Applying the two-point paraxial ray tracing, we develop a technique for relative location of microseismic events. Our technique assumes the availability of a perforation shot or an already located microseismic event, termed the master, for which the paraxial ray tracing has been performed. The ray-tracing output for the master makes it possible to compute the relative locations of adjacent microseismic events, as many as a data set contains, with an efficient algorithm that requires no additional ray tracing and reduces to solving a series of simple, low-dimensional and well-behaved optimization problems. The relative event-location approach discussed in our paper is especially well suited for surface microseismic monitoring because the high accuracy of the paraxial ray approximation in the directions orthogonal to the reference rays, typically spanning the stimulated horizons for surface microseismic geometries, ensures the calculation of precise event hypocenters at appreciable distances from the master. We test the relative location technique on field data to demonstrate its accuracy, computational efficiency, and insensitivity to velocity errors.


Obtaining accurate locations of microseismic events is as important in contemporary microseismic surveys, carried out to monitor well completions in unconventional hydrocarbon reservoirs, as computing the earthquake hypocenters in the global seismology. Because of the importance of the subject, numerous techniques for locating events, pioneered by the classical Geiger’s method (Geiger, 1912), have been proposed in seismology and similar developments and refinements, accounting for salient features of unconventional reservoirs absent in the earth on a larger scale, are currently taking place in the microseismic arena.

The dependence of event hypocenters on the underlying velocity model, recognized very early in the global seismology, has led to three groups of approaches that differ from each other in how the (generally unknown) velocities are handled: first, a velocity model might be fixed a priori and the hypocenters can be computed in that model (e.g., Geiger, 1912; Asch et al., 1996; Gambino et al., 2004; Chambers et al., 2010; Ito et al., 2012); second, initially estimated velocities might be iteratively updated based on data supplied by events themselves and simultaneously with obtaining their hypocenters (e.g., Thurber, 1986; Iyer and Hirahara, 1993; Thurber and Rabinowitz, 2000; Zhang et al., 2009; Grechka and Yaskevich, 2014; Li et al., 2014); and, third, the influence of velocities on the hypocenters of events within a selected cluster might be reduced by relying on the previously located events in the same cluster and finding the hypocenters of other events relatively to them (Waldhauser and Ellsworth, 2000).

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