A Constrained Multi-Objective Optimization Framework for Multiple Geophysical Data Sets

For this work, we used a constrained optimization approach for a joint inversionleast-squares (LSQ) algorithm to characterize a one-dimensional Earth structure usingmultiple geophysical data sets. Geophysical data sets such as receiver functions,surface wave dispersion measurements, and first arrival travel times were used forthis multi-objective optimization approach for there complementary nature with theinversion process. The multiple geophysical datasets used in this study are complementaryto each other because one geophysical dataset can recover the causativeslowness of seismic data, one is sensitive to relative changes in S-wave velocities,and another one is found to be sensitive to absolute shear velocities between discontinuities.The complementary information provided by the datasets, also reducesthe inherent ambiguity or non-uniqueness when performing inversion. Utilizing thisconstrained multi-objective optimization approach, several possible models can begenerated and a final solution among a population of alternative solutions fromthe model space can be selected when using this optimization approach. This optimization scheme definesthe entire solution space based from using different weights to map the Pareto Set. Throughnumerical and experimental testing, the Multi-Objective Optimization scheme performsinversion in a more robust, and flexible matter than inversion using a singlegeophysical dataset.