Abstract
Reflecting properties of layered geological media are substantiated in the framework of phonon-phonon mechanism of elastic wave propagation in porous media. In this scope the reflection coefficient is calculated using not impedances but impulses of phonons in adjoining porous media. Assuming for the first approximation that rocks do fulfill an average time equation we got an expression for the reflection coefficient via porosity factors of that geological medium. For calculation of reflection coefficient the wavelength is chosen as averaging line scale. These coefficients are calculated at every depth point for a set of frequencies in seismic range. Resulting curves have special depth points. Being cross-plotted in time-frequency space such points do form coherent units. These units we call effective boundaries, because they cause all reflections for the given media in the framework of considered model. Effective boundaries are not wide-band as for two half spaces but have a cutoff at some low frequency. Geological medium at a whole is characterized by the system of such effective boundaries that are capable to form a reflection waves field. To construct this field an algorithm is developed that solves the direct problem of seismic in the framework of effective boundaries theory. This algorithm is illustrated with vibroseis survey modeling for a specific geological section.
Highlights
Reflecting properties of layered geological media are substantiated in the framework of phonon-phonon mechanism of elastic wave propagation in porous media
Assuming for the first approximation that rocks do fulfill an average time equation we got an expression for the reflection coefficient via porosity factors of that geological medium
We proposed a mechanism of elastic waves propagation in rocks [1] that justified an independence of logarithmic decrement on frequency or, equivalent, justified an absence of velocity dispersion when an attenuation does take place
Summary
We proposed a mechanism of elastic waves propagation in rocks [1] that justified an independence of logarithmic decrement on frequency or, equivalent, justified an absence of velocity dispersion when an attenuation does take place. That is why we do not consider many models of elastic waves propagation in heterogeneous media among which the Biot model [3,4] is the most popular This model describes the elastic waves propagation in the media with the solid matrix and many recent works attend to it [5,6,7]. This model does not comply with the frequency independence of decrement. Justification is based on a specific type of heterogeneous medium-porous fluid-saturated rocks with an average time equation fulfilled. These were the media where an experimental testing of a proposed mechanism was allowed. The aim of the paper is to substantiate the reflection properties of layered geological media in the framework of phonon-phonon mechanism and to create on that basis an algorithm for solving the direct seismic problem
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