Deyan Draganov

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.

Seismic interferometry using multidimensional deconvolution and crosscorrelation for crosswell seismic reflection data without borehole sources

Crosswell reflection method is a high-resolution seismic imaging method that uses recordings between boreholes. The need for downhole sources is a restrictive factor in its application, for example, to time-lapse surveys. An alternative is to use surface sources in combination with seismic interferometry. Seismic interferometry (SI) could retrieve the reflection response at one of the boreholes as if from a source inside the other borehole. We investigate the applicability of SI for the retrieval of the reflection response between two boreholes using numerically modeled field data. We compare two SI approaches — crosscorrelation (CC) and multidimensional deconvolution (MDD). SI by MDD is less sensitive to underillumination from the source distribution, but requires inversion of the recordings at one of the receiver arrays from all the available sources. We find that the inversion problem is ill-posed, and propose to stabilize it using singular-value decomposition. The results show that the reflections from deep boundaries are retrieved very well using both the CC and MDD methods. Furthermore, the MDD results exhibit more realistic amplitudes than those from the CC method for downgoing reflections from shallow boundaries. We find that the results retrieved from the application of both methods to field data agree well with crosswell seismic-reflection data using borehole sources and with the logged P-wave velocity.

Passive seismic imaging in the presence of white noise sources

Passive seismic imaging is based on the relation between the reflection and the transmission responses of the subsurface. Let one have the transmission responses measured at surface points A and B of a 3D inhomogeneous medium in the presence of white noise sources in the subsurface. When these transmission responses are cross-correlated, one obtains the reflection response of the same medium as if measured at point A in the presence of an impulsive source at point B. The quality of the simulated reflection response strongly depends on the whiteness and the distribution of the noise sources. Reflectors present below the sources cause the appearance of some ghost events. Random distribution of the noise sources will, however, weaken these ghost events.

Improved surface‐wave retrieval from ambient seismic noise by multi‐dimensional deconvolution

The methodology of surface?wave retrieval from ambient seismic noise by crosscorrelation relies on the assumption that the noise field is equipartitioned. Deviations from equipartitioning degrade the accuracy of the retrieved surface?wave Greens function. A point?spread function, derived from the same ambient noise field, quantifies the smearing in space and time of the virtual source of the Greens function. By multidimensionally deconvolving the retrieved Greens function by the point?spread function, the virtual source becomes better focussed in space and time and hence the accuracy of the retrieved surface?wave Greens function may improve significantly. We illustrate this at the hand of a numerical example and discuss the advantages and limitations of this new methodology.

Seismic interferometry: a comparison of approaches

We discuss three approaches to seismic interferometry and compare their underlying assumptions. In the first approach the reflection response is reconstructed by cross-correlating the responses of many uncorrelated noise sources. In the second approach a depth image is obtained from the response of a single source, recorded by many receivers. In the third approach the Green’s function is reconstructed by cross-correlating the recordings of two receivers in a diffuse field.

Introduction to the supplement on seismic interferometry

In 1968, J. F. Claerbout derived a remarkable relation between the transmission and reflection responses of a horizontally layered medium, bounded by a free surface (Claerbout, 1968). He showed that autocorrelation of the transmission response is equal to the reflection response plus its time-reversed version (plus an impulse at time zero).

Retrieving the Earth’s Reflection Response by Multi-dimensional Deconvolution of Ambient Seismic Noise

A major assumption for retrieving the earth’s reflection response with seismic interferometry by cross-correlation of ambient noise is that subsurface sources are uniformly distributed. It has been shown that interferometry by multi-dimensional deconvolution can cope with non-uniform source arrays, but implementation of this concept requires a separation of the incident wavefield from the free-surface multiples. For transient passive sources, this separation can be implemented by time-gating in the recorded transmission panels before cross-correlation, but such methodology cannot be applied for simultaneously acting noise sources. Here we show that time-gating can also be applied after an intermediate cross-correlation step. In cross-correlated data, we isolate events around t=0, which inhabit the illumination imprint of the subsurface sources. Next, we apply multi-dimensional deconvolution with the isolated events to the events away from t=0. In this way we can effectively correct for the effects of a non-uniform subsurface source distribution in data that is already cross-correlated. With this new approach, multi-dimensional deconvolution becomes feasible for simultaneously acting noise sources.

Seismic Interferometry on background‐noise field data

Seismic Interferometry (SI) can construct reflection data from seismic background noise. In recent years, several authors developed the theory and applied it to synthetic data. With field data, the only success until now was the reconstruction of surface waves from coda and microseisms. Here, we attempt to reconstruct reflection events from noise data recorded in a desert area. The SI result shows inclined and horizontal coherent events. Some of the reconstructed events appear to align with reflections from an active survey. We cannot, however, exclude alternative explanations.