Choice of non-stationary shaping-filter parameters

As described above, a non-stationary filter can have a different impulse response for each point in the input/output space. For the non-stationary shaping filter estimation procedure, we need to define which coefficients are adjustable for every individual impulse response. For simplicity, we characterize each impulse response with the same set of adjustable coefficients: for the examples, shown here, they were one-dimensional non-causal symmetric filters about 180 ms long. Tests indicated that if the filters were shorter than the seismic wavelength, the quality of the results decreased. Increasing filter length beyond this length, however, did not alter results significantly, even in cases when the kinematics of the multiples were not accurately predicted.

When implementing the non-stationary filters, it is not strictly necessary to force each point of the input/output space to keep a unique impulse response. Rather, we apply the concept of ``micropatches'' Crawley (2000), in which points within a small neighbourhood share a single impulse response. This cuts computational memory requirements significantly, and provides an alternative method of controling spatial and temporal variabilty of impulse responses.