Calculation Of Conical (Mach) Wave Displacement Fields Radiated By Borehole Sources In Slow Formations And Inhomogeneous Media

Stationary phase solutions for the radiation patterns of borehole sources are commonly used to study the far-field seismic wavefields produced in crosshole or reverse VSP experiments, but they break down when the formation shear wave velocity is less than the tube wave velocity in the source borehole. This is because the tube wave, not the primary source, radiates the dominant shear wave signal in the form of large amplitude conical waves, which are also called Mach waves. I model this effect by considering the tube wave to be a moving secondary point source generated by the primary source of acoustic energy. A discretization of the source well allows a numerical solution of the integral equation which yields the displacement field by a general source distributed in space and time. The time at which each point source in the discretization emits energy is determined by the group velocity of the tube wave, while the radiation of the individual sources is characterized by the stress field induced by the tube wave at the borehole wall. An integration along the borehole of these point sources then yields the observed Mach wave arrivals. Since this method involves the summation of shear wave ray arrivals from the many point sources along the borehole, the method is called the Ray Summation Method (RSM). Comparison of RSM results with full waveform synthetic seismograms computed with the discrete wavenumber method confirms the accuracy of this method. Unlike the discrete wavenumber method, however, the use of ray tracing in the RSM allows computation of the Mach wave arrivals for inhomogeneous layered media as well as homogeneous models, including the waves generated by reflections of the Mach waves at interfaces and from the reflections of the tube wave itself. The interactions of the conical waves with interfaces can show unusual patterns of arrivals which would not be predicted from ordinary point source behavior.Elf-Aquitaine (Company)Massachusetts Institute of Technology. Earth Resources Laboratory (Founding Member Postdoctoral Fellowship

Reservoir Delineation Research

This report describes work performed by the Reservoir Delineation Consortium during the past year. We have made progress in the areas of theoretical analysis of wave propagation, data analysis, and significant field work at the Michigan test site. Research on wave propagation focused on developing new algorithms for rapid and flexible calculation of full waveform synthetic seismograms. These methods provide the modeling tools for surface seismic, crosshole, single hole experiments and data interpretation. Initial progress on a finite volume method is summarized, and simulations using parabolic equations, attenuation modeling, and elastic wave simulations with multiple multipole methods are also examined in this report. New work in the area of data processing and analysis is represented by hydraulic fracturing imaging via source location methods and nonlinear refraction imaging. The past year (1995) has been one of the most active in our entire experience with the Michigan test site, and a summary report documents the crosshole survey, single well imaging experiments and dipole logging performed recently. This introduction to the report describes first the wave propagation research, including a summary statement providing our motivations for continued research in this area. Briefly, while there are many algorithms currently available for modeling tasks, each of them has its own limitations and advantages in regard to both accuracy and speed. Given a strong incentive for accurate and efficient inversion or migration algorithms, there is a continuing need for improving the modeling routines that serve as the basis for data analysis. Following this motivation is a brief summary of each of the reports mentioned above. The overview concludes with a summary of the field work results and the two papers on data processing tasks

Viscous Attenuation Of Acoustic Waves In Suspensions

A model for attenuation of acoustic waves in suspensions is proposed which includes an energy loss due to viscous fluid flow around spherical particles. The expression for the complex wavenumber is developed by considering the partial pressures acting on the solid and fluid phases of the suspension. This is shown to be equivalent to the results of the Biot theory for porous media in the limiting case where the frame moduli vanish. Unlike earlier applications of the limiting case Biot theory, however, a value for the attenuation coefficient is developed from the Stokes flow drag force on a sphere instead of attempting to apply a permeability value to a suspension. If the fluid and solid particle velocities have harmonic time dependence with angular frequency w, the attenuation in this model is proportional to w2 at low frequencies and approaches a constant value at high frequencies. The predicted attenuation is very sensitive to the radius and density of the spherical particles. Accurate modeling of observed phase velocities from suspensions of spherical polystyrene particles in water and oil and successful inversion for kaolinite properties using attenuation and velocity data from kaolinite suspensions at 100 kHz show that this viscous dissipation model is a good representation of the effects controlling the propagation of acoustic waves in these suspensions. Attenuation predictions are also compared to amplitude ratio data from an oil-polystyrene suspension. The viscous effects are shown to be significant for only a limited range of solid concentration and frequency by the reduced accuracy of the model for attenuation in a kaolinite suspension at 1 MHz.Massachusetts Institute of Technology. Full Waveform Acoustic Logging ConsortiumNational Science Foundation (U.S.). Graduate Research Fellowship Progra

