Publications

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A Rayleigh wave propagates laterally without dispersion in the vicinity of the plane stress-free surface of a homogeneous and isotropic elastic halfspace. The phase speed is independent of frequency and depends only on the Poisson ratio of the medium. However, after temporal and spatial discretization, a Rayleigh wave simulated by a 3D staggered-grid finite-difference (FD) seismic wave propagation algorithm suffers from frequency- and direction-dependent numerical dispersion. The magnitude of this dispersion depends critically on FD algorithm implementation details. Nevertheless, proper gridding can control numerical dispersion to within an acceptable level, leading to accurate Rayleigh wave simulations. Many investigators have derived dispersion relations appropriate for body wave propagation by various FD algorithms. However, the situation for surface waves is less well-studied. We have devised a numerical search procedure to estimate Rayleigh phase speed and group speed curves for 3D O(2,2) and O(2,4) staggered-grid FD algorithms. In contrast with the continuous time-space situation (where phase speed is obtained by extracting the appropriate root of the Rayleigh cubic), we cannot develop a closed-form mathematical formula governing the phase speed. Rather, we numerically seek the particular phase speed that leads to a solution of the discrete wave propagation equations, while holding medium properties, frequency, horizontal propagation direction, and gridding intervals fixed. Group speed is then obtained by numerically differentiating the phase speed with respect to frequency. The problem is formulated for an explicit stress-free surface positioned at two different levels within the staggered spatial grid. Additionally, an interesting variant involving zero-valued medium properties above the surface is addressed. We refer to the latter as an implicit free surface. Our preliminary conclusion is that an explicit free surface, implemented with O(4) spatial FD operators and positioned at the level of the compressional stress components, leads to superior numerical dispersion performance. Phase speeds measured from fixed-frequency synthetic seismograms agree very well with the numerical predictions.

An efficient numerical algorithm for treating earth models composed of fluid and solid portions is obtained via straightforward modifications to a 3D time-domain finite-difference algorithm for simulating isotropic elastic wave propagation.

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Summary: Dispersion and attenuation relations are derived for both the continuous and discrete velocity-memory-stress systems governing 3D anelastic wave propagation in a standard linear solid. Phase speed and attenuation factor curves extracted from these relations enable optimal selection of spatial and temporal gridding intervals to achieve finite-difference algorithm efficiency, while simultaneously minimizing numerical inaccuracy.

In many parts of the United States, as well as other regions of the world, competing demands for fresh water or water suitable for desalination are outstripping sustainable supplies. In these areas, new water supplies are necessary to sustain economic development and agricultural uses, as well as support expanding populations, particularly in the Southwestern United States. Increasing the supply of water will more than likely come through desalinization of water reservoirs that are not suitable for present use. Surface-deployed seismic and electromagnetic (EM) methods have the potential for addressing these critical issues within large volumes of an aquifer at a lower cost than drilling and sampling. However, for detailed analysis of the water quality, some sampling utilizing boreholes would be required with geophysical methods being employed to extrapolate these sampled results to non-sampled regions of the aquifer. The research in this report addresses using seismic and EM methods in two complimentary ways to aid in the identification of water reservoirs that are suitable for desalinization. The first method uses the seismic data to constrain the earth structure so that detailed EM modeling can estimate the pore water conductivity, and hence the salinity. The second method utilizes the coupling of seismic and EM waves through the seismo-electric (conversion of seismic energy to electrical energy) and the electro-seismic (conversion of electrical energy to seismic energy) to estimate the salinity of the target aquifer. Analytic 1D solutions to coupled pressure and electric wave propagation demonstrate the types of waves one expects when using a seismic or electric source. A 2D seismo-electric/electro-seismic is developed to demonstrate the coupled seismic and EM system. For finite-difference modeling, the seismic and EM wave propagation algorithms are on different spatial and temporal scales. We present a method to solve multiple, finite-difference physics problems that has application beyond the present use. A limited field experiment was conducted to assess the seismo-electric effect. Due to a variety of problems, the observation of the electric field due to a seismic source is not definitive.

Spatially-distributed arrays of seismometers are often utilized to infer the speed and direction of incident seismic waves. Conventionally, individual seismometers of the array measure one or more orthogonal components of rectilinear particle motion (displacement, velocity, or acceleration). The present work demonstrates that measure of both the particle velocity vector and the particle rotation vector at a single point receiver yields sufficient information to discern the type (compressional or shear), speed, and direction of an incident plane seismic wave. Hence, the approach offers the intriguing possibility of dispensing with spatially-extended received arrays, with their many problematic deployment, maintenance, relocation, and post-acquisition data processing issues. This study outlines straightforward mathematical theory underlying the point seismic array concept, and implements a simple cross-correlation scanning algorithm for determining the azimuth of incident seismic waves from measured acceleration and rotation rate data. The algorithm is successfully applied to synthetic seismic data generated by an advanced finite-difference seismic wave propagation modeling algorithm. Application of the same azimuth scanning approach to data acquired at a site near Yucca Mountain, Nevada yields ambiguous, albeit encouraging, results. Practical issues associated with rotational seismometry are recognized as important, but are not addressed in this investigation.

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Stable and accurate numerical modeling of seismic wave propagation in the vicinity of high-contrast interfaces is achieved with straightforward modifications to the conventional, rectangular-staggered-grid, finite-difference (FD) method. Improvements in material parameter averaging and spatial differencing of wavefield variables yield high-quality synthetic seismic data.

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Full-waveform seismic reflection responses of an isolated porous sandstone layer are simulated with three-dimensional (3D) isotropic poroelastic and isotropic elastic finite-difference (FD) numerical algorithms. When the pore-filling fluid is brine water with realistic viscosity, there is about a ∼10% difference in synthetic seismograms observed in an AVO recording geometry. These preliminary results suggest that equivalent elastic medium modeling is adequate for general interpretive purposes, but more refined investigations (such as AVO waveform analysis) should account for poroelastic wave propagation effects. © 2007 Society of Exploration Geophysicists.