Applications of Ant Colony Optimization in determination of source parameters from total gradient of potential fields

Abstract

A unified interpretation technique, based on the computation of total gradient from first order horizontal and vertical derivatives of a measured anomaly, namely, magnetic, gravity or self-potential, can be used to determine horizontal location, depth, and the nature of the causative source geometry. The total gradient, in general, may exhibit several symmetrical bell-shaped functions of different magnitudes and with different decay rates β-termed as 'source geometry factor' to describe the nature of the causative sources. β-values have been presented for idealized source geometries producing three different types of measurements (anomalies). The non-linear inversion of the total gradient with multiple sources of different geometries is accomplished through Ant Colony Optimization (ACO) -a technique with only a few demonstrated applications in geophysical problems. We have also implemented the ACO which, in its original form, is suitable for discrete space or combinatorial optimization in a continuous model space using decimal coding. Moreover, unlike conventional techniques based on pre-specified moving/ fixed data length windows, the proposed technique uses much of the total gradient data points except at the ends of the profile (where error in the total gradient can be large). The presence of singularity in the Euler technique in the analysis of a gravity anomaly over a thick faulted slab has been overcome by the total gradient ACO method. A procedure has also been formulated for analysing gravity and reduced to pole (RTP) total field magnetic anomalies over spherical and vertical cylindrical source geometries. To evaluate the efficacy of the proposed technique, ACO results are compared with other modern techniques, namely, Particle Swarm Optimization (PSO), Enhanced Local Wavenumber (ELW) and the Euler method through simulated data contaminated with random noise and three field examples. This study has revealed that the total gradient ACO technique leads to better convergence towards the global minimum and also better inversion results than those obtained by the PSO and other techniques mentioned above. Unlike the ELW and Euler techniques, the total gradient analysis provides enhanced resolution for interfering sources.ity equation based on a moving window of a pre-specified length (ii) Enhanced local wavenumber (fixed window length around the center of the peak)/ tilt angle (Salem et al. , 2008 using a 2D moving window of a pre-specified length; and (iii) amplitude of the analytic signal analysed with a few selected points (Agarwal 1984;Roest et al. 1992;Shaw and Agarwal 1997;Keating and Sailhac 2004;Salem 2005; Srivastava and Agarwal 2010 and others). With these techniques, the interpreter first pre-selects a window length in one or two dimension(s) and then, depending upon the technique, situates the window over the centre of the peak position or moves it over the entire Geophysical Equipment Source FOR MARINE SALES AND RENTALS www.geomatrix.co.uk Our expertise covers all aspects of marine geophysical surv...

Grey wolf optimizer: a new strategy to invert geophysical data sets

“…The TG peak #4, with shape factor of 0.46 corresponds to a contact/fault (Srivastava et al . ). The drill hole data indicates two pyrite zones at depths of 4.6 and 6.1 m, respectively (Telford et al .…”

“…Srivastava et al . () developed a generalized interpretation technique, based on the computation of total gradient (TG) synonymous with amplitude of analytical signal (Nabighian et al . , b), from first‐order horizontal and vertical derivatives of a measured anomaly, for example magnetic, gravity or self‐potential.…”

“…Srivastava et al . () have shown that the source geometry factor (beta) is twice the shape factor ( q ).…”

“…Thereby the number of omega wolves is 4 in each of the examples considered. Srivastava et al (2014) developed a generalized interpretation technique, based on the computation of total gradient (TG) synonymous with amplitude of analytical signal (Nabighian et al 2005a, b), from first-order horizontal and vertical derivatives of a measured anomaly, for example magnetic, gravity or self-potential. Nabighian et al (2005a, b) using the concept of total gradient showed that the gravity and magnetic anomalies follow:…”

“…The relationships between most geophysical observables and model parameters are non-linear. Geophysical inversions have been attempted both through local optimization techniques (Inman 1975;More 1978;Menke 1984;Tarantola 1987;Pilkington 1997 among others) and non-linear optimization techniques (Shaw and Srivastava 2007;Srivastava and Agarwal 2010, Santos 2010, Srivastava et al 2014. Sen and Stoffa (2013) have given a detailed account of the use of global optimization techniques to invert various geophysical data types.…”