Inversion of seismic tomography data by Metropolis and simulated annealing algorithm

• Autorzy: Dwornik M.
• Języki publikacji: EN

Abstrakty

EN

Inversion of seismic tomography is non-uniqueness and bad-conditioned problem. Reconstruction of velocity field is a process of minimization error function between estimated and received travel times. Classical, deterministic method, like matrix decomposition or conjugate gradient, is known for finish calculation in local minimums. Other problems with deterministic methods were application of constraints to the solution. Stochastic algorithms are methods that can be helpful in solving inverse problem in seismic tomography. This paper presents application of the following two stochastic algorithms to reconstruct velocity field: Metropolis algorithm (MA) and simulated algorithm (SA). The Metropolis algorithm is an iterative method and it was first described by Metropolis et al. (1953). This method uses Boltzmann distribution to calculate probability of replacing current solution by worse one, which is modification of current. Level of acceptance is given by value of a temperature. The simulated annealing was first described by Kirkpatrick et al. (1983) and it is a modification of Metropolis algorithm. This algorithm decreased temperature during iterative process. Both algorithms were modified by adding two dimensional median filtration in a place of modification of current velocity field. This filtration was applied with some small probability. Estimation of travel times of primary seismic waves was performed using two ray-based methods: a straight line and a shortest path method (Moser 1991, Pięta & Dwornik 2009). The first method was very fast but nonrealistic in heterogeneous geological medium. The second method had over one hundred times longer calculation time, but provided real ray trajectories. The algorithms were tested in series by ten independent numerical simulations for each parameter of configuration to minimize random effects of stochastic methods. Both algorithms were initialized in two ways: by random velocity fields and by velocity field obtained by SIRT algorithm (Lo & Inderwiesen 1994). Application of median filtration and initializing by SIRT solution decreased calculation time and improved quality of inversion.

Słowa kluczowe

EN

Metropolis algorithm; Metropolis algorithm (MA); seismic tomography; inversion

• Wydawca: Wydawnictwa AGH
• Czasopismo: Geology, Geophysics and Environment
• Rocznik: 2012
• Tom: Vol. 38, no. 4
• Strony: 463--464
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Dwornik M.

• AGH University of Science and Technology, Faculty of Geology, Geophysics and Environment Protection, Department of Geoinformatics and Applied Computer Science; al. Mickiewicza 30, 30-059 Krakow, Poland

Bibliografia

• 1. Dwornik M. & Pieta A., 2009. Efficient Algorithm for 3D Ray Tracing in 3D Anisotropic Medium. 71st EAGE Conference & Exhibition incorporating SPE EUROPEC 2009, Extended Abstracts.
• 2. Kirkpatrick S., Gelatt C.D. & Vecchi M.R, 1983. Optimization by simulated annealing. Science, 220, 671-680.
• 3. Lo T. & Inderwiesen P.I., 1994. Fundamentals of seismic tomography. Geophysical Monograph Series, 6, Society of Exploration Geophysicist, 1-178.
• 4. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H. & Teller E., 1953. Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21, 6, 1087-1102.
• 5. Moser T.J., 1991. Shortest path calculation of seismic rays. Geophysics, 56, 59-67.