable length. The results imply the necessity of wavenumber (not offset) dependent correction for amplitude preserved processing.