Extracting Velocities from Diffractions
, by William S. Harlan, Jon F. Claerbout, and Fabio Rocca
By extracting diffraction events from stacked sections one may estimate
seismic velocities with migration. Extrapolation of wavefronts back in time
focuses sinal, which originates from simple sources. Migration focuses
diffractions, from bed truncations and point scatterers, but not reflections
of continuous beds; migration disperses noise.
A measure, W, exists which is minimizes and equal to the statistical entropy, H,
when the data are statistically white. We calculate W from local histograms of data.
An invertible transformation, L, alters W but not H. Whitening the signal with L
makes it more non-gaussian, focusing the energy; noise defocuses, becoming more
gaussian. Thus, for extracted signal, the best L minimizes W.
If transformation makes signal more non-gaussian, then we may extract the
highest amplitudes as signal. Only coherent summing accounts for amplitudes above
some cutoff; noise sums destructively. Artifically whitened data, simulating noise,
determine good cutoffs.
Slant stacks map lines to points, greatly concentrating bed reflections. We invert the
strongest events and substract the data, leaving diffractions and noise. Next, we migrate
with many velocities, extract focused events, and invert. We find a least-squares sum
and migrate again: since only diffractions remain, W reached a minimum at the best velocity.
We estimate interval velocities windowing and extrapolating downward.
We successfully extract diffractions and estimate velocities for a window of data containing
a growth fault. Illustrations demonstrate each step of the extraction procedure.
STANFORD