Efficient and accurate numerical simulation of seismic wave propagation is important in various Geophysical applications such as seismic full waveform inversion (FWI) problem. However, due to the large size of the physical domain and requirement on low numerical dispersion, many existing numerical methods are inefficient for numerical modelling of seismic wave propagation in an heterogenous media. Despite the great efforts that have been devoted during the past decades, it still remains a challenging task in the development of efficient and accurate finite difference method for multi-dimensional acoustic wave equation with variable velocity. In this paper we proposed a Padé approximation based finite difference scheme for solving the acoustic wave equation in threedimensional heterogeneous media. The new method is obtained by combining the Padé approximation and a novel algebraic manipulation. The efficiency of the new algorithm is further improved through the Alternative Directional Implicit (ADI) method. The stability of the new algorithm has been theoretically proved by energy method. The new method is conditionally stable with a better Courant -Friedrichs -Lewy condition (CFL) condition, which has been verified numerically. Extensive numerical examples have been solved, which demonstrated that the new method is accurate, efficient and stable.

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Abstract-In this paper, we embedded the genetic algorithm (GA) into the inner loop of the simulated annealing (SA) with a special design. The new method will boost the tunability of the searching process by providing two scales of regulation in seismic inversion problem. Moreover, a quantified uncertainty of the inversion result can be obtained when we put this strategy under Bayesian framework. Real data tests are conducted to support the theoretical calculation. Based on the conventional sparse spike inversion results, as a part of the prior information, our proposed method presents a superior quality and convincible uncertainty description.

Conventional full waveform inversion (FWI) using least square distance (LSD) between the observed and predicted seismograms suffers from local minima. Recently, earth mover's distance (EMD) has been introduced to FWI to compute the misfit between two seismograms. Instead of comparisons bin by bin, EMD allows to compare signal intensities across different coordinates. This measure has great potential to account for time and space shifts of events within seismograms. However, there are two main challenges in application of EMD to FWI. The first one is that the compared signals need to satisfy nonnegativity and mass conservation assumptions. The second one is that the computation of EMD between two seismograms is a computationally expensive problem. In this paper, a strategy is used to satisfy the two assumptions via decomposition and recombination of original seismic data. In addition, the computation of EMD based on dynamic formulation is formulated as a convex optimization problem.A primal-dual hybrid gradient method with linesearch has been developed to solve this large-scale optimization problem on GPU device. The advantages of the new method are that it is easy to implement and has high computational efficiency. Compared to LSD based FWI, the computation time of the proposed method will approximately increase by 11% in our case studies. A 1D