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We consider periodically heterogeneous fluid-saturated poroelastic media described by the Biot model with inertia effects. The weak and semistrong formulations for displacement, seepage and pressure fields involve three equations expressing the momentum and mass balance and the Darcy law. Using the two-scale homogenization method, we obtain the limit two-scale problem and prove the existence and uniqueness of its weak solutions. The Laplace transformation in time is used to decouple the macroscopic and microscopic scales. It is shown that the seepage velocity is eliminated from the macroscopic equations involving strain and pressure fields only. The plane harmonic wave propagation is studied using an example of layered medium. Illustrations show some influence of the orthotropy on the dispersion phenomena.

The Biot model is widely used to model poroelastic media. Several authors have studied its applicability to cancellous bone. In this article the feasibility of determining the Biot parameters of cancellous bone by acoustic interrogation using frequencies in the 5–15 kHz range is studied. It is found that the porosity of the specimen can be determined with a high degree of accuracy. The degree to which other parameters can be determined accurately depends upon porosity.

In a precursor to this article the Biot model was used to model poroelastic media. The question this article addresses is whether the sort of experiments described by McKelvie and Palmer, Williams, and Hosokawa and Otani can be used to determine the parameters of the Biot model. A method of computing acoustic pressure in the low 100 kHz range was developed in Buchanan and Gilbert, "Determination of the parameters of cancellous bone using high frequency acoustic measurements," which appeared in Math. Comput. Modelling. In the present work a parameter recovery algorithm which uses parallel processing is developed and tested. It is found that when it is assumed that the agreement between calculated and measured data is about two digits, porosity can be determined to within about 1–2% and permeability, pore size and the bulk moduli to within about 40%, but in most cases less than 20%.

A new hybrid algorithm of the depth solver for the wavenumber integration technique is derived. The global matrix method is adopted as the depth solver in the ocean, where there are sources and receivers present, and the reflectivity scheme is used for calculating the wave field of the porous ocean bottom. In order to hybridize both depth solvers, a novel technique has been developed where a virtual fluid layer with zero thickness is inserted between the ocean and the porous ocean bottom. This technique makes the hybrid algorithm simple to implement and compatible with any other depth solvers for the ocean bottom. Numerical simulation shows the proposed algorithm to work well.

A seismic survey is perhaps the most common geophysical technique used to locate potential oil and natural gas deposits in the geologic structures. Thanks to the rapid development of modern high-performance computing systems, the computer simulation technology plays a crucial role in processing the field data. The precision of the full-waveform inversion (FWI) essentially depends on the quality of the direct problem solver. This paper introduces a new approach to the numerical simulation of wave processes in complex heterogeneous media. The linear elasticity theory is applied to simulate the dynamic behavior of curvilinear geological layers. In contrast to the conventional approach, the producing oil formation is described in the frame of a porous fluid-filled model. It allows us to explicitly take into account the porosity, oil density, and other physical parameters. The method of setting the physically correct contact conditions between the reservoir and the geological massif based on the transport equation solution for Riemann invariants was successfully implemented. The grid-characteristic method, previously thoroughly verified on acoustic and elastic problems, was adopted. The explicit time-stepping procedure was derived for a two-dimensional case with a method of splitting along coordinate axes. This method guarantees the preservation of the scheme approximation order. The potential application of the new method to a complex model based on the data from the famous Russian oil deposit — the Bazhen Formation — is demonstrated. The seismic responses were registered on the wave fields and synthetic seismograms. The novelty of this paper relates to a uniform approach to the wave propagation simulation in the heterogeneous medium containing contacting subdomains with different rheology types.

We investigate a problem of potential interest to geophysicists. Namely, we attempt to find the shape of a magnum chamber lying in the earth crust below a volcano. This is posed as an inverse acoustics problem where we use scattered seismic waves to determine the location and form of the chamber. A simplification is to consider the finite crust to be over a semi-finite magma region. An earlier work of ours discussed the inverse problem associated with the Perkeris model ³, whereas the present work represents the crust with volcano as a perturbation of this model. In order to reformulate this inverse problem in integral equation form we first construct the Green's function for this problem. A numerical example is presented for the case of the bump being a half circle.