Numerical dispersion suppression based on joint deep learning in the space and wave number domains
ZHANG Yan1, CUI Linqi1, SONG Liwei2, DONG Hongli3,4
1. School of Computer and Information Technology, Northeast Petroleum University, Daqing, Heilongjiang 163318, China; 2. School of Physics and Electronic Engineering, Northeast Petroleum University, Daqing, Heilongjiang 163318, China; 3. Artificial Intelligence Energy Research Institute, Northeast Petroleum University, Daqing, Heilongjiang 163318, China; 4. Key Laboratory of Networking and Intelligent Control of Heilongjiang Province, Daqing, Heilongjiang 163318, China
Abstract：The finite-difference scheme is commonly applied in seismic prospecting for numerical simulation of wavefields. The simulation accuracy, however, is affected by the serious numerical dispersion caused by spatial coarse grids or low-order operators of difference. In this paper, a numerical dispersion suppression method based on the joint learning of deep convolutional neural networks (CNNs) is proposed, which uses CNNs to adaptively extract wavefield features for dispersion correction. Firstly, the sparse features of the wavefield data in the space and wavenumber domains are used to build a CNN based on residual learning for the extraction of the main features of the wavefield data. Secondly, the L1 norm is used for the sparse optimization of the network model, which can reduce the complexity of the model and enhance the generalization ability of the network. Finally, a joint objective optimization function is constructed to enable the network to learn the non-linear approximation capability of dispersion suppression under the semantics of the joint space-wavenumber domain constraints. The proposed method is applied to wavefield data from different forward models, and the results reveal that the method can effectively protect seismic signals and suppress dispersion; the combination of the network with migration learning is applied to the data from the new forward model, and good results can be achieved. Compared with similar algorithms, the proposed method boasts higher computational accuracy of coarse grids, lower computational costs, and a higher signal-to-noise ratio (SNR) of the obtained wavefield snapshot.
张岩, 崔淋淇, 宋利伟, 董宏丽. 基于空间—波数域联合深度学习的数值频散压制[J]. 石油地球物理勘探, 2022, 57(3): 510-524.
ZHANG Yan, CUI Linqi, SONG Liwei, DONG Hongli. Numerical dispersion suppression based on joint deep learning in the space and wave number domains. Oil Geophysical Prospecting, 2022, 57(3): 510-524.
ALFORD R M, KELLY K R, BOORE D M. Accuracy of finite-difference modeling of the acoustic wave equation[J]. Geophysics, 1974, 39(6):834-842.
[2]
DABLAIN M A. The application of high-order diffe-rencing to the scalar wave equation[J]. Geophysics, 1986, 51(1):54-66.
[3]
董良国, 李培明. 地震波传播数值模拟中的频散问题[J]. 天然气工业, 2004, 24(6):53-56.DONG Liangguo, LI Peiming. Dispersive problem in seismic wave propagation numerical modeling[J]. Natural Gas Industry, 2004, 24(6):53-56.
[4]
董良国, 马在田, 曹景忠, 等. 一阶弹性波方程交错网格高阶差分解法[J]. 地球物理学报, 2000, 43(3):411-419.DONG Liangguo, MA Zaitian, CAO Jingzhong, et al. A staggered-grid high-order difference method of one-order elastic wave equation[J]. Chinese Journal of Geophysics, 2000, 43(3):411-419.
[5]
裴正林, 何光明, 谢芳. 复杂地表复杂构造模型的弹性波方程正演模拟[J]. 石油地球物理勘探, 2010, 45(6):807-818.PEI Zhenglin, HE Guangming, XIE Fang. Elastic wave equation forward modeling for complex surface and complex structure model[J]. Oil Geophysical Prospecting, 2010, 45(6):807-818.
[6]
BOORE D M. Love waves in nonuniform wave guides:Finite difference calculations[J]. Journal of Geophysical Research, 1970, 75(8):1512-1527.
[7]
孙林洁, 印兴耀. 基于PML边界条件的高倍可变网格有限差分数值模拟方法[J]. 地球物理学报, 2011, 54(6):1614-1623.SUN Linjie, YIN Xingyao. A finite-difference scheme based on PML boundary condition with high power grid step variation[J]. Chinese Journal of Geophy-sics, 2011, 54(6):1614-1623.
[8]
FEI T, LARNER K. Elimination of numerical dispersion in finite-difference modeling and migration by flux-corrected transport[J]. Geophysics, 1995, 60(6):1830-1842.
[9]
BOOK D L, BORIS J P, HAIN K. Flux-corrected transport Ⅱ:Generalizations of the method[J]. Journal of Computational Physics, 1975, 18(3):248-283.
[10]
杨顶辉, 滕吉文. 各向异性介质中三分量地震记录的FCT有限差分模拟[J]. 石油地球物理勘探, 1997, 32(2):181-190.YANG Dinghui, TENG Jiwen. FCT finite difference modeling of three-component seismic records in anisotropic medium[J]. Oil Geophysical Prospecting, 1997, 32(2):181-190.
[11]
杨宽德, 杨顶辉, 王书强. 基于Biot-Squirt方程的波场模拟[J]. 地球物理学报, 2002, 45(6):853-861.YANG Kuande, YANG Dinghui, WANG Shuqiang. Wave-field simulation based on the Biot-Squirt equation[J]. Chinese Journal of Geophysics, 2002, 45(6):853-861.
[12]
郑海山, 张中杰. 横向各向同性(VTI)介质中非线性地震波场模拟[J]. 地球物理学报, 2005, 48(3):660-671.ZHENG Haishan, ZHANG Zhongjie. Synthetic seismograms of nonlinear seismic waves in anisotropic (VTI) media[J]. Chinese Journal of Geophysics, 2005, 48(3):660-671.
