A MATHEMATICAL MODEL OF THE CRUSTAL WAVEGUIDE

Abstract

The two-layer model of the upper crust waveguide developed in [Karakin, 1990a, Karakin and Kambarova, 1997] is studied. The upper layer is poroelastic and the lower layer (the waveguide proper) can be in poroviscous or elastic dilatancy states. The model is based on the concept of two concurrent processes that are alternately active in the lower layer (waveguide): dilatancy and compaction. Horizontal tectonic forces displace the upper layer relative to the lower one. As a result, the porous space in the lower layer experiences dilatancy expansion, and fluids are sucked into the waveguide from upper and lower layers. The porous structure of the waveguide is then destroyed, which is accompanied by the transition of the system into the poroviscous state. The lithostatic pressure expels the fluids upward from the waveguide. This paper is devoted to the mathematical analysis of this model. A new formulation of the boundary value problem is proposed and a wave solution of the pertinent equations is given. Self excited waves in crustal waveguides are assumed to provide the driving mechanism of the vertical fluid migration in the upper crust. This migration gives rise to oil and gas deposits if the fluid flows strike impermeable anticlinal beds (traps). This model is a constituent part of the general concept of the mechanism responsible for mud volcanism. Faults cutting the traps and reaching the surface initiate the formation of mud volcanoes. Analysis of the waveguide model can provide constraints on the feeding conditions of mud volcanoes. The concept of the upper crust fluid regime proposed in the paper reconciles the hypotheses of the organic and inorganic origins of hydrocarbon accumulations. Hydrocarbon fluxes enter the crustal waveguide both from above (organic origin) and from below (inorganic origin). These fluid fluxes are reworked in the waveguide, after which they move upward. As a result, accumulated hydrocarbons display features of different origins.