### Petroleum and Gas Reserves Exploration by Real-Time Expert Seismology and Non-Linear Seismic Wave Motion

#### Abstract

By using a non-linear 3-D elastic waves real-time expert system, the new theory of “*Non-linear Real-Time Expert Seismology*” is investigated, for the exploration of the on-shore and off-shore petroleum and gas reserves all over the world. Such a highly innovative and groundbreaking technology is working under Real Time Logic for searching the on-shore and off-shore hydrocarbon reserves developed on the continental crust and in deeper water ranging from 300 to 3000 m, or even deeper. Consequently, this real-time expert system, will be the best device for the exploration of the continental margin areas (shelf, slope and rise) and the very deep waters, as well. The proposed modern technology can be used at any depth of seas and oceans all over the world and for any depth in the subsurface of existing oil reserves.

Beyond the above, the various mechanical properties of 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 then reduced to a Helmholz differential equation. Furthermore, the Helmholtz differential equation is numerically evaluated by using the Singular Integral Operators Method (S.I.O.M.). Several properties are further analyzed 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. Thus, by using the S.I.O.M., then the acoustic pressure radiated from the above pulsating sphere is determined.

**Key word**** s: **Non-linear real-time expert seismology; Singular integral operators method (S.I.O.M.); Time-dependent hyperbolic partial differential equations; Oil and gas reserves; Petroleum reservoir engineering; Helmholtz differential equation; Real-time expert system; Wave equation

#### Keywords

#### References

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DOI: http://dx.doi.org/10.3968/j.aped.1925543820120401.295

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