Herbert F. Wang

Ultrasonic velocities in Cretaceous shales from the Williston basin

Compressional and shear‐wave velocities were measured in the laboratory from 1 bar to 4 kbar confining pressure for wet, undrained samples of Cretaceous shales from depths of 3200 and 5000 ft in the Williston basin, North Dakota. These shales behave as transversely isotropic elastic media, the plane of circular symmetry coinciding with the bedding plane. For compressional waves, the velocity is higher for propagation in the bedding plane than at right angles to it, and the anisotropy is greater for the 5000-ft shale. For shear waves, the SH‐wave perpendicular to bedding and the SV‐wave parallel to bedding propagate with the same speed, which is about 25 percent lower than that for the SH‐wave parallel to bedding. In general, compressional and shear velocities are higher for the indurated 5000-ft shale than for the friable 3200-ft shale. All velocities increase with in‐increasing confining pressure to 4 kbar. The 3200-ft shale exhibits velocity hysteresis as a function of pressure, whereas this effect is a...

The elastic coefficients of double‐porosity models for fluid transport in jointed rock

Phenomenological equations (with coefficients to be determined by specified experiments) for the poroelastic behavior of a dual porosity medium are formulated, and the coefficients in these linear equations are identified. The generalization from the single-porosity case increases the number of independent coefficients for volume deformation from three to six for an isotropic applied stress. The physical interpretations are based upon considerations of different temporal and spatial scales. For very short times, both matrix and fractures behave in an undrained fashion. For very long times, the double-porosity medium behaves like an equivalent single-porosity medium. At the macroscopic spatial level, the pertinent parameters (such as the total compressibility) may be determined by appropriate field tests. At an intermediate or mesoscopic scale, pertinent parameters of the rock matrix can be determined directly through laboratory measurements on core, and the compressibility can be measured for a single fracture. All six coefficients are determined from the three poroelastic matrix coefficients and the fracture compressibility from the single assumption that the solid grain modulus of the composite is approximately the same as that of the matrix for a small fracture porosity. Under this assumption, the total compressibility and three-dimensional storage coefficient of the composite are the volume averages of the matrix and fracture contributions.

The Influence of pore pressure and confining pressure on dynamic elastic properties of Berea sandstone

Compressional‐ and shear‐wave velocities of watersaturated Berea sandstone have been measured as functions of confining and pore pressures to 2 kbar. The velocities, measured by the pulse transmission technique, were obtained at selected pressures for the purpose of evaluating the relative importance of confining pressure and pore pressure on elastic wave velocities and derived dynamic elastic constants. Changes in Berea sandstone velocities resulting from changes in confining pressure are not exactly canceled by equivalent changes in pore pressure. For properties that involve significant bulk compression (compressional‐wave velocities and bulk modulus) an incremental change in pore pressure does not entirely cancel a similar change in confining pressure. On the other hand, it is shown that a pore pressure increment more than cancels an equivalent change in confining pressure for properties that depend significantly on rigidity (shear‐wave velocity and Poisson’s ratio). This behavior (as well as observed ...

Elasticity of orthoenstatite

Abstract Elastic constants of orthoenstatite have been determined from Brillouin-scattering measurements. They are c 11 = 2.247, c 22 = 1.779, c 33 = 2.136, c 44 = 0.776, c 55 = 0.759, c 66 = 0.816, c 23 = 0.527, c 31 = 0.541 and c 12 = 0.724 Mbar. Each elastic constant is uniquely defined by the data. Acoustic velocities measured for two directions ultrasonically on the same samples are within 1% of those determined from Brillouin-scattering spectra.

