Amplitude Balance

During a seismic survey, it can't be guaranteed that all the receivers have the same response. Neither can we promise that the energy for all shots have same energy. So, the recorded amplitude difference between traces will include not only rock information but also artifacts caused by different sources and receivers. We should remove such artifacts before performing AVA analysis.

For each trace, its amplitude square A_t can be expressed as

<B><I>AI>_<I>tI>=<I>RI>_<I>tI><I>SI>_<I>tI><I>GI>_<I>tI><I>UI>_<I>tI> B> (234)

Here, R_t is the component from the unique receiver the trace is corresponding to; S_t is from the unique source the trace is corresponding to; G_t corresponding to geometrical spreading for this trace; and U_t is the remaining amplitude component which contains the information related to rock properties. The way we balanced the amplitude is the following:

1.

Extract the same depth window for all traces and calculate the sum of the amplitude square for all traces in this window.

2.

Using the conjugate gradient method to solve for R_t, S_t, G_t and U_t using (5).

3.

The problem will be underdetermined. We regularize the problem by applying Laplacian to G_t and U_t because they should be spatially continuous.

4.

After solving R_t, S_t, G_t and U_t for each trace, we will divide all traces by their corresponding R_t, S_t and G_t to remove the artifacts.