This question is in the context of velocity model building for reflection seismic imaging (between 0km and 10km in a sedimentary basin).
This is really a rock physics question disguised as an imaging question.
A brief description of what I am trying to do:
In order to perform seismic imaging (aka seismic migration), we assume that the velocity structure of the earth is known. This allows us to place the recorded reflection amplitudes in the correct location in 3D space to give us a real representation of the underlying geology (including depth, dips, and scaled reflection coefficients).
We can obtain this laterally varying velocity model from iterative traveltime tomography of the same data. We typically account for the polar velocity anisotropy (i.e. difference in velocity of the same rock when measured parallel vs perpendicular to bedding planes) in the form of Thomsen parameters, in a symmetry model usually called TTI (tilted transverse isotropy). The final model consists of 5 spatially varying parameters:
- Theta (angle of structural dip, the axis of symmetry is assumed perpendicular to bedding)
- Phi (angle of structural strike, the axis of symmetry is assumed perpendicular to bedding)
- V0 (velocity along this axis of symmetry)
- Epsilon (Thomsen parameter describing the magnitude of large angle anisotropy)
- Delta (Thomsen parameter describing the magnitude of small angle anisotropy)
Theta and Phi are easy to obtain directly from the seismic image (this is in part why this process is iterative).
An initial model for V0, epsilon, and delta is created from sparse well data and further detail is obtained between control points by using tomography. In practice, epsilon and delta are assumed to be linearly related and that the linear relation holds throughout the dataset (this is usually a good assumption).
This leaves us solving for really just two things in tomography: V0 and delta. However, there is an intrinsic non-uniqueness, made worse by noise, in which different combinations of V0 and delta explain the data equally well (i.e. image gather flatness).
So the motivation for my question is this: How can I use a priori geologic data to guide the solution of this ill-posed inverse problem?
I am very skeptical about having the geologic structure guide V0 since my dataset is in an active foreland basin with strong active deltaic deposition. This means that my sediments (structurally deformed progradational sand-shale sequences) are very unconsolidated and compaction (therefore, depth) is the main driver of velocity rather than stratigraphy. In other words, I expect velocity contours to cross structural ones in areas of high dip (and I have evidence of these normal compaction trends from well data).
Which now leads to my question: Can I use the geologic structure to guide my Thomsen delta (i.e. the degree of anisotropy)? Does it make sense to assume that even though compaction is the main driver for velocity in unconsolidated sediments, stratigraphy is the main driver of anisotropy?
Maybe a more useful question: What other measurements or observations would I need to make to validate or reject this assumption?
If this assumption makes sense, I can add the additional constraint (as a regularization term) to the tomographic inverse problem such that the solution for delta must (at least somewhat) follow the structural dip (i.e. theta and phi).