Finding sets of acceptable solutions with a genetic algorithm with application to surface wave group dispersion in Europe

Abstract

We discuss the use of a genetic algorithm (GA) to invert data for many acceptable solutions, in contrast to inversion for a single, “optimum” solution. The GA is a directed search method which does not need linearization of the forward problem or a starting model, and it can be applied with a very large model‐space. Consequently, fewer assumptions are required and a greater range of solutions is examined than with many other inversion methods. We apply the GA to fundamental Rayleigh group dispersion estimates for paths across Central Europe and across the East European Platform to determine “average”, layered S velocity models separately for each region. The use of the GA allows an identical model parameterization and broad parameter search range to be used for both regions. The scatter of acceptable solutions shows velocity‐depth trade‐offs around the Moho, indicates the depth resolution of the inversion, and shows the uncertainty in upper mantle, S velocity estimates. The results indicate that a thicker crust and up to 0.3 km/sec (7%) higher S wave velocities in the upper 100 km of the mantle under the older East European Platform than under Central Europe explain most of the differences in the data sets.

The 13 January 2001 El Salvador earthquake: A multidata analysis

“…As shown by Sambridge [1999], this method is even more exploratory than genetic algorithm or simulated annealing, which are generally exploratory only at the beginning of the process. Lomax and Snieder [1994] also pointed out the difficulty of turning the genetic algorithm into a fully exploratory algorithm. One advantage of NA over genetic algorithm is that it requires the definition of only two tuning parameters which makes this algorithm easier to use.…”

An improved neighborhood algorithm: Parameter conditions and dynamic scaling

“…Inversion techniques are widespread in geophysics as attested by the number of scientific activities dealing with their development and their application, mostly since the beginning of the computer era. Inversion tools include linearized methods [ Nolet , 1981; Tarantola , 1987] and direct search techniques [ Sen and Stoffa , 1991; Lomax and Snieder , 1994] that gained success during the nineties parallel to the development of the power of desk computers. For inversion problems with a reduced number of unknowns, direct search methods are probably best suited because of their ability to correctly map the uncertainties of the problem in the case of non‐uniqueness (distinct equivalent solutions).…”

“…The Neighborhood Algorithm (NA) [ Sambridge , 1999] is a stochastic direct search method that belongs to the same family as Genetic Algorithms (GA) [ Lomax and Snieder , 1994] or Simulated Annealing (SA) [ Sen and Stoffa , 1991]. Compared to a basic Monte Carlo sampling, these approaches try to guide the random generation of samples by the results obtained so far on previous samples.…”

Estimation of shallow S-wave velocity structure and site response characteristics by microtremor array measurements in Tekirdag region, NW Turkey

“…We applied 50 inversions with 100 generations using different seeds of random number generators, such that a good model with smaller misfit survives to a greater extent in the next generation, while bad models are replaced by newly generated models (Yamanaka and Ishida 1996;Yamanaka 2007). The final model was selected as an acceptable solution if its average misfit was less than 10 % (Lomax and Snieder 1994). Appropriate search limits were decided after several trial runs of the inversion algorithm.…”