The optimal nearly-analytic discrete(ONAD) method is a new numerical method developed in recent years for solving the wave equation.Compared with other methods,such as popularly-used finite-difference methods,the ONAD...The optimal nearly-analytic discrete(ONAD) method is a new numerical method developed in recent years for solving the wave equation.Compared with other methods,such as popularly-used finite-difference methods,the ONAD method can effectively suppress the numerical dispersion when coarse grids are used.In this paper,the ONAD method is extended to solve the 2-dimensional SH-wave equation in the spherical coordinates.To investigate the accuracy and the efficiency of the ONAD method,we compare the numerical results calculated by the ONAD method and other methods for both the homogeneous model and the inhomogeneous IASP91 model.The comparisons indicate that the ONAD method for solving the SH-wave equation in the spherical coordinates has the advantages of less numerical dispersion,small memory requirement for computer codes,and fast calculation.As an application,we use the ONAD method to simulate the SH-wave propagating between the Earth's surface and the core-mantle boundary(CMB).Meanwhile,we investigate the SH-wave propagating in the mantle through analyzing the wave-field snapshots in different times and synthetic seismograms.展开更多
In this study,we implement forward modeling and inversion based on deep-learning strategies using an optimal nearly analytic discrete(ONAD)method.The forward-modeling method combines the ONAD method with recurrent neu...In this study,we implement forward modeling and inversion based on deep-learning strategies using an optimal nearly analytic discrete(ONAD)method.The forward-modeling method combines the ONAD method with recurrent neural network(RNN)for the fi rst time.RNN is a type of neural network that is suitable for sequential data,which uses information from both previous and current times to obtain output information.We express the ONAD method using an RNN framework to advance the time iteration of an acoustic equation.This process can simplify programming using RNN and convolution kernels.Next,we use deep learning based on the proposed forward-modeling method to study full waveform-inversion problems.Because the main purpose of inversion is to minimize the error between real and synthetic data,inversion is essentially an optimization problem.Many new optimizers are available in the framework of deep learning,such as the Adam and Nadam optimizers,which are used for optimizing velocity model in the inversion process.We perform six numerical experiments.The first two experiments demonstrate the forward-modeling results,which indicate that the forward-modeling method can effectively suppress numerical dispersion and improve computational effi ciency.The other four experiments demonstrate the inversion results,which show that the method proposed in this paper can eff ectively realize inversion imaging.We compare several optimizers used in deep learning and find that the Nadam optimizer has faster convergence and better effectiveness based on the ONAD method combined with RNN.展开更多
Using staggered-grid finite difference method to solve seismic wave equation,large spatial grid and high dominant frequency of source cause numerical dispersion,staggeredgrid finite difference method,which can reduce ...Using staggered-grid finite difference method to solve seismic wave equation,large spatial grid and high dominant frequency of source cause numerical dispersion,staggeredgrid finite difference method,which can reduce the step spatial size and increase the order of difference,will multiply the calculation amount and reduce the efficiency of solving wave equation.The optimal nearly analytic discrete(ONAD)method can accurately solve the wave equation by using the combination of displacement and gradient of spatial nodes to approach the spatial partial derivative under rough grid and high-frequency condition.In this study,the ONAD method is introduced into the field of reverse-time migration(RTM)for performing forward-and reverse-time extrapolation of a two-dimensional acoustic equation,and the RTM based on ONAD method is realized via normalized cross-correlation imaging condition,effectively suppressed the numerical dispersion and improved the imaging accuracy.Using ONAD method to image the groove model and SEG/EAGE salt dome model by RTM,and comparing with the migration sections obtained by staggered-grid finite difference method with the same time order 2 nd and space order 4 th,results show that the RTM based on ONAD method can effectively suppress numerical dispersion caused by the high frequency components in source and shot records,and archive accurate imaging of complex geological structures especially the fine structure,and the migration sections of the measured data show that ONAD method has practical application value.展开更多
基金supported by National Science Fund of Distinguished Young Scholars of China(Grant No. 40725012)40821002)National Natural Science Foundation of China (Grant No. 41074073)
文摘The optimal nearly-analytic discrete(ONAD) method is a new numerical method developed in recent years for solving the wave equation.Compared with other methods,such as popularly-used finite-difference methods,the ONAD method can effectively suppress the numerical dispersion when coarse grids are used.In this paper,the ONAD method is extended to solve the 2-dimensional SH-wave equation in the spherical coordinates.To investigate the accuracy and the efficiency of the ONAD method,we compare the numerical results calculated by the ONAD method and other methods for both the homogeneous model and the inhomogeneous IASP91 model.The comparisons indicate that the ONAD method for solving the SH-wave equation in the spherical coordinates has the advantages of less numerical dispersion,small memory requirement for computer codes,and fast calculation.As an application,we use the ONAD method to simulate the SH-wave propagating between the Earth's surface and the core-mantle boundary(CMB).Meanwhile,we investigate the SH-wave propagating in the mantle through analyzing the wave-field snapshots in different times and synthetic seismograms.
