Imaging a steep structure brings special problems to seismic reflection methods. First is the problem that the common-depth-point acquisition and processing schemes, so successful in characterizing stratigraphy and locating petroleum in large clastic deltas, rely on a normal-moveout time correction that is only valid for flat-dipping structure. The oil and gas industry has developed alternative processing schemes, known as migrations, that get around this limitation. Industry has successfully employed migration on the steep flanks for salt domes, and for the 3-d imaging of fault-stratigraphic relations. I have adapted migration methods to examine faults, and I use these methods here.

As you can see, for a simple lithologic boundary such as granite against gabbro, I would be trying to stack a positive headwall reflection together with a negative footwall reflection. The migrations I use can be cast as some kind of asymptotic inversion that will account for this, but then I would need even better ray coverage, and equally illuminate all angles of incidence. In many cases I cannot do that, and I am interested more in simply detecting and locating a structure than on describing its velocity contrast or other properties.

There are situations, however, where the sign of the reflection may be the same on both sides of the fault. One such would be where the fault includes a 100 to 500 meter-wide low-velocity zone along it. Yong-gong Li and John Vidale have proved this for several strike-slip faults in the San Andreas system, by recording and modeling fault zone trapped waves. As long as both source and receiver are outside the very narrow fault zone, the sign of the refection will be the same.

Another situation, first identified by McCaffree and Christensen, is one where the fault juxtaposes of differing magnitude or direction. In lab measurements of mylonite samples of old and once deeply-buried faults, they noticed that anisotropy in P-wave velocities is almost always larger than the anisotropy in S-wave velocities. Reflectivities from juxtaposed or intercalated mylonite units were much stronger for P-waves than for S-waves.

Such a strong P-wave reflectivity is quite different from the normal kind of simple lithologic reflectivity we usually think about. Yet it is this kind of P and not S-wave reflectivity that I think of as actually helping to image faults in the crust, and to avoid imaging other kinds of structures with an igneous or sedimentary origin.

Delta mu and thus S-wave reflectivity acts like a force couple when excited by an incident wave from above, with a positive back scatter and a negative forward scatter. Density reflectivity acts as a single force and is much like delta mu. Delta lambda, and thus P-wave reflectivity in the absence of S-wave reflectivity, acts as a point explosion, with a positive scatter in all directions. This is a stunning difference, with the effect that for faults, that may have at least as much lambda as mu reflectivity, I can stack together scattered waves from watever angles of incidence I might have.

I demontrate this above with some elastic finite-difference synthetics. Stacking summation for migration would be done in the tan windows, across both the back-scattered and forward-scattered traces. You can see that the windows do not include the P-S converted reflection back-scattered from both the delta lambda and delta mu boundaries. For the delta lambda, P-wave reflector I get good summation of data from both incidence angles. For the delta mu S-wave reflector I do not get good summation.

The effect of this is that my techniques favor the imaging of delta lambda reflectors that have more P-wave than S-wave reflectivity. I feel that the images I produce might thus show faults and other tectonic structures even in preference to other kinds of geologic boundaries such as batholith tops, relict sedimentary layering, sills, or the Moho.