NEW OBJECTIVE FUNCTIONS FOR WAVE-FORM INVERSION

Inversion is an organized search for parameter values that maximize or minimize an objective function, referred to here as a processor. This note derives three new seismic processors that require neither prior deconvolution nor knowledge of the source-receiver wavelet. The most p owerful of these is the fourwise processor, as it is applicable to dat a sets from multiple shots and receivers even when each shot has a dif ferent unknown signature and each receiver has a different unknown imp ulse response. Somewhat less powerful than the four-wise processor is the pairwise processor, which is applicable cable to a data set consis ting of two or more traces with the same unknown wavelet but possibly different gains. When only one seismogram exists the partition process or can be used. The partition processor is also applicable when there is only one shot (receiver) and each receiver (shot) has a different s ignature. In fourwise and pairwise inversions the unknown wavelets may be arbitrarily long in time and need not be minimum phase. In partiti on inversion the wavelet is assumed to be shorter in time than the dat a trace itself but is not otherwise restricted. None of the methods re quires assumptions about the Green's function.