Inversion of seismic reflection traveltimes using a nonlinear optimization scheme

Abstract

We present the use of a nonlinear optimization scheme called generalized simulated annealing to invert seismic reflection times for velocities, reflector depths, and lengths. A finite-difference solution of the eikonal equation computes reflection traveltimes through the velocity model and avoids ray tracing. We test the optimization scheme on synthetic models and compare it with results from a linearized inversion. The synthetic tests illustrate that, unlike linear inversion schemes, the results obtained by the optimization scheme are independent of the initial model. The annealing method has the ability to produce a suite of models that satisfy the data equally well. We make use of this property to determine the uncertainties associated with the model parameters obtained. Synthetic examples demonstrate that allowing the reflector length to vary, along with its position, helps the optimization process obtain a better solution. We put this to use in imaging the Garlock fault, whose geometry at depth is poorly known. We use reflection times picked from shot gathers recorded along COCORP Mojave Line 5 to invert for the Garlock fault and velocities within the Cantil Basin below Fremont Valley, California. The velocities within the basin obtained by our optimization scheme are consistent with earlier studies, though our results suggest that the basin might extend l-2 km further south. The reconstructed reflector seems to suggest shallowing of the dip of the Garlock fault at depth.

Application of advanced seismic reflection imaging techniques to mapping permeable zones at Dixie Valley, Nevada. Final technical report

“…In addition, production from the Dixie Valley geothermal field is closely associated with a fault or fault system that bounds the Stillwater Range on the west, and Dixie Valley on the east (Figure 1). In past studies, we have demonstrated the ability of our processing techniques to image the truedepth location and down-dip geometry of similar faults in the Basin and Range province (Louie and Qin, 1991;Pullammanappallil and Louie, 1993;Chavez-Perez et al, 1993), and adjacent to the offshore Santa Maria Basin, California (Honjas et al, 1993). Thus, Dixie Valley presents an opportunity to test these new, advanced methods for imaging such structures in a relatively wellunderstood, active geothermal environment.…”

“…We inverted arrival times from this event using the method of Pullammanappallil and Louie (1993) to obtain the local velocity structure along the western 2 km of the seismic line, as well as the horizontal position and depth of the event. The results are shown in Figure 33.…”

“…Simulated annealing is a Monte-Carlo estimation process that can match data to a model even where sophisticated non-linear inversion methods may fail (Pullammanappallil and Louie, 1993;Pullammanappallil and Louie, 1994). We use this method to invert P-wave arrival times from the seismic data to obtain a two-dimensional model of seismic velocities along an individual seismic line.…”

A combined first‐arrival travel time and reflection coherency optimization approach to velocity estimation

“…(1) finite-difference solution to the eikonal equation [ Vidale, 1988] to compute the first-arrival times through the model, while a modification of this ( [Pullammanappallil and Louie, 1993]) is used to get the reflection times.…”

“…The depth of resolution is limited by the type of arrivals used-first arrivals constrain the relatively shallow velocities, to depths usually less than onethird the maximum receiver offset, while reflections provide deeper constraints. Usually travel time inversion with reflected arrivals is performed using times picked off one or a limited number of reflecting horizons, as in Pullammanappallil and Louie [1993]. This leads to poor ray coverage in areas of the model not underlain by reflection picks.…”