Frequency-domain elastic full-waveform multiscale inversion method based on dual-level parallelism

The complexity of an elastic wavefield increases the nonlinearity of inversion, To some extent, multiscale inversion decreases the nonlinearity of inversion and prevents it from falling into local extremes. A multiscale strategy based on the simultaneous use of frequency groups and layer stripping method based on damped wave field improves the stability of inversion. A dual-level parallel algorithm is then used to decrease the computational cost and improve practicability. The seismic wave modeling of a single frequency and inversion in a frequency group are computed in parallel by multiple nodes based on multifrontal massively parallel sparse direct solver and MPI. Numerical tests using an overthrust model show that the proposed inversion algorithm can effectively improve the stability and accuracy of inversion by selecting the appropriate inversion frequency and damping factor in low- frequency seismic data.

Frequency-domain auto-adapting full waveform inversion with blended source and frequency-group encoding

As a high quality seismic imaging method, full waveform inversion （FWI） can accurately reconstruct the physical parameter model for the subsurface medium. However, application of the FWI in seismic data processing is computationally expensive, especially for the three-dimension complex medium inversion. Introducing blended source technology into the frequency-domain FWI can greatly reduce the computational burden and improve the efficiency of the inversion. However, this method has two issues： first, crosstalk noise is caused by interference between the sources involved in the encoding, resulting in an inversion result with some artifacts; second, it is more sensitive to ambient noise compared to conventional FWI, therefore noisy data results in a poor inversion. This paper introduces a frequency-group encoding method to suppress crosstalk noise, and presents a frequency- domain auto-adapting FWI based on source-encoding technology. The conventional FWI method and source-encoding based FWI method are combined using an auto-adapting mechanism. This improvement can both guarantee the quality of the inversion result and maximize the inversion efficiency.

Three-dimensional frequency-domain full waveform inversion based on the nearly-analytic discrete method

The nearly analytic discrete(NAD)method is a kind of finite difference method with advantages of high accuracy and stability.Previous studies have investigated the NAD method for simulating wave propagation in the time-domain.This study applies the NAD method to solving three-dimensional(3D)acoustic wave equations in the frequency-domain.This forward modeling approach is then used as the“engine”for implementing 3D frequency-domain full waveform inversion(FWI).In the numerical modeling experiments,synthetic examples are first given to show the superiority of the NAD method in forward modeling compared with traditional finite difference methods.Synthetic 3D frequency-domain FWI experiments are then carried out to examine the effectiveness of the proposed methods.The inversion results show that the NAD method is more suitable than traditional methods,in terms of computational cost and stability,for 3D frequency-domain FWI,and represents an effective approach for inversion of subsurface model structures.

A Numerical Method on Inverse Determination of Heat Transfer Coefficient Based on Thermographic Temperature Measurement

The heat transfer coefficient in a multidimensional heat conduction problem is obtained from the solution of the inverse heat conduction problem based on the thermographic temperature measurement. The modified one-dimensional correction method （MODCM）, along with the finite volume method, is employed for both two- and three-dimensional inverse problems. A series of numerical experiments are conducted in order to verify the effectiveness of the method. In addition, the effect of the temperature measurement error, the ending criterion of the iteration, etc. on the result of the inverse problem is investigated. It is proved that the method is a simple, stable and accurate one that can solve successfully the inverse heat conduction problem.

A DISCRETE ALGORITHM FOR COMPLEX FREQUENCY-DOMAIN CONVOLUTIONS

A discrete algorithm suitable for the computation of complex frequency-domain convolution on computers was derived. The Durbin's numerical inversion of Laplace transforms can be used to figure out the time-domain digital solution of the result of complex frequency-domain convolutions. Compared with the digital solutions and corresponding analytical solutions, it is shown that the digital solutions have high precision.

Estimation of vertical diffusion coefficient based on a onedimensional temperature diffusion equation with an inverse method

Diapycnal mixing is important in oceanic circulation. An inverse method in which a semi-explicit scheme is applied to discretize the one-dimensional temperature diffusion equation is established to estimate the vertical temperature diffusion coefficient based on the observed temperature profiles. The sensitivity of the inverse model in the idealized and actual conditions is tested in detail. It can be found that this inverse model has high feasibility under multiple situations ensuring the stability of the inverse model, and can be considered as an efficient way to estimate the temperature diffusion coefficient in the weak current regions of the ocean. Here, the hydrographic profiles from Argo floats are used to estimate the temporal and spatial distribution of the vertical mixing in the north central Pacific based on this inverse method. It is further found that the vertical mixing in the upper ocean displays a distinct seasonal variation with the amplitude decreasing with depth, and the vertical mixing over rough topography is stronger than that over smooth topography It is suggested that the high-resolution profiles from Argo floats and a more reasonable design of the inverse scheme will serve to understand mixing processes.

Inverse Piston Problem for the System of One-Dimensional Isentropic Flow

In this paper, the authors consider the inverse piston problem for the system of one-dimensional isentropic flow and obtain that, under suitable conditions, the piston velocity can be uniquely determined by the initial state of the gas on the right side of the piston and the position of the forward shock.

Application of Frequency-Domain Waveform Inversion Method in Marmousi Shots Data

Frequency-domain waveform seismic tomography includes modeling of wave propagation and full waveform inversion of correcting the initial velocity model. In the forward modeling, we use direct solution based on sparse matrix factorization, combined with nine-point finite-difference for the linear system of equations. In the waveform inversion, we use preconditioned gradient method where the preconditioner is provided by the diagonal of the approximate Hessian matrix. We successfully applied waveform inversion method from low to high frequency in two sets of Marmousi data. One is the data set generated by frequencydomain finite-difference modeling, and the other is the original Marmousi shots data set. The former result is very close to the true velocity model. In the original shots data set inversion, we replace the prior source with estimated source; the result is also acceptable, and consistent with the true model.

INVERSE SCATTERING PROBLEM FOR ONE-DIMENSIONAL SCHRDINGER OPERATORS RELATED TO THE GENERAL STARK EFFECT

This paper disccusses the inverse scattering problem for one-dimensional Schrodinger operatorsrelated to the general Stark effect. We provide a ganeral framework which can be applied both to theStark-effect operator and the ordinary Schrodinger operator.