Fluid pressure response to undrained compression in saturated sedimentary rock

The pore pressure response of saturated porous rock subjected to undrained compression at low effective stresses are investigated theoretically and experimentally. This behavior is quantified by the undrained pore pressure buildup coefficient, B=(dPf/dPc)|dmf=0, where Pf is fluid pressure, Pc is confining pressure, and mf is the mass of fluid per unit bulk volume. The measured values for B for three sandstones and a dolomite arc near 1.0 at zero effective stress and decrease with increasing effective stress. In one sandstone, B is 0.62 at 13 MPa effective stress. These results agree with the theories of Gassmann (1951) and Bishop (1966), which assume a locally homogeneous solid framework. The decrease of B with increasing effective stress is probably related to crack closure and to high‐compressibility materials within the rock framework. The more general theories of Biot (1955) and Brown and Korringa (1975) introduce an additional parameter, the unjacketed pore compressibility, which can be determined fr...

Elastic wave propagation and attenuation in a double-porosity dual-permeability medium

Abstract To account for large-volume low-permeability storage porosity and low-volume high-permeability fracture/crack porosity in oil and gas reservoirs, phenomenological equations for the poroelastic behavior of a double porosity medium have been formulated and the coefficients in these linear equations identified. This generalization from a single porosity model increases the number of independent inertial coefficients from three to six, the number of independent drag coefficients from three to six, and the number of independent stress–strain coefficients from three to six for an isotropic applied stress and assumed isotropy of the medium. The analysis leading to physical interpretations of the inertial and drag coefficients is relatively straightforward, whereas that for the stress–strain coefficients is more tedious. In a quasistatic analysis, the physical interpretations are based upon considerations of extremes in both spatial and temporal scales. The limit of very short times is the one most pertinent for wave propagation, and in this case both matrix porosity and fractures are expected to behave in an undrained fashion, although our analysis makes no assumptions in this regard. For the very long times more relevant to reservoir drawdown, the double porosity medium behaves as an equivalent single porosity medium. At the macroscopic spatial level, the pertinent parameters (such as the total compressibility) may be determined by appropriate field tests. At the mesoscopic scale, pertinent parameters of the rock matrix can be determined directly through laboratory measurements on core, and the compressibility can be measured for a single fracture. We show explicitly how to generalize the quasistatic results to incorporate wave propagation effects and how effects that are usually attributed to squirt flow under partially saturated conditions can be explained alternatively in terms of the double-porosity model. The result is therefore a theory that generalizes, but is completely consistent with, Biot’s theory of poroelasticity and is valid for analysis of elastic wave data from highly fractured reservoirs.

Laboratory measurements of a complete set of poroelastic moduli for Berea sandstone and Indiana limestone

Measurements have been completed for eight different poroelastic moduli of water-saturated Berea sandstone and Indiana limestone as a function of confining pressure and pore pressure. The poroelastic moduli for Indiana limestone are generally consistent to ±10%, which was verified by a formal inversion procedure for independent moduli from the eight measurements. For Indiana limestone, best fit values were drained bulk modulus, 21.2 GPa; the undrained bulk modulus, 31.7 GPa; drained Poissons ratio, 0.26; undrained Poissons ratio, 0.33; and pore pressure buildup coefficient, 0.47 at 20–35 MPa effective stress. The poroelastic moduli for Berea sandstone are generally consistent to ±20%. The greater inconsistency is most likely caused by the nonlinear variation of the moduli at different strains. For Berea sandstone, best fit values were drained bulk modulus, 6.6 GPa; undrained bulk modulus, 15.8 GPa; drained Poissons ratio, 0.17; undrained Poissons ratio, 0.34; and pore pressure buildup coefficient, 0.75 at 10 MPa effective stress.

