Optimization Algorithms with Structure Constraints for Multi-Parameter Seismic Inversion

Abstract

Multi-parameter inversion is often encountered in geophysical imaging due to the various rock physical proprieties, such as density, magnetism and up to 21 elastic moduli for anisotropic rocks. The main challenge of the multi-parameter inversion is the non-uniqueness of its solution. Optimization algorithms are utilized to min imize the appropriate objective functions. However, some higher-order algorithms are computationally expensive, and many new first-order optimization algorithms have been developed for machine learning. In this thesis, we have examined four first-order optimization algorithms for 2D seismic anisotropic tomography in an attempt to find a reliable alternative to the common conjugate gradient algo rithm. The results show that Nesternov Accelerated Gradient (NAG) is a reliable first-order algorithm since it has achieved a low loss that is comparable to the conjugate gradient and a smooth, stable convergency. To further improve the objective function of the inversion, L0-quasinorm and L1-norm have been inves tigated against L2-norm. It was found that L0 and L1 norms help increase the accuracy of the inversion, however, at the expense of its stability. Lastly, geolog ical structure constraints such as the zero cross-gradient are useful to mitigate the problem of undefined structural boundaries from inverting different types of data. Therefore, we propose to implement the zero-cross gradient method for multi-parameter inversion. Our rational is that by enforcing structural similarity in multi-parameter inversion we are reducing the number of acceptable models and ensuring a more accurate, consistent interpretation of the subsurface.

Date of Award	Dec 2021
Original language	American English