Reflection and transmission of waves at a fluid/porous‐medium interface

Abstract

We study the wave properties at a fluid/porousmedium interface by using newly derived closed-form expressions for the reflection and transmission coefficients. We illustrate the usefulness of these relatively simple expressions by applying them to a water/porousmedium interface (with open-pore or sealed-pore boundary conditions), where the porous medium consists of (1) a water-saturated clay/silt layer, (2) a water-saturated sand layer, (3) an air-filled clay/silt layer, or (4) an airfilled sand layer. We observe in the frequency range 5 Hz-20 kHz that the fast P-wave and S-wave velocities in the four porous materials are indistinguishable from the corresponding frequency-independent ones calculated using Gassmann relations. Consequently, for these frequencies we would expect the reflection and transmission coefficients for the four water/porous-medium interfaces to be similar to the ones for corresponding interfaces between water and effective elastic media (described by Gassmann wave velocities). This expectation is not fulfilled in the case of an interface between water and an air-filled porous layer with open pores. A close examination of the expressions for the reflection and transmission coefficients shows that this unexpected result is because of the large density difference between water and air.

Plane Wave at the Interface Between Water and a Gassy Poroelastic Layer With Underlying Elastic Seabed

“…Albert compared two different interfaces, the air/air-filled porous medium and the water/water-saturated porous medium [13]. Denneman et al studied the wave properties at a fluid/porous-medium interface through simple closed-form expressions for the reflection and transmission coefficients [14]. From the Biot -Gassmann theory for fluid-saturated porous rocks, Russell et al first derived a general formula for fluid-property discrimination and combined it with an AVO inversion to show its geophysical applications in the extraction of information about the fluid properties of the reservoir.…”

Low-Frequency Asymptotic Analysis of Seismic Reflection from a Fluid-Saturated Medium

“…We assume that the rearrangement occurs through elastic deformations of the cement bonds between the grains. Such an assumption is natural in many situations considered in hydrology and is quite common in the geophysical literature as well, see, e.g., [13].…”

“…It is well-known that both the transmission and reflection coefficients from a fluid-saturated porous medium are functions of frequency [19,16,39,13]. Recently, low-frequency signals were successfully used in obtaining high-resolution images of oil and gas reservoirs [20,21,11] and in monitoring underground gas storage [25].…”

A hydrologic view on Biot's theory of poroelasticity

“…We assume that the rearrangement occurs through elastic deformations of the cement bonds between the grains. Such an assumption is natural in many situations considered in hydrology and is quite common in the geophysical literature as well, see, e.g., [12].…”

“…It is known that both the transmission and reflection coefficients from a fluid-saturated porous medium are functions of frequency [18,15,35,12]. Recently, low-frequency signals were successfully used in obtaining high-resolution images of oil and gas reservoirs [19,20,10] and in monitoring underground gas storage [23].…”