Tutorial on seismic interferometry: Part 2 — Underlying theory and new advances

Abstract

In the 1990s, the method of time-reversed acoustics was developed. This method exploits the fact that the acoustic wave equation for a lossless medium is invariant for time reversal. When ultrasonic responses recorded by piezoelectric transducers are reversed in time and fed simultaneously as source signals to the transducers, they focus at the position of the original source, even when the medium is very complex. In seismic interferometry the time-reversed responses are not physically sent into the earth, but they are convolved with other measured responses. The effect is essentially the same: The time-reversed signals focus and create a virtual source which radiates waves into the medium that are subsequently recorded by receivers. A mathematical derivation, based on reciprocity theory, formalizes this principle: The crosscorrelation of responses at two receivers, integrated over different sources, gives the Green's function emitted by a virtual source at the position of one of the receivers and observed by the other receiver. This Green's function representation for seismic interferometry is based on the assumption that the medium is lossless and nonmoving. Recent developments, circumventing these assumptions, include interferometric representations for attenuating and/or moving media, as well as unified representations for waves and diffusion phenomena, bending waves, quantum mechanical scattering, potential fields, elastodynamic, electromagnetic, poroelastic, and electroseismic waves. Significant improvements in the quality of the retrieved Green's functions have been obtained with interferometry by deconvolution. A trace-by-trace deconvolution process compensates for complex source functions and the attenuation of the medium. Interferometry by multidimensional deconvolution also compensates for the effects of one-sided and/or irregular illumination.

Field observations of seismic velocity changes caused by shaking-induced damage and healing due to mesoscopic nonlinearity

“…The cross-correlation can be interpreted as the wavefield that would be measured if a source was placed at one station and a receiver at the other. Reviews and tutorials are given in Curtis et al (2006) and Wapenaar et al (2010). The velocity change can be derived by comparing individual correlation functions derived from seismic measurements recorded at different times.…”

Signal-to-Noise Ratio Estimation in Passive Correlation-Based Imaging

“…This can be obtained in open systems using the Helmholtz-Kirchhoff identity Figure 1: Schematic of passive array imaging with ambient noise sources: the grey regon is the spatial support of the noise sources, the triangles are the sensors, and the square is the reflector. [10,19], provided that the noise sources surround the region of interest. In the case of closed systems, i.e., cavities, the sources can be spatially localized provided the cavity is ergodic [1,6].…”

Electromagnetic interferometry in wavenumber and space domains in a layered earth

“…Interferometry is mainly investigated in seismics (for an overview see Schuster, 2009;Wapenaar et al, 2010aWapenaar et al, , 2010b, but can also be applied to electromagnetic wave fields and diffusive electromagnetic fields. The main purposes of applying interferometry by multidimensional deconvolution (MDD) to marine CSEM data are to suppress the airwave in a data-driven way and to minimize source position and orientation uncertainty.…”