Next: One-dimensional earth and impulsive
Up: Multidimensional seismic noise attenuation
Previous: Regularization of the filter
A surface-related multiple prediction theory
This section details how multiples are generated by convolution of shot gathers.
For a 1-D earth, the convolution can be done directly in the
f-k domain. For 2-D and 3-D earth, the convolution becomes nonstationary.
In addition, one convolution of the shot gathers tends to overpredict
high-order multiples.
If p(g|s) represents a single frequency component of the
primary reflected wavefield recorded at g after an impulsive shot at
s, then the first-order surface-related multiple,
m(g|s), can be computed with a Kirchhoff-style integral over the
reflection surface:
| |
(143) |
Equation () is expensive to evaluate, especially
for large 3-D data sets, but nevertheless widely-used for multiples
modeling.
hombre
Figure 3 The wavefield is emitted at s and
recorded at g. The multiple bounces somewhere at g'.
Next: One-dimensional earth and impulsive
Up: Multidimensional seismic noise attenuation
Previous: Regularization of the filter
Stanford Exploration Project
5/5/2005