An efficient GPU implementation for locating micro-seismic sources using 3D elastic wave time-reversal imaging
Introduction
Locating subsurface seismic sources is one of the most basic problems in geophysics. Earthquake location problems are especially widely discussed and studied in seismology. With industry's recent focus on unconventional resources such as tight gas reservoirs, shale gas, coal-bed methane, etc., locating micro-seismic events has become a technological focus in the geophysical community. By locating the micro-seismic events induced by hydraulic fracture, a reservoir engineer can depict the underground crack properties, including fracture orientation, density and dimension (Eisner et al., 2010, Maxwell and Urbancic, 2002); analyze the fracture pattern and its effect on the surrounding rock (Baig and Urbancic, 2010b, Phillips et al., 2002); identify the source mechanism (Baig and Urbancic, 2010a, Nolen-Hoeksema and Ruff, 2001); and monitor the reservoir exploitation process (Shan et al., 2002). Therefore, it is important to solve the micro-seismic location problem to facilitate unconventional oil and gas exploration and development.
The traditional earthquake location problem can be traced back to the works of Geiger in 1910 (Bratt and Bache, 1988, Geiger, 1912). Later geophysicists improved upon this work to form the Geiger method, now the most commonly used method of earthquake location. The core of the Geiger method has two parts: linearization of the nonlinear relationship between the earthquake source location and the seismic wave travel time and the use of the least squares method to solve this linear system. Due to the completeness of the evaluation system, these types of methods have been widely used in earthquake location (Flinn, 1965). These methods also have their limits, however; clear P and S wave travel times must be acquired from seismic records, which consequently must have a high signal-to-noise ratio (SNR). However, micro-seismic monitoring data are often very large datasets with a low signal-to-noise ratio. These characteristics limit traditional Geiger-type methods.
In recent years, geophysicists have applied the migration imaging principle of seismic exploration and developed migration-like locating methods that do not require seismic phase information and are suitable for low-SNR data. These methods treat micro- seismic sources in a manner analogous to diffraction within migration imaging: imaging methods from reflection seismology for processing diffraction are used to locate the source position. The corresponding locating process flow can be divided into two steps: continuation of the observation data to an underground wave field and application of the appropriate imaging conditions to obtain the source location and excitation time (Wang et al., 2013).
Time-reversal imaging micro-seismic event location technology has the advantages of being able to process low-SNR data without needing to extract seismic phase information. This approach has high locating accuracy and reliability, but because it uses wave equation time-reversal imaging technology, the number of calculations is very large. This is problematic because many applications of micro-seismic event locating occur in the real-time field monitoring of hydraulic cracks. For this reason, the location method must be computationally efficient, and therefore, these methods have not been widely used.
However, in recent years, with the heterogeneous accelerating platform developing rapidly and the coming of NVidia Compute Unified Device Architecture (CUDA), high-performance graphics processing unit (GPU) architecture has been widely applied in various intensive computing fields (Bader et al., 2011). Using GPU, many algorithms and applications in geophysics, which is traditionally among the most computationally intensive scientific research fields, have been able to run considerably more quickly. However, there has been very little work on the implementation of GPU in time-reversal imaging micro-seismic event location technology. In this paper, we focus on the implementation of high-performance 3D elastic wave seismic event location on GPU devices. After validating the high-efficiency performance in a single GPU device, we study the implementation of our method multi-GPU devices. With the acceleration brought by the use of GPU devices, which have excellent scalability, the computation time required for the 3D elastic wave time-reversal imaging micro-seismic event location method can be significantly reduced. In conclusion, by using GPU devices to run time-reversal imaging micro-seismic event location algorithms, we can achieve fast calculation speeds and high locating accuracy simultaneously.
This paper first presents the theory behind the time-reversal imaging micro-seismic event location method. It then outlines the details of the GPU implementation scheme and discusses the extensibility of the multi-GPU setup. Finally, through numerical examples, we show the validity of the principle and quantify the speedup brought by GPU devices.
Section snippets
Theory
According to the displacement representation theorem (Aki and Richards, 2002), the displacement generated by an earthquake fault can be expressed as follows:
here, represents the fault plane, represents any point on the surface of the fault, is the nth component of displacement of observation points in the direction, is the elastic modulus of the medium in the location, is the direction cosine of the fault plane
GPU implementation
The programming model for a GPU is “single instruction, multiple threads” (SIMT); that is, a command can run on a set of different data through another thread. CUDA organizes threads into block-and-grid structures; each block is assigned to a set of cores to execute in a single warp (a group of cores executing at the same time on different data) at the same time (see Fig. 2). GPU heterogeneous acceleration platforms adopt the heterogeneous offload model, which uses the GPU as a co-processor to
Numerical example
We use the finite difference method to model seismic wave propagation in a 3D elastic medium including complex topography. This method was used to generate the synthetic data sets and to propagate the time-reversed seismic signals into our model. All computations are performed with eighth-order spatial FD operators and with second-order explicit time updates. Wave-absorbing layers are implemented at the six boundaries to simulate non-reflecting boundaries (Clayton and Engquist, 1977). In this
Performance analysis
Our parallel time-reversal imaging micro-seismic event location algorithm was tested with a personal workstation with an 8-core Intel Xeon E-2650 CPU and two NVidia Tesla C2070 (Fermi) graphics cards, which each have 448 CUDA cores and 6 GB of GDDR5 onboard memory. The program runs under Centos 6.5 (64 bit). The complier environments are CUDA 6.0 and GCC 4.9.
Conclusions and future work
In this paper, we introduce the time-reversal imaging method for locating micro-seismic events with high precision. This method provides relatively high-resolution results from synthetic seismic data. Although the computation times are significantly higher than those of traditional positioning methods, the time-reversal imaging micro-seismic event location method is efficient and accurate and has excellent development prospects due to the introduction of high-performance parallel computing
Acknowledgments
The research was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant no. XDB10030500, and funded by the National Natural Science Foundation of China, China, Grant no. 41230317.
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