Extracting Lags

There are a number of ways to extract the slip distribution along a fault plane. Windowed cross-correlation is the simplest; however, it needs to be constrained. To test this out, I started with a 2D synthetic seismic section. I created 40 randomly spaced reflection coefficients with random magnitudes. I stretched one side to mimic fault deformation, shown in Figure 3. I, then, convolved it with a simple zero phase wavelet, shown in Figure 4.

 

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Figure 3 Model of reflection coefficients.

 

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Figure 4 Model after convolving with a source wavelet and bending along a fault.

The stretching and compressing creates a non-stationary problem. I am still uncertain how much of a problem this would be in real data. In this model, simple cross-correlation techniques can be a good start, but they will not completely remove the deformation.

Regardless, the first step should be to flatten the data on the fault plane, as in Figure 5.

 

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Figure 5 Model after flattening on the fault surface.

Then one trace can be extracted from each side of the fault. The problem then becomes to find the shift to apply to the trace left of the fault to make it similar to the right side of the fault.