Studies on the Parameter Inversion of the Bisq Model

Published: 2021-09-13 23:45:10
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Category: Physics

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Based on the solid/fluid-coupling anisotropic idea, the BISQ theory was extended to the transversely isotropic two-phase case. Yang and Zhang proposed general elastic wave propagation equations based on the BISQ theory, and further expanded these equations to the viscous elastic medium. However, too many system-specific parameters are included in BISQ model and this leads to great increase of computational complexity. In 2000, a new formulated BISQ model was presented by Mamadou and Erwin. In the new theory, the average fluid pressure term is independent of squirt flow length. Thus, for the formulated BISQ model, the computation process can be simplified efficiently. Moreover, velocity and attenuation dispersion predicted by the reformulated BISQ theory are of the same order of magnitude as those obtained with original BISQ theory. However, up to now, studies on the numerical simulations and parameters inversion of the formulated BISQ model are still in an elementary phase. Only a few researchers focus on this field. In 2013, Zhang et al used the staggered grid finite difference method to performed wave-field numerical simulations based on the formulated BISQ model. Zhou and Liu inverted the porosity of the formulated BISQ model with a rapid simulated annealing algorithm and obtained some better results.
Generally speaking, a parameter inversion problem can be reduced as an optimization problem. To solve the optimization problem, a suitable algorithm is important. The traditional optimal methods, for example gradient methods, perturbation methods et al., are both based on Newton iterative method. They are generally local convergent. On the other hand, the global optimal methods, such as genetic algorithm (GA), simulated annealing algorithm (SAA) and ant colony algorithm (ACA), require no prior assumptions or information of the objective functions in the general optimization problems. Thus, in recent years, global optimal methods, including the newly developed ant colony algorithm, have attracted the interest of numerous scholars. In 1991, Colorni et al first proposed the classical ant colony algorithm, which was an optimization methodology based on the foraging behavior of Argentine ants. Subsequently, Bilchev and Parmee presented the continuous ant colony algorithm in 1995; based on an intensive non-hierarchical process, Dreo and Siarry investigated a continuously interacting ant colony algorithm; Abdulkader et al solved the multi-compartment vehicle routing problem with a novel hybridized ant colony algorithm; Inkaya et al presented a new clustering methodology based on ant colony algorithm to deal with spatial clustering problem with no a priori information.However, it is well known that genetic manipulation provide the information difference in ACA, which easily leads to premature events. Recently, various niching techniques were developed to overcome the premature defect, such as crowding mechanism, fitness sharing principle, clearing mechanism, and clustering-based niching methods. Among them, fitness sharing principle is a well-known niching technique that offers a variety of modified schemes. Niching, as an evolutionary computation concept, was first formally applied to genetic algorithm. Subsequently, it has also been adopted to improve the performance of other algorithms, such as the ant colony algorithm, and promising results were obtained. Angus used the Crowding population-based ant colony optimization to investigate the travelling salesman problem; Zhang proposed the niche ant colony algorithm(NACA) based on the fitness sharing principle and applied it to the parameters inversion of Biot model and BISQ model, respectively. Further study shows that the anti-noise property and global convergence of the NACA in these two papers are not so good. In order to enhance the anti-noise property and global convergence of the NACA, the multi-scale inversion strategy based on the wavelet multi-resolution analysis was introduced.

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