Genetic Algorithm Inversion of Rayleigh Wave Dispersion from CMPCC Gathers Over a Shallow Fault Model

Abstract

Lateral shear-wave velocity imaging, based on 1D surface wave inversion, is becoming routine in commercial site characterisation. A Genetic Algorithm (GA) is applied to the inversion of fundamental mode Rayleigh wave dispersion over a 3-layered, shallow, vertical-fault model. The data are calculated using a 2D finite difference method, then sorted into CMP cross-correlated (CMPCC) gathers, from which the dispersion is measured. Dispersion is relatively smooth over flat portions of the model, as well as when the spread is equally centered over the sharp lateral discontinuity. When between one and two-fifths of the spread is “overhanging” the fault, low-frequency dispersion is corrupted by wavefield scattering. Each dispersion curve is inverted using a 1D forward model, constrained to four layers, with parameters allowed to vary within liberal limits except the layer 1 shear-wave velocity. A novel variation is that the optimisation is partially directed, by including the most successful shear-wave velocity model in the initial GA population at successive midpoints, essentially laterally constraining the inversion. When the rollalong dispersion curves are inverted, both in “continuous” and “segmented” progressions, the 2D pseudo-section clearly shows the smoothing effect encountered across a sharp lateral geological discontinuity, causing a “palaeochannel” appearance, rather than a vertical fault. However, the estimated locations of shallow and deep layer truncations can better map the position of the abrupt lateral discontinuity, rather than simply basement topography. The RMS misfit between measured and theoretical dispersion curves gives no indication of where the 1D assumption breaks down and the exact discontinuity lies.