Time-lapse inversion of crosswell radar data

The combination of differential radar tomography with conventional tracer and/or hydraulic tests facilitates high-resolution characterization of subsurface heterogeneity and enables the identification of preferential flow paths. In dynamic imaging, each tomogram is typically inverted independently, under the assumption that data sets are collected quickly relative to changes in the imaged property (e.g., attenuation or velocity); however, such snapshot tomograms may contain large errors if the imaged property changes significantly during data collection. Acquisition of less data over a shorter time interval could ameliorate the problem, but the resulting decrease in ray density and angular coverage could degrade model resolution. To address these problems, we propose a new sequential approach for time-lapse tomographic inversion. The method uses space-time parameterization and regularization to combine data collected at multiple times and to account for temporal variation. The inverse algorithm minimizes the sum of weighted squared residuals and a measure of solution complexity based on an a priori space-time covariance function and a spatiotemporally variable mean. We demonstrate our approach using a synthetic 2-D time-lapse (x, z, t) data set based loosely on a field experiment in which difference-attenuation radar tomography was used to monitor the migration of a saline tracer in fractured rock. We quantitatively show the benefits of space-time inversion by comparing results for snapshot and time-lapse inversion schemes. Inversion over both space and time results in superior estimation error, model resolution, and data reproduction compared to conventional snapshot inversion. Finally, we suggest strategies to improve time-lapse cross-hole inversions using ray-based inversion constraints and a modified survey design in which different sets of rays are collected in alternating time steps.