Transient stress-coupling between the 1992 Landers and 1999 Hector Mine, California, earthquakes

A three-dimensional finite-element model (FEM) of the Mojave block region in southern California is constructed to investigate transient stress-coupling between the 1992 Landers and 1999 Hector Mine earthquakes. The FEM simulates a poroelastic upper-crust layer coupled to a viscoelastic lower-crust layer, which is decoupled from the upper mantle. FEM predictions of the transient mechanical be- havior of the crust are constrained by global positioning system (GPS) data, inter- ferometric synthetic aperture radar (InSAR) images, fluid-pressure data from water wells, and the dislocation source of the 1999 Hector Mine earthquake. Two time- dependent parameters, hydraulic diffusivity of the upper crust and viscosity of the lower crust, are calibrated to 10 2 m 2 •sec 1 and 5 10 18 Pasec respectively. The hydraulic diffusivity is relatively insensitive to heterogeneous fault-zone permeabil- ity specifications and fluid-flow boundary conditions along the elastic free-surface at the top of the problem domain. The calibrated FEM is used to predict the evolution of Coulomb stress during the interval separating the 1992 Landers and 1999 Hector Mine earthquakes. The predicted change in Coulomb stress near the hypocenter of the Hector Mine earthquake increases from 0.02 to 0.05 MPa during the 7-yr interval separating the two events. This increase is primarily attributed to the recovery of decreased excess fluid pressure from the 1992 Landers coseismic (undrained) strain field. Coulomb stress predictions are insensitive to small variations of fault-plane dip and hypocentral depth estimations of the Hector Mine rupture.

Homogeneous vs heterogeneous subduction zone models: Coseismic and postseismic deformation

A finite-element model (FEM) incorporating geologic properties characteristic of a subduction zone is compared with FEMs approximating homogeneous elastic half-spaces (HEHS)s to investigate the effect of heterogeneity on coseismic and postseismic deformation predictions for the 1995 Colima-Jalisco M_w =8.0 earthquake. The FEMs are used to compute a coefficient matrix relating displacements at observation points due to unit dislocations of contact-node pairs on the fault surface. The Greens function responses are used to solve the inverse problem of estimating dislocation distributions from coseismic GPS displacements. Predictions from the FEM with heterogeneous material properties, loaded with either of the HEHS dislocation distributions, significantly overestimate coseismic displacements. Postseismic deformation predictions are also sensitive to the coseismic dislocation distribution, which drives poroelastic and viscoelastic relaxation. FEM-generated Greens functions, which allow for spatial variations in material properties, are thus preferable to those that assume a simple HEHS because the latter leads to dislocation distributions unsuitable for predicting the postseismic response.

Depth variation of seismic anisotropy and petrology in central European lithosphere: A tectonothermal synthesis from spinel lherzolite

Spinel lherzolite xenoliths from the Neogene Kozakov volcano in central Europe, yielding temperatures from 680°C to 1065°C and estimated to originate from depths of 32 to 70 km, provide an exceptionally continuous record of the depth variation in seismic and petrological properties of subcontinental lithospheric mantle. Extraction depths of the xenoliths and thermal history and rheological properties of the mantle have been evaluated from a tectonothermal model for basaltic underplating associated with Neogene rifting. The chemical depletion of sub-Kozakov mantle decreases with depth, the Mg number in olivine decreasing from ∼91.4 to 90.5 and the Cr number in spinel, decreasing from ∼38.9 to 14.7. Texturally, the sampled mantle consists of an equigranular upper layer (32–43 km), an intermediate protogranular layer (43–67 km), and a lower equigranular layer (below 67 km). Olivine petrofabrics show strong axis concentrations, which change with depth from orthorhombic symmetry in the equigranular upper layer to axial symmetry in the lowermost layer. Calculated compressional and shear wave anisotropies, which average 8% and 6%, respectively, show significant depth trends that correlate with variations in depth of olivine fabric strengths and symmetries. Comparisons of the xenolith anisotropies with field observations of Pn anisotropy and SKS shear wave splitting in the region suggest that foliation is horizontal in the upper layer of the lithospheric mantle and vertical in the middle and lower layers. The depth variation in mantle properties and complexity in central Europe is the result of Devonian to Early Carboniferous convergence, continental accretion, and crustal thickening, followed by Late Carboniferous to Permian extension and gravitational collapse and final modification by Neogene rifting, thinning, and magmatic heating.