Shallow-water attenuation of multiples by inversion (SWAMI)

In marine geophysics it is difficult to acquire very short offsets due to a number of operational constraints. This is a widely recognised problem in shallow water because SRME needs the near offset primary reflections to predict the free surface multiples. However, given the data with multiples measured at the available offsets, we can derive a multichannel prediction filter which is an excellent approximation of the sea-bed reflector and any other reflectors included in the design. The filter is designed by minimizing the energy in the output of a prediction error process, in a somewhat analogous manner to predictive deconvolution. By use of the focal transform, it is constrained to be composed of a sparse set of hyperbolic functions based upon the wave equation. Given this filter, we may proceed to predict the multiples and remove them as part of an adaptive subtraction scheme.