3D Seismic Heterogeneity Characterization for Karst, Fault and Fold Imaging: Statistical Approach
The effective elastic properties C of a random heterogeneous medium can be presented in terms of average value C and the fluctuation C . In such medium, the amplitude of spatial correlation function will have non-zero value because the inclusions and matrix will have different elastic properties of. The higher contrast between the inclusions and host rock, the higher will be the amplitude of the spatial correlation function, and viceversa. The heterogeneities having smaller and larger slowness are characterized by positive and negative normalized fluctuation, respectively. Theoretical modeling results, based on normalized fluctuation of traveltime slowness, to detect seismic heterogeneities in 3D random media is shown. We have used the radius of the spatial correlation function to calculate the extension of the inclusion in X-, Y- and Z-direction to demarcate the shape of heterogeneity. Upscaling of the physical properties of the medium is performed to calibrate the result to the seismic frequency range by changing the averaging window size. The properties of the medium inside the averaging window are assumed statistically homogeneous. Results obtained from this method show that as the size of the sliding window decreases the resolution of the heterogeneity increases.