Kees Wapenaar

Seismic interferometry—turning noise into signal

Turning noise into useful data—every geophysicists dream? And now it seems possible. The field of seismic interferometry has at its foundation a shift in the way we think about the parts of the signal that are currently filtered out of most analyses—complicated seismic codas (the multiply scattered parts of seismic waveforms) and background noise (whatever is recorded when no identifiable active source is emitting, and which is superimposed on all recorded data). Those parts of seismograms consist of waves that reflect and refract around exactly the same subsurface heterogeneities as waves excited by active sources. The key to the rapid emergence of this field of research is our new understanding of how to unravel that subsurface information from these relatively complex-looking waveforms. And the answer turned out to be rather simple. This article explains the operation of seismic interferometry and provides a few examples of its application.

Spurious multiples in seismic interferometry of primaries

Seismic interferometry is a technique for estimating the Green’s function that accounts for wave propagation between receivers by correlating the waves recorded at these receivers. We present a derivation of this principle based on the method of stationary phase. Although this derivation is intended to be educational, applicable to simple media only, it provides insight into the physical principle of seismic interferometry. In a homogeneous medium with one horizontal reflector and without a free surface, the correlation of the waves recorded at two receivers correctly gives both the direct wave and the singly reflected waves. When more reflectors are present, a product of the singly reflected waves occurs in the crosscorrelation that leads to spurious multiples when the waves are excited at the surface only. We give a heuristic argument that these spurious multiples disappear when sources below the reflectors are included. We also extend the derivation to a smoothly varying heterogeneous background medium.

Tutorial on seismic interferometry: Part 1 — Basic principles and applications

Seismic interferometry involves the crosscorrelation of responses at different receivers to obtain the Green’s function between these receivers. For the simple situation of an impulsive plane wave propagating along the x-axis, the crosscorrelation of the responses at two receivers along the x-axis gives the Green’s function of the direct wave between these receivers. When the source function of the plane wave is a transientas in exploration seismology or a noise signalas in passive seismology, then the crosscorrelation gives the Green’s function, convolved with the autocorrelation of the source function. Direct-wave interferometry also holds for 2D and 3D situations, assuming the receivers are surrounded by a uniform distribution of sources. In this case, the main contributions to the retrieved direct wave between the receivers come from sources in Fresnel zones around stationary points. The main application of direct-wave interferometry is the retrieval of seismic surface-wave responses from ambient noise and the subsequent tomographic determination of the surfacewave velocity distribution of the subsurface. Seismic interferometry is not restricted to retrieving direct waves between receivers. In a classic paper, Claerbout shows that the autocorrelation of the transmission response of a layered medium gives the plane-wave reflection response of that medium. This is essentially 1D reflected-wave interferometry. Similarly, the crosscorrelation of the transmission responses, observed at two receivers, of an arbitrary inhomogeneous medium gives the 3D reflection response of that medium. One of the main applications of reflected-wave interferometry is retrieving the seismic reflection response from ambient noise and imaging of the reflectors in the subsurface. A common aspect of direct- and reflected-wave interferometry is that virtual sources are created at positions where there are only receivers without requiring knowledge of the subsurface medium parameters or of the positions of the actual sources.

Reflection images from ambient seismic noise

One application of seismic interferometry is to retrieve the impulse response (Greens function) from crosscorrelation of ambient seismic noise. Various researchers show results for retrieving the surface-wave part of the Greens function. However, reflection retrieval has proven more challenging. We crosscorrelate ambient seismic noise, recorded along eight parallel lines in the Sirte basin east of Ajdabeya, Libya, to obtain shot gathers that contain reflections. We take advantage of geophone groups to suppress part of the undesired surface-wave noise and apply frequency-wavenumber filtering before crosscorrelation to suppress surface waves further. After comparing the retrieved results with data from an active seismic exploration survey along the same lines, we use the retrieved reflection data to obtain a migrated reflection image of the subsurface.

Retrieval of reflections from seismic background‐noise measurements

The retrieval of the earths reflection response from cross?correlations of seismic noise recordings can provide valuable information, which may otherwise not be available due to limited spatial distribution of seismic sources. We cross?correlated ten hours of seismic background?noise data acquired in a desert area. The cross?correlation results show several coherent events, which align very well with reflections from an active survey at the same location. Therefore, we interpret these coherent events as reflections. Retrieving seismic reflections from background?noise measurements has a wide range of applications in regional seismology, frontier exploration and long?term monitoring of processes in the earths subsurface.

Retrieving the Green’s function in an open system by cross correlation: A comparison of approaches (L)

We compare two approaches for deriving the fact that the Green’s function in an arbitrary inhomogeneous open system can be obtained by cross correlating recordings of the wave field at two positions. One approach is based on physical arguments, exploiting the principle of time-reversal invariance of the acoustic wave equation. The other approach is based on Rayleigh’s reciprocity theorem. Using a unified notation, we show that the result of the time-reversal approach can be obtained as an approximation of the result of the reciprocity approach.

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

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.

Passive seismic interferometry by multidimensional deconvolution

We introduce seismic interferometry of passive data by multidimensional deconvolution (MDD) as an alternative to the crosscorrelation method. Interferometry by MDD has the potential to correct for the effects of source irregularity, assuming the first arrival can be separated from the full response. MDD applications can range from reservoir imaging using microseismicity to crustal imaging with teleseismic data.

Green's function retrieval by cross-correlation in case of one-sided illumination

The cross-correlation of acoustic wave fields at two receivers yields the exact Greens function between these receivers, provided the receivers are surrounded by sources on a closed surface. In most practical situations the sources are located on an open surface and as a consequence the illumination of the receivers is one-sided. In this Letter we discuss the conditions for accurate Greens function retrieval for the situation of one-sided illumination. It appears that the Greens function retrieval method benefits from the fact that the earth is inhomogeneous, without relying on assumptions about disorder.

Synthesis of an inhomogeneous medium from its acoustic transmission response

In 1968 Claerbout showed that the reflection response of a horizontally layered medium can be synthesized from the autocorrelation of its transmission response. During a workshop on passive imaging methods at the 2002 SEG conference, Claerbout showed that this result can be obtained straightforwardly from the principle of conservation of acoustic power. In this paper I briefly review this derivation and show that the 3D generalization can be obtained along the same lines using a power reciprocity theorem. The resulting expression confirms Claerbout9s conjecture that “by crosscorrelating noise traces recorded at two locations on the surface, we can construct the wave field that would be recorded at one of the locations if there was a source at the other.”