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AAPG GEO 2010 Middle East
Geoscience Conference & Exhibition
Innovative Geoscience Solutions – Meeting Hydrocarbon Demand in Changing Times
March 7-10, 2010 – Manama, Bahrain

Particle Swarm and Differential Evolution Optimization - Global Optimization for Geophysical Inversion

Puneet Saraswat1

(1) Applied Geophysics, Indian School of Mins University, dhanabd, India.

Inversion of pre- and post-stack seismic data for acoustic and shear impedance is highly non-linear and ill-posed. In this paper we report on the application of two new global optimization schemes, namely, Particle Swarm Optimization (PSO) and Differential Evolution (DE) to the problem of stochastic inversion of post-stack seismic data. A starting model is drawn from a fractional Gaussian distribution (based on a fractal model) and a suitably defined objective function is optimized in search of acceptable models using PSO and DE. Our investigations reveal that both the methods have nice convergence properties. However, the DE converges at least 10 times faster than PSO. We demonstrate the performance of these methods with application to synthetic and field seismic data.
The social behavior observed in a flock (swarm) of birds and in insects searching food has been simulated to develop a global optimization strategy popularly known as the Particle Swarm Optimization (PSO). Particle Swarm Optimization (PSO) emulates the social behaviours in a flock of birds (swarm) in solving an optimization problem. It utilizes both local and global properties of the swarm to formulate a novel search strategy that guides the swarm towards the best solution with constant updating of the cognitive and social knowledge of the particles in the swarm.

Differential Evolution (DE) is a novel parallel direct search method which utilizes NP parameter vectors
xi,G, i = 0, 1, 2, ... , NP-1. (11)
as a population for each generation G. NP doesn’t change during the minimization process. It is a Evolutionary algorithm suggested by Storn and Price(1996).It is based on swarm optimization along with genetic mutation , recombination and selection criteria to optimize a given problem.It also utilizes local and global properties of swarm along with their genetic development.
We used PSO and DE for Inverting the Seismic Log data(both real and synthetic) and comparing the computed and observed seismogram(generated using Convolution forward model , Inverted for Acoustic Impedance and results showed an appropriate match with the observed value one and was obtained within 1000 iterations and swarm of 100 in PSO and 10 times the unknown parameters in DE.The model parameters are resolved satisfactorily in both the cases.
error function used

We used the PSO and DE algorithm described above to invert synthetic as well as field Seismic data. For both these cases, we selected 100 particles in the swarm and executed the routine for 1000 iterations. We generated Seismic data from well log for a number of cases from simple single trace well log to multiple traces log and inverted for Acoustic Impedance and Reflectivity series ranging from 70-500 layered earth . We worked out on synthetic seismogram(from a well log) and Ricker wavelet (30 Hz ,2ms)

We also considered real seismic data of Oil and Natural Gas Corporation of India for Mehsana district of Gujarat (fig4) and Inverted it using PSO and DE

In this study we reported the utility of swarm intelligence in solving multi-parameter optimization problems in geophysics. Seismic data has been inverted using a classical particle swarm and differential evolution optimizer with 100 individuals in a swarm. For synthetic as well as field data sets, the solutions obtained explain the observed data satisfactorily besides exhibiting acceptable resolution for the model parameters.