James G. Berryman

Exact seismic velocities for transversely isotropic media and extended Thomsen formulas for stronger anisotropies

A different type of approximation to the exact anisotropic wave velocities as a function of incidence angle in transversely isotropic (TI) media is explored. This formulation extends Thomsen’s weak anisotropy approach to stronger deviations from isotropy without significantly affecting the equations’ simplicity. One easily recognized improvement is that the extreme value of the quasi-SV-wave speed vsv (θ) is located at the correct incidence angle θ= θex rather than always being at the position θ=45° . This holds universally for Thomsen’s approximation, although θex ≡45° actually is never correct for any TI anisotropic medium. Wave-speed magnitudes are more closely approximated for most values of the incidence angle, although there may be some exceptions depending on actual angular location of the extreme value. Furthermore, a special angle θ= θm (close to theextreme point of the SV-wave speed and also needed by the new formulas) can be deduced from the same data normally used in weak anisotropy data analy...

Random polycrystals of grains containing cracks: Model of quasistatic elastic behavior for fractured systems

A model study on fractured systems was performed using aconcept that treats isotropic cracked systems as ensembles of crackedgrains by analogy to isotropic polycrystalline elastic media. Theapproach has two advantages: (a) Averaging performed is ensembleaveraging, thus avoiding the criticism legitimately leveled at mosteffective medium theories of quasistatic elastic behavior for crackedmedia based on volume concentrations of inclusions. Since crack effectsare largely independent of the volume they occupy in the composite, sucha non-volume-based method offers an appealingly simple modelingalternative. (b) The second advantage is that both polycrystals andfractured media are stiffer than might otherwise be expected, due tonatural bridging effects of the strong components. These same effectshave also often been interpreted as crack-crack screening inhigh-crack-density fractured media, but there is no inherent conflictbetween these two interpretations of this phenomenon. Results of thestudy are somewhat mixed. The spread in elastic constants observed in aset of numerical experiments is found to be very comparable to the spreadin values contained between the Reuss and Voigt bounds for thepolycrystal model. However, computed Hashin-Shtrikman bounds are much tootight to be in agreement with the numerical data, showing thatpolycrystals of cracked grains tend to violate some implicit assumptionsof the Hashin-Shtrikman bounding approach. However, the self-consistentestimates obtained for the random polycrystal model are nevertheless verygood estimators of the observed average behavior.

Poroelastic Response of Orthotropic Fractured Porous Media

An algorithm is presented for inverting either laboratory or field poroelastic data for all the drained constants of an anisotropic (specifically orthotropic) fractured poroelastic system. While fractures normally weaken the system by increasing the mechanical compliance, any liquids present in these fractures are expected to increase the stiffness somewhat, thus negating to some extent the mechanical weakening influence of the fractures themselves. The analysis presented in this article quantifies these effects and shows that the key physical variable needed to account for the pore-fluid effects is a factor of (1 − B), where B is Skempton’s second coefficient and satisfies 0xa0≤ B < 1. This scalar factor uniformly reduces the increase in compliance due to the presence of communicating fractures, thereby stiffening the fractured composite medium by a predictable amount. One further aim of the discussion is to determine the number of the poroelastic constants that needs to be known by other means to determine the rest from remote measurements, such as seismic wave propagation data in the field. Quantitative examples arising in the analysis show that, if the fracture aspect ratio

Changes in geophysical properties caused by fluid injection into porous rocks: analytical models

{a_f simeq 0.1}

Weak consolidation model for wave propagation in ocean sediments

and the pore fluid is liquid water, then for several cases considered, Skempton’s

Poroelasticity Generalized for Polycrystalline Composites

{B simeq 0.9}