Elastic parabolic equation solutions for underwater acoustic problems using seismic sources

Abstract

Several problems of current interest involve elastic bottom range-dependent ocean environments with buried or earthquake-type sources, specifically oceanic T-wave propagation studies and interface wave related analyses. Additionally, observed deep shadow-zone arrivals are not predicted by ray theoretic methods, and attempts to model them with fluid-bottom parabolic equation solutions suggest that it may be necessary to account for elastic bottom interactions. In order to study energy conversion between elastic and acoustic waves, current elastic parabolic equation solutions must be modified to allow for seismic starting fields for underwater acoustic propagation environments. Two types of elastic self-starter are presented. An explosive-type source is implemented using a compressional self-starter and the resulting acoustic field is consistent with benchmark solutions. A shear wave self-starter is implemented and shown to generate transmission loss levels consistent with the explosive source. Source fields can be combined to generate starting fields for source types such as explosions, earthquakes, or pile driving. Examples demonstrate the use of source fields for shallow sources or deep ocean-bottom earthquake sources, where down slope conversion, a known T-wave generation mechanism, is modeled. Self-starters are interpreted in the context of the seismic moment tensor.

Elastic parabolic equation solutions for oceanic T-wave generation and propagation from deep seismic sources

“…Transmission loss in elastic sediment layers is calculated using the dilatation and scaling factors associated with the Lam e parameters of the media where the source and receiver are located. 17,18 …”

“…29 Elastic self-starter fields derived for the (u r ,w) formulation 20 have recently been implemented and tested in underwater propagation scenarios, 17 and have been benchmarked against normal mode solutions. 30 Specifically, self-starters representing purely compressional (explosive) and purely shear (faulting) type sources demonstrated varied acoustic fields in the water column.…”

“…The seismic moment tensor has been used to show the shear seismic self-starter corresponds to a fault plane perpendicular to the (r,z) computational domain that slips in the r direction. 17 These starters can be combined to represent a large class of realistic seismic sources. Transmission loss in elastic sediment layers is calculated using the dilatation and scaling factors associated with the Lam e parameters of the media where the source and receiver are located.…”

“…Recently benchmarked seismic source fields for elastic parabolic equation solutions provide a new tool for investigation of T-wave generating mechanisms and subsequent propagation through the deep ocean 17 or coastal areas. 18 A key benefit is that T-waves in a) Electronic mail: scott.frank@marist.edu range-dependent environments can be generated without added theoretical and computational steps required by hybrid methods or coupled normal mode solutions.…”

Root finding in the complex plane for seismo-acoustic propagation scenarios with Green's function solutions

“…Figure 3 shows the solution from the Green's function formulation (dashed curve) compared to a solution computed using a wave number integration model, OASES (solid curve), 17 that is known to give accurate results for range-independent seismo-acoustic problems, including those with compressional sources. 18 Assuming the bottom depth is H ¼ 500 m, the source depth is z s ¼ H þ d ¼ 600 m (i.e., d ¼ 100 m), and using the geoacoustic parameters given in Table II losses differ (with greater differences when the receiver depths are closer to the interface). At ranges farther from the source, the shapes of the curves and computed losses move closer to each other and become in excellent agreement.…”