Weaver Richard L, Lobkis Oleg I
Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, 216 Talbot Lab, 104 S. Wright Street, Urbana, Illinois 61801, USA.
J Acoust Soc Am. 2005 Jun;117(6):3432-9. doi: 10.1121/1.1898683.
Recent intense interest in diffuse field correlation functions, with applications to passive imaging in underwater acoustics and seismology, has raised questions about the degree with which a retrieved waveform can be expected to conform to the Green's function, and in particular the degree with which a ray arrival may be discerned. On considering a simple scalar wave model consisting of fields with distributed random sources, the difffuse field-field correlation function R is defined as a sum of correlation integrals, one for each of the many distinct distributed sources. It is then shown that this ensemble of fields has a correlation function with expectation (R) equal to the Green's function. This model also lends itself to calculations of the variance of R, and thus to estimates of the degree to which an R calculated using finite amounts of data will conform to the Green's function. The model predicts that such conformation is strongest at low frequencies. Ray arrivals are detectable if sufficient data have been collected, but the amount of data needed scales in three dimensions with the square of the source-receiver separation, and the square of the frequency. Applications to seismology are discussed.
近期，人们对扩散场相关函数产生了浓厚兴趣，其应用于水下声学和地震学中的被动成像，这引发了一些问题，即对于所恢复的波形，预期其符合格林函数的程度如何，特别是能否辨别出射线到达的程度。在考虑一个由具有分布式随机源的场组成的简单标量波模型时，扩散场 - 场相关函数(R)被定义为相关积分的总和，对于众多不同的分布式源中的每一个都有一个积分。然后表明，这个场的系综具有期望为((R))且等于格林函数的相关函数。该模型还便于计算(R)的方差，从而便于估计使用有限数据量计算出的(R)符合格林函数的程度。该模型预测，这种符合在低频时最强。如果收集到足够的数据，射线到达是可检测的，但所需的数据量在三维空间中与源 - 接收器间距的平方以及频率的平方成比例。文中还讨论了其在地震学中的应用。
