An example of lateral-inhomogeneity effects on seismic traveltimes in a zero-offset VSP experiment

Abstract

SUMMARY 2-D random media with ellipsoidal autocorrelation functions are used to point out the effects of lateral inhomogeneities on zero-offset VSP data. The ellipsoidal autocorrelation functions allow the characterization of lateral and vertical inhomogeneities by two independent scaling factors a and b in the two Cartesian directions; a for lateral inhomogeneities and b for vertical inhomogeneities. Thus we can describe 2-D media by taking non-zero finite values of a and b, or 1-D media by extending to infinity one of the two scaling factors. Here we consider two models: (i) a 2-D model where a and b are finite and non-zero, and (ii) a 1-D model with the same vertical realization of inhomogeneities (i.e. the same value for b) but with a tending to infinity. By comparing zero-offset VSP synthetic seismograms obtained from these two models, we observe that the seismic pulse through the 2-D model arrives earlier than the pulse through the 1-D model. The time difference between these two arrivals increases linearly with the depth of receivers. We have reported time difference up to 10 ms per 1000 m. This time difference is also directly related to the scale of lateral inhomogeneities a.