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Introduction

Seismic imaging based on the single scattering assumption, also known as Born approximation, consists of two main steps: wavefield reconstruction which serves the purpose of propagating recorded data from the acquisition surface back into the subsurface, followed by an imaging condition which serves the purpose of highlighting locations where scattering occurs. This framework holds both when the source of seismic waves is located in the subsurface and the imaging target consists of locating this source, as well as when the source of seismic waves is located on the acquisition surface and the imaging target consists of locating the places in the subsurface where scattering or reflection occurs. In this paper, I concentrate on the case of imaging seismic sources located in the subsurface, although the methodology discussed here applies equally well for the more conventional imaging with artificial sources.

An example of seismic source located in the subsurface is represented by micro-earthquakes triggered by natural causes or by fluid injection during reservoir production or fracturing. One application of micro-earthquake location is monitoring of fluid injection in brittle reservoirs when micro-earthquake evolution in time correlates with fluid movement in reservoir formations. Micro-earthquakes can be located using several methods including double-difference algorithms (Waldhauser and Ellsworth, 2000), Gaussian-beam migration (Rentsch et al., 2007,2004), diffraction stacking (Gajewski et al., 2007) or time-reverse imaging (Gajewski and Tessmer, 2005; Artman et al., 2010).

Micro-earthquake location using time-reverse imaging, which is also the technique advocated in this paper, follows the same general pattern mentioned in the preceding paragraph: wavefield-reconstruction backward in time followed by an imaging condition extracting the image, i.e. the location of the source. The main difficulty with this procedure is that the onset of the micro-earthquake is unknown, i.e. time $ { t } =0$ is unknown, so the imaging condition cannot be simply applied as it is usually done in zero-offset migration. Instead, an automatic search needs to be performed in the back-propagated wavefield to identify the locations where wavefield energy focuses. This process is difficult and often ambiguous since false focusing locations might overlap with locations of wavefield focusing. This is particularly true when imaging using an approximate model which does not explain all random fluctuations observed in the recorded data. This problem is further complicated if the acquisition array is sparse, e.g. when receivers are located in a borehole. In this case, the sparsity of the array itself leads to artifacts in the reconstructed wavefield which makes the automatic picking of focused events even harder.

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Figure 1.
Schematic representation of focus constructions using time reversal. Each line in the plots represents a wavefront reconstructed at the source from a given receiver. The panels represent the following cases: (a) dense acquisition, complete angular coverage and correct velocity, (b) dense acquisition, partial angular coverage and correct velocity, (c) dense acquisition, partial angular coverage and incorrect velocity, and (d) sparse acquisition, partial angular coverage and incorrect velocity. Panel (d) represents the worst case scenario for micro-earthquake imaging.
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The process by which sampling artifacts are generated is explained in Figures 1(a)-1(d). Each segment in Figure 1(a) corresponds to a wavefront reconstructed from a receiver. For dense, uniform and wide-aperture receiver coverage and for reconstruction using accurate velocity, the wavefronts overlap at the source position, Figure 1(b). This idealized situation resembles the coverage typical for medical imaging, although the physical processes used are different. However, if the velocity used for wavefield reconstruction is inaccurate, then the wavefronts do not all overlap at the source position, Figure 1(c), thus leading to imaging artifacts. Likewise, if receiver sampling is sparse, reconstruction at the source position is incomplete, Figure 1(d), even if the velocity used for reconstruction is accurate. The cartoons depicted in Figures 1(a)-1(d) represent an ideal situation with receivers surrounding the seismic source, which is not typical for seismic experiments. In those cases, source illumination is limited to a range which correlates with the receiver coordinates.

In general, artifacts caused by unknown velocity fluctuations and receiver sampling overlap and, although the two phenomena are not equivalent, their effect on the reconstructed wavefields are analogous. As illustrated in the following sections, the general character of those artifacts is that of random wavefield fluctuations. Ideally, the imaging procedure should attenuate those random wavefield fluctuations irrespective of their cause in order to support automatic source identification.


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Next: Conventional imaging condition Up: Micro-earthquake monitoring with sparsely-sampled Previous: Micro-earthquake monitoring with sparsely-sampled

2013-08-29