Until recently, an equivalent time domain method was not possible. Claerbout1998 discovered that multi-dimensional time filters can be mapped into 1-D, therefore making it possible to do inverse filtering. Crawley et al. (1998) showed how non-stationary filters could more accurately predict seismic data. Fomel (1999) demonstrated how Spitz's method could be changed to work with time domain PEFs.
In the first section of the paper, we perform time domain multiple suppression by a two step method. We first estimate a space-varying PEF from data (a CMP gather) and a noise model (an estimate of the multiples obtain by downward continuing through the water column twice). We then separate out the signal (primaries) from the noise (multiples) by a simple inversion scheme.
In the second portion of the paper we present a better way to separate multiples in velocity space. Lumley et al. (1994) described a CMP gather as a sum of hyperbolic events. They then inverted this velocity-space transform into (,v) space, muted multiples, and transformed back into (t,h) space. Guitton and Symes (1999) showed that a Huber functional Huber (1973) produces a velocity scan where reflection energy is better behaved. We invert into () using the Huber functional, rather than an L2 functional. We show that the Huber method provides more separation between primary and multiple trends, and therefore improved multiple suppression.