## 1. Introduction

[2] The production of geothermal energy and unconventional resources from tight and low-permeability reservoirs is achieved by hydraulic stimulation of the rock through borehole injection to create permeable zones, a process that involves fracture initiation and/or activation of discontinuities such as faults and joints due to pore pressure and in situ stress perturbations. Hydraulic stimulation of rock is typically accompanied by multiple microseismic events [*Zoback and Harjes*, 1997; *Fehler et al.*, 1998; *Audigane et al.*, 2002; *Rutledge and Phillips*, 2002], which are believed to be associated with rock failure. While the true nature and source of such events remains to be fully understood [*Trifu*, 2002], alternative mechanisms for triggering microearthquake (MEQ) events have been proposed in the literature. Among the existing hypotheses, pore pressure relaxation is widely studied in the literature [*Nur and Booker*, 1972; *Fletcher and Sykes*, 1977; *Ohtake*, 1974; *Pearson*, 1981; *Talwani and Acree*, 1985; *Zoback and Harjes*, 1997; *Shapiro*, 2008].

[3] The pore pressure hypothesis postulates that a rise in fluid pressure in a reservoir increases the pressure in the connected pore space of the rock, thereby increasing the pore pressure and decreasing the effective normal compressional stress on the rock surfaces. In critical locations of the rock the fall in the compressional stress can result in sliding along some of the preexisting cracks. The pore pressure relaxation hypothesis is supported by several observations [*Shapiro et al.*, 2005a, 2005b]. The spatiotemporal distribution of MEQ events has been observed to have signatures of a diffusion-like process (including a forward triggering front and back front of seismicity waves [*Audigane et al.*, 2002; *Shapiro et al.*, 2003; *Parotidis et al.*, 2004]) consistent with the diffusive nature of pore pressure distribution. Other observations supporting the above hypothesis are related to the ellipsoid-shaped seismicity clouds after normalization of the event coordinates by their occurrence time [*Shapiro et al.*, 2003] and the spatial density of MEQ events [*Shapiro et al.*, 2005b].

[4] If pore pressure diffusion can be used to explain the spatiotemporal signatures of microseismic event clouds, the MEQ events are expected to reveal important information about the distribution of hydraulic diffusivity or permeability in reservoirs. This concept has been exploited in the development of seismicity-based reservoir characterization (SBRC) methods of *Shapiro et al.* [1997, 2002, 2005a, 2005b] and *Rothert and Shapiro* [2003] where hydraulic rock properties are estimated from analysis and integration of injection-induced MEQ monitoring measurements. The SBRC analysis involves solving the parabolic equation of pore pressure diffusion in the rock mass and comparing the distribution of pore pressure with the rock criticality distribution to identify locations that undergo failure. In this context, rock criticality at a given location refers to the minimum pore pressure required to trigger a seismic event.

[5] The microseismic signals contain information about the triggering source locations and have been used to understand the hydraulic fracturing process [e.g., *Foulger et al.*, 2004; *Vandamme et al.*, 1994; *Warpinski et al.*, 1999]. Detection and interpretation of microseismic events is useful for estimating the reservoir permeability, the stimulated zone and fracture growth, as well as the geometry of the geological structures and the in situ stress state [*Warpinski et al.*, 2001; *Pine and Batchelor*, 1984]. While the SBRC approach is a useful framework for estimating large-scale reservoir properties, it can be substantially improved by developing more sophisticated inversion algorithms that offer a number of important estimation properties (features). First, the process can be automated in an iterative or sequential manner. Second, the inversion can be implemented to account for the uncertainties in the prior models or the observed microseismic events. Third, and more importantly, through a stochastic inversion approach, a mechanism can be included for quantitative assessment of the quality of the solution obtained and for rigorous characterization of solution uncertainty. The need for such a stochastic inversion approach is imperative in light of the significant uncertainties that exist in describing the spatial distribution of rock physical properties. As we will discuss soon, an outstanding challenge in applying state-of-the-art inversion method for MEQ data integration is the discrete nature of these events, which does not fit into most of the conventional estimation methods that are designed for assimilating continuous data.

[6] Adopting the pore pressure relaxation hypothesis in this study, the initiation of MEQ events can be associated with pore pressure and stress values that exceed the rock criticality. Hence, the distribution of MEQ observations in the reservoir can be correlated with pore pressure distribution, which is in turn related to hydraulic properties of the reservoir rock. Therefore, the MEQ events are viewed as a new source of monitoring measurements that, after interpretation into prior descriptive models, are expected to reveal important information about the distribution of rock flow properties.

[7] In this view, the clouds of microseismic observations in the reservoir consist of discrete events that contain information about the approximate seismic source locations where rock failure has occurred. Since most established model calibration algorithms are designed to integrate continuous measurements, inverting the discrete microseismic events calls for development of inversion methods to handle discrete data types. In some cases, however, it may be possible to equivalently interpret discrete data sets as continuous measurements (through a simple conversion) that can be readily processed using well-established inversion techniques. One way to model the MEQ data is to consider the density of these discrete events. This interpretation leads to combining (counting) the discrete microseismic events at each location in the reservoir and interpreting the results as the distribution of “seismicity density”. This conceptual framework is followed in this paper by taking advantage of kernel density estimation (KDE) methods [*Scott*, 1992; *Wand and Jones*, 1995].

[8] The KDE methods are common for smoothing data and estimating nonparametric probability density functions [*Scott*, 1992; *Wand and Jones*, 1995]. We use this approach to convert discrete MEQ events into a map of seismicity density as a continuous representation of the data. Detailed description of this method is provided in section 2. The continuous representation of MEQ data can then be used with a data integration technique to estimate the relevant reservoir properties, in this case permeability distribution. The data integration of our choice in this paper is the ensemble Kalmn filter (EnKF) [*Evensen*, 1994, 2007]. We evaluate the feasibility of using the EnKF for estimating permeability distributions from the KDE-based continuous representation of microseismic measurements.

[9] The EnKF has been widely established as a practical data integration method for large-scale nonlinear dynamical systems and has been received favorably by the scientific and research community in a range of applications including hydrology [*Reichle et al.*, 2002], meteorology and oceanography [*Evensen and van Leeuwen*, 1996; *Houtekamer and Mitchell*, 1998; *Madsen and Canizares*, 1999], groundwater model calibration [*Chen and Zhang*, 2006; *Franssen and Kinzelbach*, 2008; *Nowak*, 2009; *Schöniger et al.*, 2011], and oil reservoir characterization [*Nævdal et al.*, 2005; *Wen and Chen*, 2005; *Jafarpour and McLaughlin*, 2009; *Aanonsen et al.*, 2009; *Jafarpour and Tarrahi*, 2011]. *Evensen* [2009] reviews the EnKF formulation and its wide range of applications. *Ehrendorfer* [2007] presents a review of important issues that are encountered in implementing the EnKF. Despite the existing limitations in operational implementation of the EnKF for more complex (non-Gaussian) and challenging large-scale problems, this approach has become popular as a promising approximate nonlinear estimation method in several applications. In this paper, we propose applying the EnKF for MEQ data integration and evaluate its performance using several numerical experiments. Throughout the paper, all EnKF updates are applied to the natural logarithm of permeability.

[10] The remainder of the paper is outlined as follows. We begin with section 2, which covers an overview of the proposed framework followed by a description of each step of the formulation and a concise presentation of the experimental setup used to test the described methodology. Next, we present and discuss the results of applying the proposed approach to a series of two-dimensional and three-dimensional experiments in section 3. We close the paper with section 4, which includes general remarks about the presented formulation, its advantages, limitations and possible future extensions.