Abstract:
Studying seismic wave propagation in non-deterministic media is interesting as some parts of the Earth (e.g. in the continental lower crust) may be amenable to a stochastic description. In this paper we study the acoustic response of a 1-D binary stochastic fractal medium and separate the single- from the multiple-scattered wavefield. We show that, for our models with scales that (partly) overlap the seismic bandwidth, amplitude changes occur due to both the presence of multiple scattering and the multiscale nature of the impedance contrasts. We study these changes as functions of σc (a measure of the nominal bimodal reflection coefficient), ka (a measure of the relative length scales of the medium compared to the wavelength of the probing waves) and γ, the scatterer density. As our models are binary (two lithologies), the results should be interpreted as an upper bound for the general class of acoustic 1-D stochastic fractal model responses. We present a measure to quantify the interference of single- and multiple-scattered wavefields, and use this measure to study the importance of the three aforementioned dependences. Since stochastic fractal media have been proposed for Ivrea-type lower crust, we relate our results to such a model and find that amplitudes may increase by up to 45±15 per cent. The contribution of multiple scattering to this increase ranges from 1±1 to 20±15 per cent, the main contribution being due to the multiscale nature of the impedance contrasts. We claim that the parameters used to model Ivrea-type lower crust (σc=5 per cent, γ≈5×10-2, 1≤ka≤24 and μ=9.6×10-1) are robust, although we recognize that the scatterer density γ is determined by the vertical sampling Δz in our models. The heuristic argument that extra geometrical spreading in two/three dimensions will further diminish the importance of multiple-scattering effects, combined with our results, makes it tempting to claim that multiple scattering is not important for 2/3-D generalizations of our 1-D models. However, in the light of indirect evidence for the importance of multiple scattering in Ivrea-type lower crust reported by other authors, we argue that elasticity (P-S conversions) may be important. Therefore, we believe that it is necessary to study the 2-D case with a similar direct approach to that presented in this paper before a satisfactory conclusion can be drawn about the validity of the standard processing of deep seismic reflection data and the importance of multiple scattering.