Wave Transmission through Random Layering with Pressure Release Boundary Conditions

This paper considers the statistical properties of the waves generated by a point source in the subsurface and transmitted towards the surface through a randomly layered medium. The problem is analyzed in a regime of separation of scales and with pressure release boundary conditions at the surface. Using a probabilistic representation of the spectral density of the waves received at the surface, the transmitted intensity is analyzed. Conserved quantities specific to the pressure release boundary conditions are evaluated and the power delay spread is computed. In particular a waveguiding effect that is produced by the reflections from the surface and from the random medium is identified and analyzed. This effect is different from the propagation in a standard waveguide from the point of view of the decay of the intensity.

[1]  Benjamin S. White,et al.  Reflection of waves generated by a point source over a randomly layered medium , 1991 .

[2]  George Papanicolaou,et al.  Transport equations for elastic and other waves in random media , 1996 .

[3]  Liliana Borcea,et al.  Filtering Deterministic Layer Effects in Imaging , 2009, SIAM Rev..

[4]  Josselin Garnier,et al.  Wave Propagation and Time Reversal in Randomly Layered Media , 2007 .

[5]  Benjamin S. White,et al.  Localization and backscattering spectrum of seismic waves in stratified lithology , 1990 .

[6]  Liliana Borcea,et al.  Filtering Deterministic Layer Effects in Imaging , 2012, SIAM Rev..

[7]  Liliana Borcea,et al.  Coherent Interferometry in Finely Layered Random Media , 2006, Multiscale Model. Simul..

[8]  S. A. Gredeskul,et al.  Waveguiding properties of randomly stratified media , 1988 .

[9]  Jean-Pierre Fouque,et al.  Pressure Fields Generated by Acoustical Pulses Propagating in Randomly Layered Media , 1998, SIAM J. Appl. Math..

[10]  A. T. Hoop.  Handbook of radiation and scattering of waves , 1995 .

[11]  Bjoern Ursin,et al.  Review of elastic and electromagnetic wave propagation in horizontally layered media , 1983 .

[12]  George Papanicolaou,et al.  Frequency Content of Randomly Scattered Signals , 1991, SIAM Rev..

[13]  Josselin Garnier,et al.  Imaging in Randomly Layered Media by Cross-Correlating Noisy Signals , 2005, Multiscale Model. Simul..

[14]  Josselin Garnier,et al.  Time reversal super resolution in randomly layered media , 2006 .

[15]  Josselin Garnier,et al.  Time-reversal refocusing for point source in randomly layered media , 2005 .

[16]  B. M. Shevtsov.  Statistical characteristics for wave-packet scattering in a layered randomly inhomogeneous medium above a reflecting surface , 1987 .

[17]  G. Papanicolaou,et al.  Reflection and Transmission of Acoustic Waves by a Locally-Layered Random Slab , 1999 .

[18]  Josselin Garnier,et al.  Coupled paraxial wave equations in random media in the white-noise regime , 2009, 0903.0449.