Permeability Estimation From Velocity Anisotropy In Fractured Rock

Cracks in a rock mass subjected to a uniaxial stress will be preferentially closed depending on the angle between the fracture normal vectors and the direction of the applied stress. If the prestress fracture orientation distribution is isotropic, the effective elastic properties of such a material after application of the stress are then transversely isotropic due to the overall alignment of the cracks still open. Velocity measurements in multiple directions are used to invert for the probability density function describing orientations of crack normals in such a rock. This is accomplished by expanding the crack orientation distribution function into generalized spherical harmonics. The coefficients in this expansion are functions of the crack density and the crack aspect ratio distribution. The information on fracture distribution obtained from the velocity inversion allows an estimation of the anisotropic permeability of the fractured rock system. Permeability estimates are based on the number of cracks open of each aspect ratio, and the contribution of a given crack is weighted by the cosine of the angle between the crack and the direction of the applied pressure gradient. This approach yields a prediction of permeability as a function of the angle from the uniaxial stress axis. The inversion for crack orientation is applied to ultrasonic velocity measurements on Barre granite, and permeability predictions for this sample are presented. The inversion results are good and reproduce velocity measurements well, and the permeability predictions show some of the expected trends. Initial comparisons of the predictions with available permeability data, however, show deviations suggesting that further information on partial crack closure and connectivity of cracks should be included in the permeability model.Massachusetts Institute of Technology. Full Waveform Acoustic Logging ConsortiumUnited States. Dept. of Energy (Grant DE-FG02-86ER13636)National Science Foundation (U.S.). Graduate Research Fellowship Progra

Detection Of Fracture Orientation Using Azimuthal Variation Of P-Wave Avo Responses

Azimuthally-dependent P-wave AVO (amplitude variation with offset) responses can be related to open fracture orientation and have been suggested as a geophysical tool to identify fracture orientation in fractured oil and gas reservoirs. A field experiment recently conducted over a fractured reservoir in the Barinas Basin (Venezuela) provides data for an excellent test of this approach. Three lines of data were collected in three different azimuths, and three component receivers were used. The distribution of fractures in this reservoir was previously obtained using measurements of shear wave splitting from P-S converted waves from the same dataset (Ata and Michelena, 1995). In this work, we use P-wave data to see if the data can yield the same information using azimuthal variation of P-wave AVO responses. Results obtained from the azimuthal P-wave AVO analysis corroborate the results previously obtained using P-S converted waves. This analysis with field data is an example of the high potential of P-waves to detect fracture effects on seismic wave propagation.Massachusetts Institute of Technology. Earth Resources Laboratory. Reservoir Delineation Consortiu

Permeability Estimation From Velocity Anisotropy In Fractured Rock

Cracks in a rock mass subjected to a uniaxial stress will be preferentially closed depending on the angle between the fracture normal and the direction of the applied stress. If the prestress fracture distribution is isotropic, the effective elastic properties of such a material are then transversely isotropic due to the preferred alignment of the cracks. Velocity measurements in multiple directions are used to invert for the probability density function describing orientations of crack normals in such a rock. We suggest a means of using the results on fracture distribution from the velocity inversion to estimate the anisotropic permeability of the fracture system. This approach yields a prediction of permeability as a function of the angle from the uniaxial stress direction.Massachusetts Institute of Technology. Full Waveform Acoustic Logging ConsortiumUnited States. Dept. of Energy (Grant DE-FG02-86ERI3636)National Science Foundation (U.S.). Graduate Research Fellowship Progra

