COMPARATIVE STUDY OF META-HEURISTIC SEARCH ALGORITHMS USING SEISMIC WAVEFORM INVERSION

Abstract

Seismic inverse problems include minimization of error between the observed and synthetic seismograms to obtain the model parameters that will provide quantitative information about the subsurface. Generally we face two problems: 1) the model space is very large and 2) the error function is multimodal. Existing calculus based methods are local in scope and easily get trapped in local minima of error function. Other methods such as Simulated Annealing (SA), Genetic Algorithm (GA) and Harmony Search (HS) can be applied to solve such global optimization problems and these don't depend on starting model and do not require any gradient information. All these methods bear analogy to natural systems and are robust in nature. For e.g. HS was conceptualized using musical process of searching for perfect state of harmony SA based on freezing of liquid or recrystallization of metals in an annealing process'and GA based on natural selection and the mechanism of population genetics. We have applied the recently developed HS meta-heuristic algorithm successfully, to the inversion of band limited synthetic data in the presence of random noiseand compared the results obtained with SA and GA. For this purpose a prototype program was designed in C sharp. The use of plane wave reflectivity seismogram enables us to do large number of forward calculations very rapidly. We found that by performing a few HS inversion with varying pitch and bandwidth, we can approximately locate the best fit value in minimum iteration. However, it is found that HS converges much faster and provides best fitness and model parameters values, in comparison to SA or GA even if high iteration is given. This happens because the guidance of search has very low probability for randomization in HS. Further, HS is able to vary the adaption rate from beginning to end of computations, which resembles SA. It also considers several vectors simultaneously in a manner similar to GA. Hence HS takes care of complexity of problems very easily.