Search

We present an iterative algorithm formulated in the space-frequency domain to simulate the propagation of waves in a bounded poro-viscoelastic rock saturated by a two-phase fluid. The Biot-type model takes into account capillary forces and viscous and mass coupling coefficients between the fluid phases under variable saturation and pore fluid pressure conditions. The model predicts the existence of three compressional waves or Type-I, Type-II and Type-III waves and one shear or S-wave. The Type-III mode is a new mode not present in the classical Biot theory for single-phase fluids. Our differential and numerical models are stated in the space-frequency domain instead of the classical integrodifferential formulation in the space-time domain. For each temporal frequency, this formulation leads to a Helmholtz-type boundary value problem which is then solved independently of the other frequency problems, and the time-domain solution is obtained by an approximate inverse Fourier transform. The numerical procedure, which is first-order correct in the spatial discretization, is an iterative nonoverlapping domain decomposition method that employs an absorbing boundary condition in order to minimize spurious reflections from the artificial boundaries. The numerical experiments showing the propagation of waves in a sample of Nivelsteiner sandstone indicate that under certain conditions the Type-III wave can be observed at ultrasonic frequencies. [ABSTRACT FROM AUTHOR]

Modeling acoustic waves generated by a localized source is always vexed by the nagging problem of spurious reflections and wraparound arising when the wavefront reaches the boundary of the numerical mesh. This difficulty may be circumvented by using a very large computational domain, which is very inefficient, or can be tackled by using some kind of absorbing boundary technique, which has not yet found a universally satisfactory solution. In this work, the wave equation is modified by introducing a term that is nonzero only in a narrow strip near the boundary. Then, a splitting technique permits to compute part of the solution analytically (hence, at no computational cost), while an application of Weyl's formula for the exponential of a matrix leads to a second-order accurate scheme that completes the algorithm. An application to SH seismic wave modeling shows that the performance of the present method is competitive with standard ones. Moreover, there is evidence for a potential application to the modeling of wave propagation in porous media, where stiff differential equations arise. [ABSTRACT FROM AUTHOR]