Non-physical energy in seismic interferometry

Abstract

Non-physical arrivals produced by seismic interferometry, the process whereby Green’s functions are synthesized between two points by cross-correlation, crossconvolution or deconvolution, are often considered to provide little information about the Earth’s subsurface. Their contributions are usually suppressed in interferometric Green’s function estimates to suit existing methods of seismic velocity estimation which favour the more familiar physical arrivals. In this thesis we show that the non-physical arrivals retrieved in exploration-type settings are useful for determining the long-wavelength seismic velocity structure and can be used to obtain improved Green’s function estimates. First, we estimate the seismic velocity and layer thickness by measuring the signal coherency along traveltime curves between two receivers in a collection of traces consisting of cross-correlated wavefields, known as the correlation gather. The traveltime curves represent the traveltime differences between wavefields recorded at the two receivers. When the procedure is used to find the velocity and thickness of the uppermost layer, the traveltime curves implicitly incorporate the physical and non-physical wavefields in the Green’s function estimates. When the procedure is applied to a model with more than one layer, the traveltime curves correspond to non-physical wavefields only in the Green’s function estimates. Instead of suppressing multiple reflections as in conventional methods, the procedure incorporates the traveltimes of multiple reflections to constrain velocity and thickness estimates. The procedure above is most suitable for recovering the first-layer seismic velocity. We propose a simpler method to estimate the seismic velocities corresponding to deeper layers. We find that the Green’s functions contain very weak reflections, but are dominated by non-physical refractions if retrieved using a limited source aperture. The seismic velocities are easily identifiable as repeating bright spots after transforming the refraction-dominated Green’s functions to the − p domain. We show that non-physical reflections can be used constructively to provide physical reflections, and therefore improved Green’s function estimates, by using a cross-convolution operation in a new variant of seismic interferometry, called source-receiver interferometry. We also show that non-physical reflections associated with the cross-correlation of reflections from different interfaces allow for the direct estimation of interval velocities and layer thicknesses. This method removes the necessity to first find the root-mean-square velocities and two-way traveltimes required to compute the interval velocities by Dix inversion. Overall, this thesis significantly improves our understanding of how nonphysical energy in seismic interferometry both provides useful information about the Earth’s subsurface and contributes to physical energy in particular interferometric methods.