G. C. Papanicolaou and K. Solna. Ray theory for a locally layered random medium. In preparation, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of its parameters. An important aspect of the estimation procedure is that it takes the tool into account. Realizing the importance of the approximation presented by O Doherty and Anstey [11] a number of authors have reexamined it and extended it to more general wave propagation scenarios [1, 3, 4, 6, 8, 9, 12, 13, 17]. Here we consider acoustic wave propagation in a layered medium with weak fluctuations. Based on the analysis in [8, 17] we obtain an approximation that reveals how the tool affects the propagating wave. Note that apparent attenuation becomes important only for relatively long propagation ....

G. C. Papanicolaou and K. Solna. Ray theory for a locally layered random medium. In preparation, 1998.

.... p z = 0: Notice that for a homogeneous medium ( and K constants) we recover the second order wave equation as we know it. The surprising fact in the O Doherty Anstey problem is that the pulse di uses about its moving center due to the disordered multiple scattering of the wave energy [1, 2, 10, 17, 26, 28]. O Doherty and Anstey s motivation for studying pulse spreading was to explore whether the scattering associated with ne scale layering in the earth could explain the observed damping of 21 seismic (acoustic) waves used in the oil exploration industry. A similar phenomenon occurs for water ....

Papanicolaou G. and K. Slna, (1998) Ray theory for a locally layered random medium, submitted to Waves in Random Media.

....locally laminated microstructure. The model is motivated by sedimentary rock structures where sedimentary cycles produce a tilted stack of layers. On top of this local variation there are coarse scale features that come from macroscopic geological events. For such a medium we have analyzed [19, 21] the spreading of an acoustic pulse due to the microscale variations in the medium parameters and in Section 5 we summarize the results. The motivation for modeling in terms of a random medium is that a detailed description of the effects of the rough microscale medium fluctuations are often not ....

....could explain the observed damping of seismic waves. In a series of papers [1, 2, 3, 4, 5, 7, 12, 13, 20] the O Doherty Anstey approximation and its generalizations have been rigorously derived, under various conditions for the medium model. They all assume, however, a strictly layered medium. In [19, 21] and this paper we follow the line of research initiated by O Doherty and Anstey, but consider more general three dimensional wave propagation problems. 1.3 Outline of paper In Section 2 we describe the model for the locally layered medium and the important scaling assumptions concerning pulse ....

[Article contains additional citation context not shown here]

Papanicolaou G. and K. Slna, Ray theory for a locally layered random medium, submitted to Waves in Random Media, (1998). 19

....well as no resolution at all (black) TRM (usually called the Phase Conjugation Mirror, in this setting) The key to the statistical stability of time reversed signals is their frequency spread. This stabilization of pulses has been seen in other contexts in stochastic equations and random media [SP00] but not in connection with time reversal, as it is presented and analyzed here. In this paper, we explore analytically and numerically the phenomenon of super resolution in time reversal in a regime of parameters where the e ects of the random medium are fully developed. This regime can be ....

....of it tends to make super resolution counter intuitive and somewhat mysterious. The explanation is that super resolution is a time domain phenomenon and it is the re compressed pulse in space and time that is statistically stable. Pulse stabilization in randomly layered media is well understood, SP00] and references therein, and the reason for this stabilization is similar to the one encountered in time reversal here. In the asymptotic limit of high frequency, short correlations and long propagation distances, described in the previous section, we also have statistical decorrelation of the ....

[Article contains additional citation context not shown here]

Knut Solna and George Papanicolaou. Ray Theory for a Locally Layered Random Medium. Random Media, 10:155-202, 2000.

....zero mean, stationary stochastic process bounded below by ( 1 d) with d a positive constant. It is assumed to have a rapidly decaying correlation function. Note that the random modulation includes the smooth function . This model can be transformed, by a change of variables as in Appendix C of [38], to the more special one in which the modulation term is a function of depth only. Hence, in the sequel we assume = z= 2 ) The uctuation embodies the random character of the medium. The forcing is due to the point source F (x; z; t) f(t= x) z z s )e; 3.3) 6 z x Point source ....

....generalized to the case with random variations also in the density . Here, for ease of presentation, we will deal exclusively with the models de ned by (3.1) 3.3) and (3.4) 3.5) and the layered versions thereof. We assume (x; z) z and the case with general is discussed in Appendix C of [38, 36]. The strongly heterogeneous model (3.2) is relevant for instance in the context of re ection seismology, in a region with strong variations in the earth parameters. Then the incident pulse is typically about 50m wide, which is large relative to the strong (in amplitude) ne scale medium ....

[Article contains additional citation context not shown here]

K. Solna and G. Papanicolaou. Ray theory for a locally layered random medium. http://georgep.stanford.edu/ papanico/pubs.html, 1999.

No context found.

PAPANICOLAOU, G. & SLNA, K., 2000, Ray theory for a locally layered random medium, Waves in Random Media, Vol. 10, pp. 151-198.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC