Characterization of the Spectrum of a Random Medium from Trace Measurements

Imaging provides the ability to determine the geometrical structure of the Earth. However, some portion of the structure cannot be reliably determined from seismic imaging so other approaches must be taken for characterization. Characterization of some portions of the structure can best be done using a random media approach. Such approaches provide valuable tools for understanding scattering and attenuation in the Earth. We have used numerical modeling of wave propagation through random media to better understand what characteristics of the medium can be inferred from analysis of seismic traces. We have recently developed an approach for using traces recorded along a receiver array within a 2D heterogeneous medium to characterize the spatial heterogeneity in the medium. We compare the spectrum of the spatial fluctuation of medium velocity with the spectrum of the spatial fluctuation in integrated rectified trace amplitudes measured along the receiver array. We find that the two spatial spectra are coincident over a wide spatial wavenumber range. We have also investigated the application of the method to surface reflection data calculated in simulations of a homogeneous layer over a heterogeneous half space. The method can determine not only information about the random component of structure but has also been shown to be capable of providing information about fracture characteristics, which is important in petroleum exploration and fluid-flow modeling.