Seismic interferometry by crosscorrelation and by multidimensional deconvolution: a systematic comparison

Abstract

S U M M A R YSeismic interferometry, also known as Green's function retrieval by crosscorrelation, has a wide range of applications, ranging from surface-wave tomography using ambient noise, to creating virtual sources for improved reflection seismology. Despite its successful applications, the crosscorrelation approach also has its limitations. The main underlying assumptions are that the medium is lossless and that the wavefield is equipartitioned. These assumptions are in practice often violated: the medium of interest is often illuminated from one side only, the sources may be irregularly distributed, and losses may be significant. These limitations may partly be overcome by reformulating seismic interferometry as a multidimensional deconvolution (MDD) process. We present a systematic analysis of seismic interferometry by crosscorrelation and by MDD. We show that for the non-ideal situations mentioned above, the correlation function is proportional to a Green's function with a blurred source. The source blurring is quantified by a so-called interferometric point-spread function which, like the correlation function, can be derived from the observed data (i.e. without the need to know the sources and the medium). The source of the Green's function obtained by the correlation method can be deblurred by deconvolving the correlation function for the point-spread function. This is the essence of seismic interferometry by MDD. We illustrate the crosscorrelation and MDD methods for controlled-source and passive-data applications with numerical examples and discuss the advantages and limitations of both methods.

On Green's function retrieval by iterative substitution of the coupled Marchenko equations

“…This problem has been mitigated to some extent by separating upgoing and downgoing waves prior to redatuming, which was made possible by the deployment of multicomponent receivers (Mehta et al 2007). Wapenaar et al (2011) demonstrated that redatuming of the complete wavefield can be achieved by multidimensional deconvolution of the separated wavefields. To establish this technology, knowledge was required of the Green's functions (including all orders of internal multiples) as they would be recorded at depth due to sources at the surface.…”

Inter-source seismic interferometry by multidimensional deconvolution (MDD) for borehole sources

“…We follow the derivation in Wapenaar et al (2011) by separating the wavefield at D  into outgoing and incoming components, and approximating the normal derivative of the wavefield in the high frequency regime by multiplying each component with a pseudodifferential operator jH  , where the minus-sign applies to outgoing waves, plus-sign to incoming waves. Because it is homogeneous outside D,…”

“…Alternatively, SI by MDD has the potential of correcting for a non-ideal source distribution and intrinsic losses by deblurring the correlation function by the interferomeric point-spread function Bakulin 2009, van der Neut et al 2011). Wapenaar et al (2011) derived a form of inter-receiver SI by MDD for receivers in the subsurface and sources on the surface. We show that by invoking source and receiver reciprocity, one can obtain a similar form of inter-source SI by MDD to create a virtual acquisition geometry corresponding to borehole sources and receivers.…”

Improving Repeatability of Land Seismic Data Using Virtual Source Approach Based on Multidimensional Deconvolution

“…A deeper insight into the correlation function composition gives a relationship that can be used in MDD (Wapenaar et al, 2011): Here integration is performed over the receiver array along the surface , is the subsurface reflection response, depending solely on the properties of the medium and not on the source signatures, is the point-spread function:…”