No abstract

Laboratory measured seismic velocities of various rocks as a function of pressure and saturation are inverted to obtain their spectra of pore shapes. The inversion is based on the theory of closing of the pores as a function of pressure and the velocity changes that result. The rocks are modeled in terms of a matrix and spheroidal pores of different aspect ratios. To obtain the volume concentration of pores of each aspect ratio, two inversion schemes were formulated and examined. The linearized iterative inversion scheme gave a better result. The inversion was applied to both high‐porosity sedimentary rocks and low‐porosity igneous rocks. It worked well for all the rocks considered. The method has the power to resolve different aspect‐ratio cracks. It is predictive, i.e., using the pore aspect ratio spectrum from the inversion of velocity of a rock under one saturation condition, the velocities under a different saturation condition can be predicted via the direct problem. There are significant differences between the pore aspect ratio spectra of different rock types. For the Westerly granite, the pore aspect ratio spectrum obtained from velocity data is comparable to direct SEM observations.

The propagation and dispersion characteristics of guided waves in a fluid‐filled borehole are studied using dispersion curves and modeling full‐wave acoustic logs by synthetic microseismograms. The dispersion characteristics of the pseudo‐Rayleigh (reflected) and Stoneley waves in a borehole with and without a tool in the center are compared. Effects of different tool properties are calculated. The effect of a rigid tool is to make the effective borehole radius smaller. As an approximation, dispersion characteristics of the guided waves in a borehole with a tool can be calculated as a purely fluid‐filled borehole with a smaller effective radius. Theoretical waveforms (microseismograms) of elastic waves propagating in a borehole are calculated using a discrete wavenumber integration. With an appropriate choice of parameters, our results look similar to the acoustic waveforms recorded in a limestone and a shale formation. Several factors affect the shape of an acoustic log microseismogram. The effective radius of the borehole determines the relative amplitudes of the modes generated. Poisson’s ratio of the formation is the primary factor determining the relative amplitude of the leaky mode following the compressional arrival. Attenuation affects the duration and decay rate of the guided waves.

Results are presented from experiments carried out in conjunction with the U. S. Geological Survey at the Hubbard Brook Experimental Forest near Mirror Lake, New Hampshire. The study focuses on our ability to obtain orientation and transmissivity estimates of naturally occurring fractures. The collected data set includes a four‐offset hydrophone vertical seismic profile, full waveform acoustic logs at 5, 15, and 34 kHz, borehole televiewer, temperature, resistivity, and self‐potential logs, and borehole‐to‐borehole pump test data. Borehole televiewer and other geophysical logs indicate that permeable fractures intersect the Mirror Lake boreholes at numerous depths, but less than half of these fractures appear to have significant permeability beyond the annulus of drilling disturbance on the basis of acoustic waveform log analysis. The vertical seismic profiling (VSP) data indicate a single major permeable fracture near a depth of 44 m, corresponding to one of the most permeable fractures identified in the acoustic waveform log analysis. VSP data also indicate a somewhat less permeable fracture at 220 m and possible fractures at depths of 103 and 135 m; all correspond to major permeable fractures in the acoustic waveform data set. Pump test data confirm the presence of a hydraulic connection between the Mirror Lake boreholes through a shallow dipping zone of permeability at 44 m in depth. Effective fracture apertures calculated from modeled transmissivities correspond to those estimated for the largest fractures indicated on acoustic waveform logs but are over an order of magnitude larger than effective apertures calculated from tube waves in the VSP data set. This discrepancy is attributed to the effect of fracture stiffness. A new model is presented to account for the mechanical strength of asperities in resisting fracture closure during the passage of seismic waves during the generation of VSPs.

Methods for the determination of in situ P and S wave attenuation from full waveform acoustic logs are developed. For P waves, the peak amplitude ratios of the refracted P waves from two different receivers can be used with geometrical spreading taken into account. For S waves, owing to the contamination by the guided waves, its attenuation cannot be determined directly. Instead, S wave attenuation is determined from the attenuation of the guided waves using the partition coefficients (normalized partial derivatives of the phase velocity with respect to the body wave velocities). Analytical forms of these partition coefficients are presented here, along with examples for a number of different rock formations (granite, limestone, sandstone and soft sediments). The results show that in high velocity rocks, the fluid attenuation controls the guided wave attenuation except near the cutoff frequency of the pseudo‐Rayleigh wave. For low velocity rock formations, especially in the case where the S wave velocity is lower than the fluid velocity, the S wave attenuation is the main contributor to the guided wave attenuation. Synthetic microseigmogram calculated with the measured body wave attenuation agrees well with the actual microseismograms.

A general expression is derived for the dispersion relations and the impulse response of a radially layered borehole. The model geometry consists of a central fluid cylinder surrounded by an arbitrary number of solid annuli. A Thomson-Haskell type propagator matrix is used to relate stresses and displacements across the layers. Although the model is completely general, the geometries considered here are restricted to those of a cased bole. Layers of steel, cement, and formation surround the innermost fluid layer. Synthetic microseismograms containing all body and interface waves are calculated for a variety of model parameters.Formation body wave arrivals are relatively unaffected by the presence of a casing. They may, however, be hard to identify if cement velocities are close to or larger than those of the formation. The Stoneley and pseudoRayleigh wave arrivals are strongly influenced by the casing parameters. They respond to the combined effects of the steel, the cement, and the formation.

In Vertical Seismic Profiling surveys tube waves are generated by compressional waves impinging on subsurface fractures or permeable zones. The problem of generation of these waves by a non-normal incident P wave for an inclined borehole intersecting a tilted parallel wall fracture is formulated theoretically. The amplitude of tube waves depends on the permeability. the length of the fracture, and on the frequency. The relative effects of these parameters are studied individually. The problem is also formulated for a thin oblate ellipsoidal (penny-shaped) fracture. The results for the two fracture models are compared and contrasted.Field data from Tyngsboro, Massachusetts are shown for open fractures in granite. From tube wave amplitudes normalized to P wave amplitudes, calculated permeabilities are on the order of one hundred millidarcys.

The distribution of fracture permeability in granitic rocks was investigated by measuring the distribution of vertical flow in boreholes during periods of steady pumping. Pumping tests were conducted at two sites chosen to provide examples of moderately fractured rocks near Mirror Lake, New Hampshire and intensely fractured rocks near Oracle, Arizona. A sensitive heat‐pulse flowmeter was used for accurate measurements of vertical flow as low as 0.2 liter per minute. Although boreholes were spaced at intervals ranging from 10 to 50 meters, acoustic televiewer logs showed little direct continuity of individual fractures from borehole to borehole in either the moderately fractured rocks or intensely fractured rocks. Results indicated that nearly all inflow and outflow to boreholes occurred by means of one or two discrete fractures in both cases. These fractures did not appear very different from other prominent fractures indicated on televiewer and resistivity logs for these boreholes. Hydraulic connections between boreholes apparently were composed of conduits formed by the most permeable portions of intersecting fractures. Most flow in the moderately fractured rocks occurred at isolated fractures at a depth of about 45 meters indicating a nearly horizontal zone of fracture permeability composed of orthogonal, steeply dipping fractures. Previous studies have identified a zone of horizontal permeability in the lower part of the boreholes in the intensely fractured rocks, but flowmeter tests indicated that flow also entered and exited individual boreholes by means of one or two steeply dipping fractures. These results indicate zones of fracture permeability in crystalline rocks are composed of irregular conduits that cannot be approximated by planar fractures of uniform aperture, and that the orientation of permeability zones may be unrelated to the orientation of individual fractures within those zones.