ALBERT

Notes: Measurements of seismic anisotropy in fractured rock are used at present to deduce information about the fracture orientation and the spatial distribution of fracture intensity. Analysis of the data is based upon equivalent-medium theories that describe the elastic response of a rock containing cracks or fractures in the long-wavelength limit. Conventional models assume frequency independence and cannot distinguish between microcracks and macrofractures. The latter, however, control the fluid flow in many subsurface reservoirs. Therefore, the fracture size is essential information for reservoir engineers. In this study we apply a new equivalent-medium theory that models frequency-dependent anisotropy and is sensitive to the length scale of fractures. The model considers velocity dispersion and attenuation due to a squirt-flow mechanism at two different scales: the grain scale (microcracks and equant matrix porosity) and formation-scale fractures. The theory is first tested and calibrated against published laboratory data. Then we present the analysis and modelling of frequency-dependent shear-wave splitting in multicomponent VSP data from a tight gas reservoir. We invert for fracture density and fracture size from the frequency dependence of the time delay between split shear waves. The derived fracture length matches independent observations from borehole data.

Notes: The last 10–15 years have produced a considerable amount of research into the geological disposal of radioactive wastes. This has had some very beneficial spin-offs for the geosciences. There are, however, a number of areas where it is difficult for earth scientists to provide quantitative information required for the types of long-term safety assessment being performed at present. With the likely increased stringency with which we may begin to treat other industrial wastes, much is to be learned from the radioactive waste experience. This article reviews some of the geological issues in constraining long-term predictions, discusses how geological data are used, and questions exactly what it is that we are trying to achieve in the management of these wastes and in the regulations concerning their disposal.

Notes: Abstract In 1962, a 2,980-foot deep well was drilled for D. I. Foreman in Middle Castle Creek Valley, Owyhee County, Idaho. This well, which flowed approximately 3,600 gpm, yielded water of 170°F from basalt and silicic volcanic formations; original shut-in pressure was 105 psi. However, leakage began to occur around the casing, and in 1967, a suit was filed on behalf of the Idaho Department of Water Administration to have the well repaired.The Andrew Well Drilling Company, of Idaho Falls, was hired to repair the well, and was on the site in November 1968. Additional casing, packers, and pressure grouting sealed the well adequately. The effect of closure of the foreman well on ground water of the entire area was dramatic. As an example, within 8 hours of closure, water in an observation well 5.7 miles away, rose more than a tenth of a foot. Net increase in this observation well since closure has been 26 feet.

Notes: Three-dimensional numerical modeling is used to characterize ground water flow and contaminant transport at the Shoal nuclear test site in north-central Nevada. The fractured rock aquifer at the site is modeled using an equivalent porous medium approach. Field data are used to characterize the fracture system into classes: large, medium, and no/small fracture zones. Hydraulic conductivities are assigned based on discrete interval measurements. Contaminants from the Shoal test are assumed to all be located within the cavity. Several challenging issues are addressed in this study. Radionuclides are apportioned between surface deposits and volume deposits in nuclear melt glass, based on their volatility and previous observations. Surface-deposited radionuclides are released hydraulically after equilibration of the cavity with the surrounding ground water system, and as a function of ground water flow through the higher-porosity cavity into the low-porosity surrounding aquifer. Processes that are modeled include the release functions, retardation, radioactive decay, prompt injection, and ingrowth of daughter products. Prompt injection of radionuclides away from the cavity is found to increase the arrival of mass at the control plane but is not found to significantly impact calculated concentrations due to increased spreading. Behavior of the other radionuclides is affected by the slow chemical release and retardation behavior. The transport calculations are sensitive to many flow and transport parameters. Most important are the heterogeneity of the flow field and effective porosity. The effect of porosity in radioactive decay is crucial and has not been adequately addressed in the literature. For reactive solutes, retardation and the glass dissolution rate are also critical.

Notes: There are many geological situations where moving ground water transfers a significant amount of heat. Yet, while convective heat transfer is a common phenomenon, it is very difficult to treat analytically. In this paper we present a simple model of convective heat transfer in porous materials and a numerical method of solving the model. The model is then applied to three diverse field situations: (1) a thermal anomaly on the Hartville uplift in eastern Wyoming; (2) a fault-controlled hydrothermal system near Monroe, Utah; and (3) the Luanshya copper mine in the Republic of Zambia. In each case heat transfer by moving ground water is shown to explain the observed thermal anomalies satisfactorily. Our results indicate that in certain situations the effect of ground-water flow needs to be considered in making local and regional assessments of heat-flow data. Furthermore, temperature measurements can be very useful in estimating aquifer recharge, particularly when thermal conductivity and structural information are available.

