Linear velocity spectrum (Thesis chapter IV)
, by Alfonso Gonzalez-Serrano and Jon F. Claerbout
The wave equation velocity spectrum of a CMP is defined as its image in Snell
midpoint coordinates for a non-zero reference ray parameter p-initial. In this
space energy is a local function of velocity. Velocity estimation is possible
with the LMO method. In stratified media with constant velocity between
reflectors, the LMO method estimates interval velocity without the need of
geometric approximations. The LMO method can also be used to quantify strong
velocity variations between reflectors. The phase shift metthod is a convenient
way to downward continue in Snell midpoint coordinates. Stolt's method can be
combined witha hyperbolic deformation to improve the quality of imaging. Because
downward continuation operators are referenced to a slant propagation anlge,
accurate operators to image wide anle energy are unnecessary. The fifteen degree
finite difference method in (h, tauo, w) can thus be used at wide angles. This
method is not too sensitive to the downward continuation velocity. A varialbe
velocity v(h, tauo) can be used to improve the image. Also we can apply a stepout
filter concurrent with downward continuation. Examples with synthetic and field
data show that the linear velocity specturm can resolve both narrow and wide
velocity variations when using the appropriate reference parameters. The wave
equation velocity spectrum is also a convenient model space when linearity and
locality properties are desired.
STANFORD