Wang, Shucheng (China University of Petroleum–Beijing) | Xia, Muming (China University of Petroleum–Beijing) | Zhou, Hui (China University of Petroleum–Beijing) | Wang, Ning (China University of Petroleum–Beijing) | Fang, Jinwei (China University of Petroleum–Beijing)
In this paper, lattice Boltzmann method (LBM) is employed in forward modeling of seismic P-wave propagation. By choosing different relaxation factors in numerical experiments and using spectrum ratio method, the relationship between the quality factor
Presentation Date: Wednesday, September 27, 2017
Start Time: 4:45 PM
Presentation Type: ORAL
In this paper, the Lattice Spring Model (LSM) is adopted in forward modeling of elastic waves propagation in solid medium by combination with the Verlet Algorithm. Different from the traditional methods, such as Finite Difference Method (FDM), Finite Element Method (FEM) etc., LSM is a new method which is not based on the wave equations, but on the microcosmic mechanism that causes wave propagation. Firstly, the origin and history of LSM is introduced. Secondly, the theoretical framework of LSM is elaborated and a stability condition for the evolution of this system is deduced. Then, some numerical results of LSM are demonstrated and they are compared with the wave fields obtained by FDM. Finally, a brief conclusion is drawn based on the previous discussions.
First devised by Grest and Webman in 1984, Lattice Spring Model (LSM) is a collection of linear springs connected at nodes distributing on a cubic lattice used for describing solid medium (Grest and Webman, 1984; Hassold and Srolovitz, 1989). In order to model materials of different Poisson’s ratios, angular springs are added to the original linear spring system (Wang, 1989). Ladd and Kinney (1997) developed this model by taking the idea of elastic element to improve its calculation precision. Such a simple model is sufficient to simulate heterogeneous elastic medium, and its application can be seen in modeling deformation and failure (Ladd and Kinney, 1997; Buxton et al., 2001; Zhao et al., 2011).
As is known to all, extensive research has been performed to solve the dynamic problems involving waves, and FDM is the most frequently used numerical method, which solves the wave equation by finite difference approximation of its partial derivative (Toomey and Bean, 2000). Yim and Sohn (2000) adopted a model similar to LSM for visualization of ultrasonic waves, but the evolution of wave fields are calculated by FDM. Pazdniakou and Adler (2012) made a further introduction of LSM and laid the foundation for its potential application in wave propagation in porous media in the low frequency band. Xia et al. (2014) modeled P waves from low frequencies (seismic frequency) to high frequencies (sonic log frequency) by importing a stability conditional for LSM dynamics.
Zhang, Qingchen (China University of Petroleum) | Zhou, Hui (China University of Petroleum) | Wang, Jie (SINOPEC Geophysical Research Institute) | Zuo, Anxin (China University of Petroleum) | Xia, Muming (China University of Petroleum)
Due to the gradient calculation requiring cross-correlation of the forward wavefields and back-propagated residual wavefields at each time step, the great storage amount becomes an obstacle of practical application of full-waveform inversion, especially in three-dimensional elastic case in time domain. In this paper we extend the efficient boundary storage to the time domain three-dimensional elastic full-waveform inversion on multi-GPU. Based on the efficient boundary storage strategy, the storage amount can be reduced dramatically. As a result, we can save the partial forward wavefields directly on the GPU memory and reconstruct the full forward wavefields synchronized with back-propagated residual wavefields along the reverse time direction. This strategy avoids frequent CPU-to-GPU or GPU-to-CPU memory copy (extremely time-consuming) at the cost of the recomputation (little time-consuming) of the forward wavefields. Our forward simulation tests show that the GPU’s supercomputing effect can be fully exploited with this strategy. In addition, we perform a three-parameter simultaneous inversion of P-, S-wave velocities and density. The favorable inversion results verify that our algorithm is feasible and efficient.
Xia, Muming (China University of Petroleum) | Zhou, Hui (China University of Petroleum) | Li, Qingqing (China University of Petroleum) | Yuan, Jiang (China University of Petroleum) | Zuo, Anxin (China University of Petroleum) | Qu, Shan (China University of Petroleum)
SUMMARY This paper presents a novel method known as Lattice Spring Model (LSM) to model P-waves for different frequencies. We detailed the basic theories and governing equations for LSM, and the Verlet Algorithm originally devised for molecular dynamics was used for the evolution of the wave field. By introducing a stability condition, the new method can be used to model waves in a wide frequency band, and such a theory was tested by some numerical examples. INTRODUCTION The usual ways to simulate elastic waves are the Finite Element Method (FEM), Boundary Element Method (BEM), and Finite Difference Method (FDM). In this abstract, we are trying to develop a Lattice Spring Model (LSM) for the numerical analysis of waves in a wide frequency band.