Notes: Ray tracing through gradients in anisotropic materials is complicated by singularities where the two quasi-shear wave slowness sheets cross or touch. Difficulties associated with such points can be removed by explicitly including polarization in the ray tracing equations. Slowness sheet and wavefront plots show the polarization and velocity behavior of various anisotropy models of aligned cracks in the upper crust. A simple scaling of the elastic tensor with depth can be shown to be approximately correct for models of aligned cracks within an isotropic host matrix with a linear velocity gradient. Ray tracing examples for models of aligned cracks within a strong vertical velocity gradient in the uppermost crust demonstrate various features of azimuthal anisotropy, including amplitude and polarization anomalies and shear-wave splitting. Quasi-shear wave polarizations typically twist along ray paths, with stronger twisting near the symmetry axis in hexagonally symmetric media. Strong anisotropy can cause unusual effects, such as ray paths which have three turning points in laterally homogeneous models.

Notes: Quasi-shear wave polarizations typically twist along ray paths through gradient regions in anisotropic media, causing frequency dependent coupling between the qS-waves. This coupling is much stronger than the analogous coupling between P- and SV-waves in isotropic gradients because of the small difference between the qS-wave velocities. Geometrical ray theory is typically valid for qS-waves only at relatively high frequencies, and does not converge to the isotropic result in the limit of infinitely weak anisotropy. Using the plane-wave layered response, we show examples of this coupling and how it may cause frequency dependent shear-wave polarizations. We consider two special cases where the coupling is especially strong in hexagonally symmetric media: (i) intersection singularities where the slowness sheets cross, and (ii) kiss singularities where the slowness sheets touch at the symmetry axis. We show numerical and asymptotic solutions for the pulses generated in these situations. In some cases, far-field excitation of both quasi-shear waves (and shear-wave splitting) will result from an incident wave composed of only one of the quasi-shear waves.

Notes: Zeroth-order ray theory is frequently used to calculate synthetic seismograms in media which are both anisotropic and inhomogeneous. One of the principal features of such media is that the polarization vectors of the two quasi-shear (qS) waves are determined by the nature of the anisotropy. Thus, a shear wave entering a region of anisotropy will generally be split into two separate polarizations. Ray theory predicts that these two waves will propagate independently, at different velocities, throughout the anisotropic region. Ray theory solutions also show that in inhomogeneous media, the polarization vectors will rotate along the ray. The rotations of these polarization vectors are strongly influenced by the symmetry and orientation of the anisotropy system, but only weakly depend upon the strength of the anisotropy. In contrast, in isotropic media the polarization of S-waves is determined from the initial conditions and only varies slowly due to the ray curvature. The polarization only changes in the ray direction and at any point does not rotate about the ray.In this paper we show that in the limit of infinitely weak anisotropy, solutions calculated using ray theory in anisotropic media conflict with the known results calculated for a similar isotropic medium. We show this fundamental breakdown in ray theory occurs because coupling between the qS waves is ignored in the zeroth approximation. Thus, the isotropic limit is not equivalent to the high-frequency limit of anisotropic ray theory. The coupling is particularly important in weakly anisotropic media, where the qS velocities are similar, but the same effect is still present in media exhibiting stronger anisotropy. This coupling must be taken into account when calculating waveforms.We show that this coupling may be modelled by treating the ‘error’ terms, produced by substituting a zeroth-order ray theory Green's function into the wave equation, as source terms distributed throughout the medium. For weakly anisotropic media where the qS ray paths are similar, this volume integral may be simplified using perturbation and asymptotic methods and evaluated as a simple integral along the ray path. In the isotropic limit this expression correctly describes the polarization of shear waves along the ray. This integral is easy to compute, requiring only quantities already used in ray tracing and traveltime calculations. A prior knowledge of the location, or even the existence of kiss, intersection, point or other singularities along the ray path, is not required for the method to give accurate results. We present some numerical examples for some simple cases previously investigated by less general or more expensive techniques.

Notes: Reciprocal relationships between the plane-wave reflection/transmission coefficients in anisotropic media are derived directly from the transformed wave equations without use of Betti's theorem. If the eigensolutions are normalized correctly, coefficients with the rǒles of the incident and generated waves reversed are equal, provided the sign of slowness parallel to the interface is also reversed.