Full Waveform Inversion Based on Modified Quasi‐Newton Equation Quasi‐Newton Equation

Abstract

Waveform inversion is a kind of method to reveal the underground structure and lithology through minimizing the residual error between predicted wavefield and true seismic record using full‐wavefield information. In this paper, we briefly present the principle of the conventional Quasi‐Newton algorithm, and then exploit a new modified Quasi‐Newton equation to modify the conventional Davidon‐Fletcher‐Powell (DFP) and Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) algorithms. Different from past Quasi‐Newton methods, this modified BFGS considers gradient values, model information and objective function values to approximate the inverse matrix of Hessian matrix. Moreover, it almost does not increase the calculation amount for each iteration. The numerical experiment shows that compared with the conventional Quasi‐Newton method, the modified BFGS algorithm can not only preserve the inverse accuracy, but also significantly improve calculation efficiency.

3D hybrid-domain full waveform inversion on GPU

“…This could avoid the direct calculation of Jacobi matrix and partly overcome the computational bottleneck of FWI. Since then, more and more researches, involving parallel computation (Kim et al, 2013;Operto et al, 2007), algorithm (Brossier et al, 2009;Krebs et al, 2009;Liu et al, 2013c;Shin et al, 2001), modeling (Hustedt et al, 2004;Jo et al, 1996) etc., have been done to solve the FWI problems, of which local minima caused by the nonlinearity of the objective function is a key one. Bunks et al (1995) presented a multi-scale inversion through decomposing the seismic data by scale with filtering, considering there are much fewer local minima at long scales.…”

Preconditioned Conjugate Gradient Algorithm‐Based 2D Waveform Inversion for Shallow‐Surface Site Characterization

“…By using all the amplitude and phase information for seismic datasets, full-waveform inversion (FWI) [6,7] matches the observed and predicted data to reveal a highresolution and high-precision underground velocity model, and it can meet the need for velocity parameters imposed by complex structural imaging. is technique has gradually become a research hotspot in the field of seismic data inversion [8][9][10]. Previous FWI works have primarily focused on the inversion of P and S waves [11][12][13][14], but the development of surface wave FWI has become feasible [8] due to the dominance of surface wave energy in the near-surface wavefield (the vertically induced Rayleigh wave accounts for 70% of the horizontally induced Love wave for 90% of the near-surface wavefield) [15].…”

“…However, this new approximate-HM only explained the source geometric spreading. Another approach is to construct the approximate-HM by combining information from a gradient, model, and cost function, including L-BFGS [27,28], the corrected pseudo-Newton algorithm [10], and the pseudo-Newton algorithm [29].…”

The Chaotic EM Algorithm based on the L-BFGS Operator and its Application in the Path Optimization

“…, then Hessen matrix is deduced as follows (5). The specific derivation process reference the literature [10].…”

“…But the basic EM algorithm the same with other global intelligent algorithm, has premature convergence and later local search accuracy is not higher, the defects of slow convergence speed [1]. Aimed at the shortcoming of the EM algorithm, this paper puts forward algorithm to improve the local optimization strategy, adopts the high precision local optimization operatorconfined quasi-Newton operator [5] (Limited-memory BROYDEN-FLETCHER-GOLDFARB-SHANNO, L-BFGS), taking to the late algorithm to the optimal individual near solution domain for optimal; and uses the chaos mapping [6], increase the diversity of species. Particle Swarm algorithm [7] (Particle Swarm Optimization, PSO) as a more mature intelligent algorithm, in the optimization of continuous domain has very good effect, its improved algorithm, such as acceleration coefficient changing with time of Particle Swarm algorithm (Time-varying accelerator coefficients Particle Swarm Optimization, TVAC) [7][8][9] better optimization ability, thus used as a comparison with the algorithm of this paper, the simulation results show that LBFGS-EM algorithm is the basic type of electromagnetic (EM) algorithm in convergence speed and better ability to jump out of local optimal performance, comparison with the Particle Swarm Optimization (PSO) algorithm and the acceleration coefficient changing with time of Particle Swarm Optimization (PSO) algorithm in terms of solution accuracy and fast convergence is better; By in the path planning problem (0-1) application results show that the LBFGS-EM algorithm can search the best path, comparison with the genetic algorithm, particle swarm algorithm has better adaptability in discrete domain problem.…”