and assuming the P-wave polarization in the direction of the gradient
of , derive the elastic P-wave amplitude transport equation and
show its similarity to the corresponding equation for the case of
acoustic variable-density wave propagation.
Consider a 2-D common-midpoint gather , which
contains a geometric event
constant amplitude along a hyperbolic shape
The gather gets transformed by the slant-stack (Radon transform) operator
is a waveform-correcting half-order
Using the theory of geometric integration, show that
will contain a geometric event
Find and .
Using the hyperbolic traveltime approximation
makes the geometric imaging analysis equivalent to analyzing wave
propagation in a constant-velocity medium. In particular, we can easily
verify that the traveltime satisfies the isotropic eikonal equation
Suppose that you switch to the more accurate shifted-hyperbola approximation
How would you need to modify the eikonal equation?
How would you need to modify the following expressions for the escape time and location for use in the angle-domain Kirchhoff time migration?