Equivalence of the virtual-source method and wave-field deconvolution in seismic interferometry

Abstract

Seismic interferometry and the virtual-source method are related approaches for extracting the Green's function that accounts for wave propagation between receivers by making suitable combinations of the waves recorded at these two receivers. These waves can either be excited by active, controlled, sources, or by natural incoherent sources. We compare this technique with the deconvolution of the wave field recorded at different receivers. We show that the deconvolved wave field is a solution of the same wave equation as that for the physical system, but that the deconvolved wave forms may satisfy different boundary conditions than those of the original system. We apply this deconvolution approach to the wave motion recorded at various levels in a building after an earthquake, and show how to extract the building response for different boundary conditions. Extracting the response of the system with different boundary conditions can be used to enhance, or suppress, the normal-mode response. In seismic exploration this principle can be used for the suppression of surface-related multiples.

Interferometry by Deconvolution of Multicomponent Multioffset GPR Data

“…In the left-hand side of (2), a reflection response occurs at the receiver level due to a source at that same level. We have hereby created a new response through deconvolution that can be understood as a weighted form of cross correlation, for which reason we call it IbD [23]. A straight division as described in (2) can be numerically unstable, and a stabilized version is given bŷ…”

Spectral power density of the random excitation for the photoacoustic wave equation

“…Eq. (32) states that the spectral power density of the system can be obtained correlating the calculated photoacoustic pressure waves at different locations due to the random excitation. Therefore, the impulse response of photoacoustic systems can be obtained utilizing the method presented in the next section and the representation theorems of the convolution type and the correlation type.…”

“…For example, Snieder obtained the Green's function for the diffusive medium. 21 There are a lot of applications of this technique in the fields of ultrasound, [21][22][23][24][25][26][27][28] exploration seismology, 21,29,30 structural engineering, 31,32 numerical modeling, 33 and crustal seismology. 21,[23][24][25]34 In this work, the superposition of the Green's function and its complex conjugate (time reversal counterpart) is retrieved from the correlation of photoacoustic waves excited by random point sources a Electronic mail: hakan.erkol@boun.edu.tr 2158-3226/2014/4(9)/097103/11 C Author(s) 2014 4, 097103-1 inside the volume.…”

Elastodynamic Marchenko Focusing, Green's Function Retrieval and Imaging

“…Note that G +,+ and G −,+ are defined in the actual medium, whereas R(p, z i , τ) is defined in a reference medium that is identical to the actual medium below z i and reflection-free above z i . Resolving R from equation (4) involves "seismic interferometry by deconvolution" (Snieder et al, 2006;Vasconcelos and Snieder, 2008;van der Neut et al, 2011). We illustrate this with a numerical example.…”