Introduction

Microseismic monitoring is a technique that can provide real-time information about subsurface stimulated fracture networks. Microseismic data analysis involves passive seismic source localization (Maxwell, 2014). The traditional method is arrival-time inversion with traveltime picking adopted from global earthquake seismology (Warpinski et al., 1998; Gibowicz and Kijko, 2013). However, traveltimes can be difficult to pick (Duncan and Eisner, 2010). Alternative source localization methods without traveltime picking have been suggested, including the method described by Rentsch et al. (2007,2010) and inspired by Gaussian-beam migration, time reversal imaging (Gajewski and Tessmer, 2005; Artman et al., 2010) and diffraction moveout stacking (Gajewski et al., 2007; Kao and Shan, 2004).

Conventional assumption for time-reversal microseismic localization is based on wave-equation imaging with densely sampled data and a known velocity. However, sparse downhole geophones and subjective velocity estimation both involve randomness which interferes with wavefield reconstruction and degrades the accuracy of source localizations (Sava, 2011). Complementarily, surface-sensor networks can be denser and more portable than borehole sensors, which resolves the problem of receivers sparsity; a surface network can be designed and optimized with the given aperture and fold requirements (Duncan and Eisner, 2010). Yet the surface network is still sensitive to velocity errors under conventional depth imaging methods (Eisner et al., 2009).

As noted by Kao and Shan (2004) and Gajewski et al. (2007), passive seismic events can be focused by diffraction-type migration because of their similarity to diffractions in zero-offset sections. Migration applied on time-delayed data resembles reverse wavefield propagation, in which signals focus at source locations and true activating times. Microseismic monitoring can benefit from migration-based detection techniques that obtain a high value of the stack along the moveout curve, which overcomes the low signal-to-noise ratio (SNR) of the unstacked data (Chambers et al., 2010; Gharti et al., 2010; Duncan and Eisner, 2010; Bradford et al., 2013). Recently, Anikiev et al. (2013) and Staněk et al. (2015) suggested source mechanism correction combined with diffraction stacking in microseismic imaging.

Path-integral imaging provides an efficient way to image diffractions in time coordinates without velocity picking and produces a velocity independent image of the subsurface (Landa et al., 2006). Methodology of path-integral diffraction imaging (Burnett et al., 2011) is summation of a set of constant velocity images, generated by velocity continuation (Fomel, 2003b); in time domain, diffraction apices remain stationary whereas diffraction flanks change their shape. Stacking superimposes diffraction apices constructively and cancels flanks. An efficient workflow for path-integral imaging that combines velocity continuation and summation within analytical integration was recently proposed by Merzlikin and Fomel (2015). This method only requires a crude velocity range as a constraint instead of detailed velocity estimation. Furthermore, time-domain migration itself is not sensitive to prior velocity models (Fomel, 2014), and velocity analysis can be performed using double path-integral formulation (Merzlikin and Fomel, 2015; Schleicher and Costa, 2009).

In this paper, we propose to apply path-integral time-domain migration in a similar direct analytical way on microseismic data for imaging of passive sources. Prior estimation of the velocity model is not required. Instead, only a rough velocity range is necessary. The unknown activation times can be scanned since passive seismic energy will focus at true times and locations. This resembles the focusing of energy in back propagation wave process. We use synthetic data experiments to test the proposed method.