Spectral factorization

The trouble with the autocorrelation of the CSG is that we are not accustomed to it. We don't know how to think about it. We would rather have the CSG itself. This suggests spectral factorization. In one dimension it is ancient knowledge that spectral factorization finds us an impulse response function of the system. Using the helix Claerbout (1998), in helioseismology Rickett and Claerbout (1999a) Rickett and Claerbout (1999b) we found that we can recover a multidimensional causal acoustic impulse response of the sun instead of "autocorrelation wavelets" that helioseismologists had been getting. Now we conjecture that we can do something similar here:

CONJECTURE: A spectral factorization of the (autocorrelation of the) shot-geophone reflection data should give us the "multidimensional impulse response" of the earth.

There are some pitfalls with spectral factorization, but they are fairly well understood and they have often been overcome in the past.