Cross-well seismic tomography can be used to develop high-resolution seismic slowness (1/velocity) estimates along planes through aquifers. Unfortunately, the relation between seismic slowness and hydraulic conductivity is poorly understood, resulting in poor characterization of hydraulic properties from seismic data. This relation is generally developed from laboratory measurements, but slowness values measured with very high frequencies in the lab are often poorly correlated with lower frequency cross-well and surface seismic slowness values. To address this problem, we developed an approach to infer the relation between slowness and hydraulic conductivity using field scale geophysical and hydrogeologic measurements. We first develop an a priori relation between the conductivity measurements and the cross-well slowness estimates. Multiple three-dimensional slowness realizations, conditioned on the cross-well estimates, are then generated and remapped into log conductivity fields using the a priori slowness to log conductivity relation. We simulate groundwater flow and tracer transport through these conductivity fields and calculate the residuals between measured and simulated concentration arrival time quantiles and drawdown. The slope and intercept of the relation between slowness and log hydraulic conductivity and the dispersivity are then estimated for each slowness realization to minimize the sum of these squared residuals. We demonstrate this approach for the Kesterson aquifer, California, where seismic tomography provided valuable information about aquifer properties. The groundwater flow and tracer transport simulations, through the estimated conductivity fields, yield reasonable fits to the observed tracer concentration histories for two multiple-well tracer tests (one of which was not used in the inversion) and to the measured drawdown. This approach provides estimates of seismic slowness and hydraulic conductivity, and information about the relation between slowness and log conductivity for a field site.
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