Time-dependent Seismic Tomography of Geothermal Systems

Temporal changes in seismic wave speeds in the Earth’s crust have been measured at several geothermal areas, notably The Geysers in California, in studies that used three-dimensional seismic tomography. These studies used conventional tomography methods to invert seismic-wave arrival time data sets for different epochs independently and assumed that any differences in the derived structures reflect real temporal variations. Such an assumption is dangerous because the results of repeated tomography experiments would differ even if the structure did not change, simply because of variation in the seismic ray distribution caused by the natural variation in earthquake locations. This problem can be severe when changes in the seismicity distribution are systematic, as, for example, when many data come from earthquake swarms. The sudden change in the ray distribution can produce artifacts that mimic changes in the seismic wave speeds at the time of a swarm. Even if the source locations did not change (if only explosion data were used, for example), derived structures would inevitably differ because of observational errors. In order to determine what changes are real and what are artifacts, we have developed a new tomography method, tomo4d, that inverts multiple data sets simultaneously, imposing constraints to minimize the differences between the models for different epochs. This problem is similar to that of seeking models similar to some a priori initial assumption, and a method similar to “damped least squares” can solve it. We present an algorithm for performing this computation efficiently. Using our program, inverting multiple epochs simultaneously is comparable in difficulty to inverting them independently. We illustrate the program’s performance using synthetic arrival times. INTRODUCTION A variety of physical processes can cause the seismic-wave speeds in geothermal and hydrocarbon reservoirs to vary with time. These include changes in the stiffness of the rock matrix caused by drying or wetting of clay minerals (Boitnott & Boyd, 1996) and changes in pore-fluid compressibility caused by CO2 flooding (Wang et al., 1998; Daley et al., 2007) or fluid extraction (Gunasekera et al., 2003). Figure 1 shows the particularly strong changes that occurred in The Geysers geothermal reservoir, California, in the 1990s. Measuring such variations has many important applications, e.g., monitoring of reservoir exploitation and of underground CO2 sequestration.