Philosophical Ramblings

In view of the imposing theoretical developments over the last seventy-five years, it might be easy to claim that there isn't much more to do. Maybe the basic theory is actually in place and all we need to do is continue to let Moore's law (computer speed doubles every 18 months) bail us out. Its quite easy to argue that Moore's law is about to expire so I don't think we should consider relying on that. As far as theory is concerned, I can also argue that we don't understand wave propagation in real rocks (even in the simple acoustic heterogeneous case) as well as most of us seem to think. Anisotropic wave propagation can be modeled, but precisely what parameters we should use and how we should estimate them is still not generally accepted. Generation of a full elastic synthetic data set, as was done in an isotropic or acoustic sense over the SEG/EAGE salt model, is at least a decade away from being a routine undertaking.

I remember hearing that at one of AMOCO's Friday afternoon "brainstorming" sessions in the late 1980's, the question "What it the biggest problem we face today?" was posed. Someone wrote . This was immediately corrected to which of course was then erased (they had a real chalkboard in that room) and rewritten . Ignoring Thomsen's and for the moment, I think we still do not do as great of a job estimating that elusive 3D as some may think. If we can't do that, what hope do we have of estimating Thomsen's anisotropic parameters?

One can also argue that our current images still contain too much noise. They are corrupted by many events which we would like to call noise, but at least to my way of thinking are actually signal. Multiples and various forms of elastic wave phenomena produce migration artifacts when imaged with our current collection of algorithms that ignore such events. One-way equations are particularly susceptible to producing artifacts from turning wave events. Its quite natural to ask if this coherent but undesirable part of the wavefield can be used in some constructive manner.

With a few exceptions over the last 15 years, we have almost totally ignored highly mathematical inversion 1984 (); 1987 (); 2003 () approaches to velocity estimation and migration. In an earlier paragraph, I mentioned inverse scattering. This wave-equation based concept, as popularized by Art Weglein, A. J. Berkhout, and Eric Verschuur has already produce a 3D multiple suppression approach that shows tremendous promise in resolving at least one of the issue mentioned in the previous paragraph. The conjugate to the inverse scattering series approach might be called an imaging series. By carefully removing coherent noise (such as multiple energy) and then apply the imaging series in the right way it is at least theoretically possible to get the right image with the wrong velocity. I think its not within the scope of this paper to go into to much detail, but this inverse method appears to offer a new and exciting solution to the ever changing seismic imaging problem. As is the case with multiple suppression this method demands data with complete source-receiver reciprocity.

In my opinion, the time is ripe to revisit these methods with new vigor and effort. Whether or not we can find enough people to do the research is beginning to be questioned. I fear that we no longer have the JKF vision to do what it takes to invent the future. Whether or not we will ever have the computer power to do it is also in doubt. Since doing the inversion by Tarantola's method not only requires source-receiver reciprocity, but measurement at very low frequencies as well we may never be able to do inversion in an acceptable manner.

I would like to hope that the next 75 years will be as productive as the last. When viewed from the present, going from pencil and paper calculations to single purpose analog machines to modern digital computers is a breathtaking panorama. Hopefully the "back to the past" view 75 years hence will be as good as this one and provide solutions to the data acquisition, parameter estimation and processing questions we still can't answer today.