Discrete tomography and joint inversion for loosely connected or unconnected physical properties: application to crosshole seismic and georadar data sets

摘要

Tomographic inversions of geophysical data generally include an underdetermined component. To compensate for this shortcoming, assumptions or a priori knowledge need to be incorporated in the inversion process. A possible option for a broad class of problems is to restrict the range of values within which the unknown model parameters must lie. Typical examples of such problems include cavity detection or the delineation of isolated ore bodies in the subsurface. In cavity detection, the physical properties of the cavity can be narrowed down to those of air and/or water, and the physical properties of the host rock either are known to within a narrow band of values or can be established from simple experiments. Discrete tomography techniques allow such information to be included as constraints on the inversions. We have developed a discrete tomography method that is based on mixed-integer linear programming. An important feature of our method is the ability to invert jointly different types of data, for which the key physical properties are only loosely connected or unconnected. Joint inversions reduce the ambiguity in tomographic studies. The performance of our new algorithm is demonstrated on several synthetic data sets. In particular, we show how the complementary nature of seismic and georadar data can be exploited to locate air- or water-filled cavities