Seismic Delineation Of A Geothermal Reservoir

Surface seismic reflection surveys and VSP's have been extensively carried out in the Monteverdi area, within the Larderello region. Calibration of these seismic observations with data from numerous deep wells allowed the interpretation of the 2-D traverses so that a good geologic-structural reconstruction for the whole area was achieved. Many important reflectors were detected inside the Metamorphic basement by VSP's acquired in several wells in the area. These reflections were attributed to changes in petrophysical characteristics of the medium, particularly changes in fracture density, rather than to contrasts in lithology. Since at this time the main goal of the exploration in the Larderello region is the location of producing layers inside the basement, a major effort was applied to acquiring and modeling numerous VSP's in existing wells. In particular, a multioffset VSP was carried out in the COLLA 2 well with the specific goal of detecting fractured horizons within the reservoir of the Monte:verdi area. Because of the three-dimensionality of the seismic wave propagation in such a complicated geological structure, the standard onedimensional VSP modeling is not reliable. Therefore, 2-D and 3-D methods of modeling were applied. The modeling of the VSP data predicts important reflections at the depths corresponding to the main fractured zones intersected by drilling. These fractured zones should show subhorizontal distribution and thickness of tens of meters

Detection of Abiotic Methane in Terrestrial Continental Hydrothermal Systems: Implications for Methane on Mars

The recent detection of methane in the Martian atmosphere and the possibility that its origin could be attributed to biological activity, have highlighted the importance of understanding the mechanisms of methane formation and its usefulness as a biomarker. Much debate has centered on the source of the methane in hydrothermal fluids, whether it is formed biologically by microorganisms, diagenetically through the decomposition of sedimentary organic matter, or inorganically via reduction of CO2 at high temperatures. Ongoing research has now shown that much of the methane present in sea-floor hydrothermal systems is probably formed through inorganic CO2 reduction processes at very high temperatures (greater than 400 C). Experimental results have indicated that methane might form inorganically at temperatures lower still, however these results remain controversial. Currently, methane in continental hydrothermal systems is thought to be formed mainly through the breakdown of sedimentary organic matter and carbon isotope equilibrium between CO2 and CH4 is thought to be rarely present if at all. Based on isotopic measurements of CO2 and CH4 in two continental hydrothermal systems, we suggest that carbon isotope equilibration exists at temperatures as low as 155 C. This would indicate that methane is forming through abiotic CO2 reduction at lower temperatures than previously thought and could bolster arguments for an abiotic origin of the methane detected in the martian atmosphere

The pd <--> pi+ t reaction around the Delta resonance

The pd pi+ t process has been calculated in the energy region around the Delta-resonance with elementary production/absorption mechanisms involving one and two nucleons. The isobar degrees of freedom have been explicitly included in the two-nucleon mechanism via pi-- and rho-exchange diagrams. No free parameters have been employed in the analysis since all the parameters have been fixed in previous studies on the simpler pp pi+ d process. The treatment of the few-nucleon dynamics entailed a Faddeev-based calculation of the reaction, with continuum calculations for the initial p-d state and accurate solutions of the three-nucleon bound-state equation. The integral cross-section was found to be quite sensitive to the NN interaction employed while the angular dependence showed less sensitivity. Approximately a 4% effect was found for the one-body mechanism, for the three-nucleon dynamics in the p-d channel, and for the inclusion of a large, possibly converged, number of three-body partial states, indicating that these different aspects are of comparable importance in the calculation of the spin-averaged observables.Comment: 40 Pages, RevTex, plus 5 PostScript figure