基金supported by the National Key Research and Development Project of China (No. 2017YFC1500301)the Joint Earthquake Research Program of the National Natural Science Foundation and the China Earthquake Administration (No. U1839206)the National Natural Science Foundation of China (No. 41974114)
文摘In this study,we implement forward modeling and inversion based on deep-learning strategies using an optimal nearly analytic discrete(ONAD)method.The forward-modeling method combines the ONAD method with recurrent neural network(RNN)for the fi rst time.RNN is a type of neural network that is suitable for sequential data,which uses information from both previous and current times to obtain output information.We express the ONAD method using an RNN framework to advance the time iteration of an acoustic equation.This process can simplify programming using RNN and convolution kernels.Next,we use deep learning based on the proposed forward-modeling method to study full waveform-inversion problems.Because the main purpose of inversion is to minimize the error between real and synthetic data,inversion is essentially an optimization problem.Many new optimizers are available in the framework of deep learning,such as the Adam and Nadam optimizers,which are used for optimizing velocity model in the inversion process.We perform six numerical experiments.The first two experiments demonstrate the forward-modeling results,which indicate that the forward-modeling method can effectively suppress numerical dispersion and improve computational effi ciency.The other four experiments demonstrate the inversion results,which show that the method proposed in this paper can eff ectively realize inversion imaging.We compare several optimizers used in deep learning and find that the Nadam optimizer has faster convergence and better effectiveness based on the ONAD method combined with RNN.
基金financially supported by the National Key R&D Program of China(No.2018YFC1405900)the National Natural Science Foundation of China(No.41674118)+1 种基金the Fundamental Research Funds for the Central Universities(No.201822011)the National Science and Technology Major Project(No.2016ZX05027-002)。
文摘Using staggered-grid finite difference method to solve seismic wave equation,large spatial grid and high dominant frequency of source cause numerical dispersion,staggeredgrid finite difference method,which can reduce the step spatial size and increase the order of difference,will multiply the calculation amount and reduce the efficiency of solving wave equation.The optimal nearly analytic discrete(ONAD)method can accurately solve the wave equation by using the combination of displacement and gradient of spatial nodes to approach the spatial partial derivative under rough grid and high-frequency condition.In this study,the ONAD method is introduced into the field of reverse-time migration(RTM)for performing forward-and reverse-time extrapolation of a two-dimensional acoustic equation,and the RTM based on ONAD method is realized via normalized cross-correlation imaging condition,effectively suppressed the numerical dispersion and improved the imaging accuracy.Using ONAD method to image the groove model and SEG/EAGE salt dome model by RTM,and comparing with the migration sections obtained by staggered-grid finite difference method with the same time order 2 nd and space order 4 th,results show that the RTM based on ONAD method can effectively suppress numerical dispersion caused by the high frequency components in source and shot records,and archive accurate imaging of complex geological structures especially the fine structure,and the migration sections of the measured data show that ONAD method has practical application value.
