Frequency-dependent energy attenuation and velocity dispersion in periodic layered media.

According to Brajanovski periodic layered model, a fractural medium can be equivalent to layered media with periodic distribution of fractural layers and background layers, but the analytical solution given by Brajanovski can only interpret the dispersion and attenuation effects of single characteristic unit model. In order to study the dispersion and attenuation features of multiple characteristic units, forward modeling methods are needed. Based on the theory of two-phase medium, Biot deduced the propagation equation of longitudinal waves in fluid-saturated porous media. However, there are two problems in the forward modeling using time-domain equation. One is the influences of boundary reflection, and the other is the introduction of cumulative error. For convenience, time-domain equation is rewritten in the frequency domain, thus constructing a one-dimensional rock physics model. Then, forward method is used to study the dispersion and attenuation features of fluid-saturated medium. Numerical simulation results are found to be in good agreement with the analytical solution. Furthermore, the frequency-domain forward method can analyze the velocity dispersion and energy attenuation of longitudinal waves in any multilayered fracture medium. By analyzing those numerical simulation results, it can be obtained that, as the length of characteristic unit increases or the number of characteristic unit decreases, both the starting frequency of dispersion and the peak frequency of attenuation shift to low, whatever the attenuation peaks are equal. In addition, the effects of porosity, permeability and fluid saturation on energy attenuation and velocity dispersion are also studied. Finally, the stress field and displacement field distributions of fluid-saturated fractural medium are given by the frequency-domain forward modeling method. [ABSTRACT FROM AUTHOR]