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.
The increase in number and strength of shallow induced seismicity connected to the Groningen gas field since 2003 and the occurrence of a M L 3.6 event in 2012 started the development of a full probabilistic seismic hazard assessment (PSHA) for Groningen, required by the regulator. Densification of the monitoring network resulted in a decrease of the location threshold and magnitude of completeness down to ∼ M L = 0.5. Combined with a detailed local velocity model, epicentre accuracy could be reduced from 0.5-1 km to 0.1-0.3 km and a vertical resolution ∼0.3 km. Time-dependent seismic activity is observed and taken into account into PSHA calculations. Development of the Ground Motion Model for Groningen resulted in a significant reduction of the hazard. Comparison of different implementations of the PSHA, using different source models, based on either a compaction model and production scenarios or on extrapolation of past seismicity, and methods of calculation, shows similar results.
We introduce seismic interferometry of passive data by multidimensional deconvolution ͑MDD͒ 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.
The last few years there has been a growing number of body-wave observations in noise records. In 1973 Vinnik conjectured that P-waves would even be the dominant wavemode, at epicentral distances of about 40 degrees and onwards from an oceanic source. At arrays far from offshore storms, surface waves induced by nearby storms would not mask the body-wave signal and hence primarily P-waves would be recorded. We measured at such an array in Egypt and indeed found a large proportion of P-waves. At the same time, a new methodology is under development to characterize the lithosphere below an array of receivers, without active sources or local earthquakes. Instead, transmitted waves are used which are caused by distant sources. These sources may either be transient or more stationary. With this new methodology, called seismic interferometry, reflection responses are extracted from the coda of transmissions. Combining the two developments it is clear that there is a large potential for obtaining reflection responses from low-frequency noise. A potential practical advantage of using noise instead of earthquake responses would be that an array only needs to be deployed for a few days or weeks instead of months, to gather enough illumination. We used a few days of continuous noise, recorded with an array in the Abu Gharadig basin, Egypt. We split up the record in three distinct frequency bands and in many small time windows. Using array techniques and taking advantage of all three-component recordings we could unravel the dominant wavemodes arriving in each time window and in each frequency band. The recorded wavemodes, and hence the noise sources, varied significantly per frequency band, and -to a lesser extent-per time window. Primarily P-waves were detected on the vertical component for two of the three frequency bands. For these frequency bands, we only selected the time windows with a favorable illumination. By subsequently applying seismic interferometry, we retrieved P-wave reflection responses and delineated reflectors in the crust, the Moho and possibly the Lehmann discontinuity.
 A number of seismic methods exist to image the lithosphere below a collection of receivers, using distant earthquakes. In the current practice, especially mode-conversions in teleseismic phases are utilized. We present a new method that takes advantage of the availability of global phases. This method is called global-phase seismic interferometry (GloPSI). With GloPSI, zero-offset reflections are extracted from reverberations near the array caused by global seismicity. We exemplify GloPSI with data from the Hi-CLIMB experiment (2002)(2003)(2004)(2005) and migrate the obtained reflection responses. This results in a 800 km long reflectivity profile through the Himalayas and a large part of the Tibetan Plateau.Citation: Ruigrok, E., and K. Wapenaar (2012), Global-phase seismic interferometry unveils P-wave reflectivity below the
S U M M A R YIn recent years, there has been an increase in the deployment of relatively dense arrays of seismic stations. The availability of spatially densely sampled global and regional seismic data has stimulated the adoption of industry-style imaging algorithms applied to converted-and scattered-wave energy from distant earthquakes, leading to relatively high-resolution images of the lower crust and upper mantle. We use seismic interferometry to extract reflection responses from the coda of transmitted energy from distant earthquakes. In theory, higher-resolution images can be obtained when migrating reflections obtained with seismic interferometry rather than with conversions, traditionally used in lithospheric imaging methods. Moreover, reflection data allow the straightforward application of algorithms previously developed in exploration seismology. In particular, the availability of reflection data allows us to extract from it a velocity model using standard multichannel data-processing methods. However, the success of our approach relies mainly on a favourable distribution of earthquakes. In this paper, we investigate how the quality of the reflection response obtained with interferometry is influenced by the distribution of earthquakes and the complexity of the transmitted wavefields. Our analysis shows that a reasonable reflection response could be extracted if (1) the array is approximately aligned with an active zone of earthquakes, (2) different phase responses are used to gather adequate angular illumination of the array and (3) the illumination directions are properly accounted for during processing. We illustrate our analysis using a synthetic data set with similar illumination and source-side reverberation characteristics as field data recorded during the 2000-2001 Laramie broad-band experiment. Finally, we apply our method to the Laramie data, retrieving reflection data. We extract a 2-D velocity model from the reflections and use this model to migrate the data. On the final reflectivity image, we observe a discontinuity in the reflections. We interpret this discontinuity as the Cheyenne Belt, a suture zone between Archean and Proterozoic terranes.
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 Green's 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 Green's function. By multidimensionally deconvolving the retrieved Green's 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 Green's function may improve significantly. We illustrate this at the hand of a numerical example and discuss the advantages and limitations of this new methodology.
S U M M A R YObtaining new seismic responses from existing recordings is generally referred to as seismic interferometry (SI). Conventionally, the SI responses are retrieved by simple crosscorrelation of recordings made by separate receivers: one of the receivers acts as a 'virtual source' whose response is retrieved at the other receivers. When SI is applied to recordings of ambient seismic noise, mostly surface waves are retrieved. The newly retrieved surface wave responses can be used to extract receiver-receiver phase velocities. These phase velocities often serve as input parameters for tomographic inverse problems. Another application of SI exploits the temporal stability of the multiply scattered arrivals of the newly retrieved surface wave responses. Temporal variations in the stability and/or arrival time of these multiply scattered arrivals can often be linked to temporally varying parameters such as hydrocarbon production and precipitation. For all applications, however, the accuracy of the retrieved responses is paramount. Correct response retrieval relies on a uniform illumination of the receivers: irregularities in the illumination pattern degrade the accuracy of the newly retrieved responses. In practice, the illumination pattern is often far from uniform. In that case, simple crosscorrelation of separate receiver recordings only yields an estimate of the actual, correct virtual-source response. Reformulating the theory underlying SI by crosscorrelation as a multidimensional deconvolution (MDD) process, allows this estimate to be improved. SI by MDD corrects for the non-uniform illumination pattern by means of a so-called point-spread function (PSF), which captures the irregularities in the illumination pattern. Deconvolution by this PSF removes the imprint of the irregularities on the responses obtained through simple crosscorrelation. We apply SI by MDD to surface wave data recorded by the Malargüe seismic array in western Argentina. The aperture of the array is approximately 60 km and it is located on a plateau just east of the Andean mountain range. The array has a T-shape: the receivers along one of the two lines act as virtual sources whose responses are recorded by the receivers along the other (perpendicular) line. We select time windows dominated by surface wave noise travelling in a favourable direction, that is, traversing the line of virtual sources before arriving at the receivers at which we aim to retrieve the virtual-source responses. These time windows are selected through a frequency-dependent slowness analysis along the two receiver lines. From the selected time windows, estimates of virtual-source responses are retrieved by means of crosscorrelations. Similarly, crosscorrelations between the positions of the virtual sources are computed to build C The
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