Seismic wave propagation stitching: Matching local and global techniques

Multiple methods exist for modeling with synthetic seismograms, each with its own characteristic application; local and detailed; global and asymptotic; body and/or surface waves. Events such as the nuclear tests in the Tarim Basin in China, recorded at regional distances require more than one such characteristic. A successful model would need detail close in and a global result. The ability to join two methods can therefore be very powerful. Within this text the exploration is of finite difference and discrete wavenumber integration methods. The basis of the conversion between methods is the idea in Huygen's principle of representing a wave front as multiple sources, then propagated as an alternate method. Modeling detail locally, finite difference eventually becomes computationally intensive or undetailed. Representation theory replaces finite difference with discrete wavenumber integration propagating to the receiver at a regional distance. The requirement for multiple sources means that efficiency and optimization of methods are paramount