On constrained optimization schemes for joint inversion of geophysical datasets.

摘要

In the area of geological sciences, there exist several experimental techniques used to advance in the understanding of the Earth. We implement a joint inversion least-squares (LSQ) algorithm to characterize one dimensional Earth's structure by using seismic shear wave velocities as a model parameter. We use two geophysical datasets sensitive to shear velocities, namely Receiver Function and Surface Wave dispersion velocity observations, with a choice of an optimization method: Truncated Singular Value Decomposition (TSVD) or Primal-Dual Interior-Point (PDIP). The TSVD and the PDIP methods solve a regularized unconstrained and a constrained minimization problem, respectively. Both techniques include bounds into the model parameter with a different methodology. An improvement in the final model is expected not only for using more than one single dataset, i.e. each dataset is chosen to identify different properties with greater resolution, but also because our constrained optimization approach provides us with direct control over the model space. We conduct a numerical experimentation with five synthetic crustal velocity models, and conclude that the PDIP method provides a more robust approximated model in terms of satisfying geophysical constraints, accuracy, and efficiency with respect to the TSVD approach. Our future goals include extending this work for Earth's velocity models by using real geophysical data, and possibly higher dimensional spaces including the use of parallel computing. Also we plan to further investigate if the addition of explicit smooth constraints, and other data sets like gravity and magnetic data may improve the resolution of the final model.