Elastodynamics for Non-linear Seismic Wave Motion in Real-Time Expert Seismolo

Abstract

Based on the new theory of Real-Time Expert Seismology, a non-linear 3-D elastic wave real-time expert system is used for the exploration globa on-shore and off-shore petroleum and gas reserves. This highly innovative and ground-breaking technology uses elastic (seismic) waves moving in an unbounded subsurface medium to searching the on-shore and off-shore hydrocarbon reserves developed on the continental crust and in deeper water ranging from 300 to 3000+ m. This modern technology can be used in any depth of sea, in oceans all over the world, and for any depth in the subsurface of existing oil and gas reserves. Furthermore, the various mechanical properties of the rock regulating the wave propagation phenomenon appear as spatially-varying coefficients in a system of time-dependent hyperbolic partial differential equations. The propagation of the seismic waves through the earth subsurface is described by the wave equation, which is finally reduced to a Helmholz differential equation. Then the Helmholtz differential equation is numerically evaluated by using the Singular Integral Operators Method (SIOM). Also, several properties are analysed and investigated for the wave equation. Finally, an application is proposed for the determination of the seismic field radiated from a pulsating sphere into an infinite homogeneous medium. The acoustic pressure radiated from the above pulsating sphere is determined by the SIOM.