[13]
丰赟, 周竹生, 沙椿. 瑞雷波数值模拟中的数值频散校正策略及实例分析[J].中南大学学报(自然科学版), 2012, 43(6):2231-2237.FENG Yun, ZHOU Zhusheng, SHA Chun. Numerical dispersion correction method and cases analysis in numerical modeling of Rayleigh surface wave[J]. Journal of Central South University (Science and Technology), 2012, 43(6):2231-2237.
[14]
Etgen J T. A Tutorial on Optimizing Time Domain Finite-difference Schemes:"Beyond Holberg"[R]. Stanford Exploration Project, 2007.
[15]
张志禹, 谭显波, 黄璐瑶, 等. 抗频散有限差分波动方程数值模拟及逆时偏移[J]. 石油地球物理勘探, 2014, 49(6):1115-1121.ZHANG Zhiyu, TAN Xianbo, HUANG Luyao, et al. Anti-dispersion finite difference simulation and reverse-time migration for wave equations[J]. Oil Geophysical Prospecting, 2014, 49(6):1115-1121.
[16]
LIU Y. Globally optimal finite-difference schemes based on least squares[J]. Geophysics, 2013, 78(4):T113-T132.
[17]
雍鹏, 黄建平, 李振春, 等. 优化的时空域等效交错网格有限差分正演模拟[J]. 中国石油大学学报(自然科学版), 2017, 41(6):71-79.YONG Peng, HUANG Jianping, LI Zhenchun, et al. Forward modeling by optimized equivalent staggered-grid finite-difference method for time-space domain[J]. Journal of China University of Petroleum (Edition of Natural Science), 2017, 41(6):71-79.
[18]
BAI W, WANG Z, LIU H, et al. Optimisation of the finite-difference scheme based on an improved PSO algorithm for elastic modelling[J]. Exploration Geophysics, 2020, 52(2):1-12.
[19]
MIAO Z Z, ZHANG J H. Reducing error accumulation of optimized finite-difference scheme using minimum norm[J]. Geophysics, 2020, 85(5):T275-T291.
[20]
HE Z, ZHANG J, YAO Z. Determining the optimal coefficients of the finite difference method using the Remez exchange algorithm[J]. Geophysics, 2019, 84(3):S137-S147.
[21]
唐超, 文晓涛, 王文化. 基于最小范数优化交错网格有限差分系数的波动方程数值模拟[J]. 石油地球物理勘探, 2021, 56(5):1039-1047.TANG Chao, WEN Xiaotao, WANG Wenhua. Numerical simulation of wave equations based on minimum-norm optimization of staggered-grid finite-difference coefficients[J]. Oil Geophysical Prospecting, 2021, 56(5):1039-1047.
[22]
韩卫雪, 周亚同, 池越. 基于深度学习卷积神经网络的地震数据随机噪声去除[J]. 石油物探, 2018, 57(6):862-869, 877.HAN Weixue, ZHOU Yatong, CHI Yue. Deep lear-ning convolutional neural networks for random noise attenuation in seismic data[J]. Geophysical Prospecting for Petroleum, 2018, 57(6):862-869, 877.
[23]
张岩, 李新月, 王斌, 等. 基于联合深度学习的地震数据随机噪声压制[J]. 石油地球物理勘探, 2021, 56(1):9-25, 56.ZHANG Yan, LI Xinyue, WANG Bin, et al. Random noise suppression of seismic data based on joint deep learning[J]. Oil Geophysical Prospecting, 2021, 56(1):9-25, 56.
[24]
王维波, 徐西龙, 盛立, 等. 卷积神经网络微地震事件检测[J]. 石油地球物理勘探, 2020, 55(5):939-949.WANG Weibo, XU Xilong, SHENG Li, et al. Detection of microseismic events based on convolutional neural network[J]. Oil Geophysical Prospecting, 2020, 55(5):939-949.
[25]
张逸伦, 喻志超, 胡天跃, 等. 基于U-Net的井中多道联合微地震震相识别和初至拾取方法[J]. 地球物理学报, 2021, 64(6):2073-2085.ZHANG Yilun, YU Zhichao, HU Tianyue, et al. Multi-trace joint downhole microseismic phase detection and arrival picking method based on U-Net[J]. Chinese Journal of Geophysics, 2021, 64(6):2073-2085.
[26]
闫星宇, 顾汉明, 罗红梅, 等. 基于改进深度学习方法的地震相智能识别[J].石油地球物理勘探, 2020, 55(6):1169-1177.YAN Xingyu, GU Hanming, LUO Hongmei, et al. Intelligent seismic facies classification based on an improved deep learning method[J]. Oil Geophysical Prospecting, 2020, 55(6):1169-1177.
[27]
宋磊, 印兴耀, 宗兆云, 等. 基于先验约束的深度学习地震波阻抗反演方法[J].石油地球物理勘探, 2021, 56(4):716-727.SONG Lei, YIN Xingyao, ZONG Zhaoyun, et al. Deep learning seismic impedance inversion based on prior constraints[J]. Oil Geophysical Prospecting, 2021, 56(4):716-727.
[28]
唐杰, 孟涛, 韩盛元, 等. 基于多分辨率U-Net网络的地震数据断层检测方法[J]. 石油地球物理勘探, 2021, 56(3):436-445.TANG Jie, MENG Tao, HAN Shengyuan, et al. A fault detection method of seismic data based on MultiResU-Net[J]. Oil Geophysical Prospecting, 2021, 56(3):436-445.
[29]
KAUR H, FOMEL S, PHAM N. Overcoming numerical dispersion of finite-difference wave extrapolation using deep learning[C]. SEG Technical Program Expanded Abstracts, 2019, 38:2318-2322.
