On the effectiveness of joint inversion

Tuesday, October 23, 2018 - 3:05pm - 3:55pm
Keller 3-180
Jodi Mead (Boise State University)
Simultaneous joint inversion of multiple data sets has become quite common in geophysics. For example, we have inverted electrical resistivity (ER) and ground penetrating radar (GPR) measurements made at the surface to image the near subsurface. Both measurements are sensitive to conductivity and are linked through Maxwell’s equations. This gives an excellent opportunity to jointly invert for a common parameter set. If the media of interest has low conductivity ER measurements may not contain enough information to produce a meaningful image. GPR on the other hand is sensitive to conductivity through reflectivity and attenuation, so if attenuation is strong in the media the observed wavefield may not be able to produce a meaningful image. Therefore, the combination of ER and GPR datasets gives information across a wide range of frequencies that has the potential to produces images not possible through individual inversions.

Even though there is good physical evidence that these two datasets should produce a better image than if each were individually inverted, we are also investigating how the joint inversion reduces the ill-posedness of the individual inversions. The degree of ill-posedness can be measured by the decay rate of the singular values of the forward operator. We extend discrete techniques of stacking matrices in joint inversion, to combining Green’s function solutions of multiple differential equations representing different types of data. The singular values of the joint operators indicate the effectiveness of combining multiple types of physics. This knowledge provides mathematical justification for joint inversion, and can be determined before the complicated machinery of discretizing and solving the problem is implemented.