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The finite difference method is widely used in seismic wave numerical simulation, reverse time migration and full waveform inversion. However, the numerical dispersion problem seriously affects the...

Full waveform inversion and reverse time migration are active research areas for seismic exploration. Forward modeling in the time domain determines the precision of the results, and numerical solutions of finite difference have been widely adopted as an important mathematical tool for forward modeling. In this article, the optimum combined of window functions was designed based on the finite difference operator using a truncated approximation of the spatial convolution series in pseudo-spectrum space, to normalize the outcomes of existing window functions for different orders. The proposed combined window functions not only inherit the characteristics of the various window functions, to provide better truncation results, but also control the truncation error of the finite difference operator manually and visually by adjusting the combinations and analyzing the characteristics of the main and side lobes of the amplitude response. Error level and elastic forward modeling under the proposed combined system were compared with outcomes from conventional window functions and modified binomial windows. Numerical dispersion is significantly suppressed, which is compared with modified binomial window function finite-difference and conventional finite-difference. Numerical simulation verifies the reliability of the proposed method.

Jia Jun Weng,*,1 Li Hua Wang,*,1 Hao Zhu,2 Wen Rong Xu,1 Yu Mei Wei,1 Zhi Yang Wang,1 Wen Juan Yu,1 Hua Fang Li1,3–41Department of Psychiatry, Shanghai Mental Health Center, Shanghai Jiao Tong University of Medicine, Shanghai, People’s Republic of China; 2Department of Anesthesiology, Renji Hospital, Shanghai Jiao Tong University of Medicine, Shanghai, People’s Republic of China; 3Shanghai Key Laboratory of Psychotic Disorders, Shanghai, People’s Republic of China; 4Clinical Research Center, Shanghai Jiao Tong University School of Medicine, Shanghai, People’s Republic of China*These authors contributed equally to this workObjective: Some lines of evidence show that D2/D3 receptor partial agonist pramipexole may be effective in the treatment of extrapyramidal symptoms (EPS) and psychiatric symptoms of schizophrenia. Therefore, we analyzed whether a low dose of pramipexole (0.375–0.75 mg/day) has efficacy on EPS and symptoms of schizophrenia while maintaining tolerability.Methods: Ten subjects with EPS [including drug-induced parkinsonism (DIP) and akathisia] were recruited in a stage-1, open-label pilot study. All the subjects were treated with a low dose of pramipexole. The evaluations were performed at baseline, day 3, week 1, week 2, week 4, week 6, and week 8. The ratings of SAS, BARS, PANSS, CDSS, and CGI-S and adverse effects (AE) were recorded in every visit.Results: SAS total scores decreased significantly during the study in patients with DIP (P

The implicit finite-difference schemes make the process of numerical simulation possess higher accuracy and stability. However, most of the conventional implicit schemes have the limitation of lower computational efficiency because of the requirement of solving large scale matrix equation. In this paper, we first propose an optimized implicit staggered-grid finite-difference scheme based on first order velocity-stress elastic wave equation. Then we transform the new scheme from the time-space domain into the time-wavenumber domain, and construct the objective function by means of the two norm theory. Different from traditional global optimized schemes, we select the simulated annealing algorithm to get optimized coefficients. According to the shot records and wavefield snapshots acquired by homogeneous medium model and complex medium model numerical simulations, the optimized implicit staggered-grid finite-difference scheme not only reduces the calculating amount, but also suppresses the numerical dispersion, thus improves the precision of numerical simulation remarkably.

The finite-difference method has been widely utilized in seismic wave numerical modeling, seismic imaging, and full waveform inversion; the accuracy of finite-difference numerical solution directly affects the result of seismic imaging and inversion. We can truncate spatial convolutional counterpart of the pseudo-spectral method to get finite-difference operators using truncated windows, and the properties of truncated windows in their amplitude responses play a major role in finite-difference approximation. In specific, the accuracy of finite-difference approximation can be determined by the properties of main lobe and side lobe in the amplitude response of window functions, narrower main lobe and larger attenuation of side lobe bring higher accuracy of finite-difference approximation, and significantly suppress numerical dispersion. According to it, we propose an optimized method based on Chebyshev auto-convolution combined window function which has narrow main lobe and large attenuation of side lobe. Through adjusting three parameters of the Chebyshev auto-convolution combined window function, we visually and more intuitively control the properties of main lobe and side lobe to adjust the accuracy of finite-difference approximation. The optimized explicit finite-difference operator increases the accurate wave number coverage range and reduces the volatility of accuracy error, which indicates that the accuracy of low-order operators can reach that of high-order operators. In respect of economics, it effectively reduces the computational cost and improves the computational efficiency.