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

Abstract

S U M M A R Y 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 l-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 l-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 l-D model. The time difference between these two arrivals increases linearly with the depth of receivers. We have reported time difference up to 10ms per 1000m. This time difference is also directly related to the scale of lateral inhomogeneities a.

An example of seismic time picking by third‐order bicoherence

“…When the noise correlation in the measurements is considerable, the correlation peak can be substantially distorted, resulting in imprecise and even biased estimation of the time delay. The synthetic data computed by Ikelle et al (1993) and Ikelle and Yung (1994) in their studies of wave propagation through random media provide a good example of data with considerable noise correlation. In picking the arrival times in this data set, we found that the crosscorrelation technique suffers both from the severely restricted signal bandwidth and from the presence of coda.…”

The effect of random isotropic inhomogeneities on the phase velocity of seismic waves

“…In a randomly inhomogeneous medium characterized by homogeneous statistics (such a medium is said to be stationary), the phase velocity of the direct arrivals differs from the averaged velocity or from the inverse averaged slowness. Recently this phenomenon, termed 'velocity shift', has been considered by Miiller, Roth & Korn (1992), Roth, Miiller & Snieder (1993), van Avendonk & Snieder (1994) and Ikelle & Yung (1994).…”