Modeling of pseudo-acoustic P-waves in orthorhombic media with a lowrank approximation |

where is the seismic pressure wavefield and is the wave propagation velocity.

Assuming the model is homogeneous
,
after a Fourier transform in space,
we get the following explicit expression in the wavenumber domain:

Equation 2 has the following analytical solution:

which leads to the well-known second-order time-marching scheme (Etgen, 1989; Soubaras and Zhang, 2008) :

Equation 5 provides a very accurate and efficient solution
in the case of a constant-velocity medium with the aid of FFTs.
When the seismic wave velocity varies in the medium,
equation 5 turns into a reasonable approximation by replacing with , and taking small time steps, .
However, FFTs can no longer be applied directly to evaluate
the inverse Fourier transform,
because a space-wavenumber mixed-domain term appears in the integral operation:

In the case of orthorhombic acoustic modeling, we derive a new phase operator to replace of the isotropic model. We describe the details in the next section.

Modeling of pseudo-acoustic P-waves in orthorhombic media with a lowrank approximation |

2013-07-26