Study of normal mode solutions for seismo-acoustic propagation scenarios, A: a generalized range-independent case, earthquake modeling using seismic moment tensors, and an improved moment tensor inversion method

Abstract

This work presents improvements to the study of tsunamigenic offshore earthquakes and complex earthquakes, i.e., earthquakes that are better represented as multiple events, through the use of underwater acoustic normal mode solutions and updated inversion techniques. When considering offshore earthquakes, normal mode solutions, i.e., analytic solutions that can be expressed as an infinite sum of residues, are used to model the acoustic field generated by an event. The environment under consideration, an ocean environment where water is overlying the seafloor, is approximated as a fluid layer overlying an elastic bottom. A source, such as an explosion or earthquake, is represented as a point source that is located in either the water column or the sediment layer. Using a generalized Green's function formulation for normal mode solutions, accurate solutions are obtained for various source cases and are benchmarked against elastic parabolic equation solutions that have been previously benchmarked against wavenumber integration solutions. Normal mode solutions for seismo-acoustic propagation problems using generalized Green's functions can then be used to study tsunamigenic earthquakes. Moment tensor representations of earthquake sources are used to find forcing terms that represent earthquakes of varying shear-to-compressional composition. The extension of this technique to a range-dependent environment where a coupling integral technique is used to ensure mode coupling across range segments is then explored. When considering complex events that do not necessarily occur offshore, the environment being considered is now the earth rather than the ocean. In this case it is beneficial to find characteristics of the earthquake instead of studying pressure fields generated by events. Using normal mode solutions of this new system, a matrix-vector equation may be found which, through least-squares inversion techniques, can characterize a complex earthquake as two near-simultaneous events rather than a single event. This allows for a more accurate characterization of the earthquake being modeled. A statistical test is used to compare results from a single source inversion to results obtained with a double source inversion and select the most appropriate number of sources for any given earthquake.