Full waveform inversion of repeating seismic events to estimate time-lapse velocity changes

Seismic monitoring provides valuable information regarding the time-varying changes in subsurface physical properties caused by natural or man-made processes. However, the resulting changes in the earth's subsurface properties are often small both in terms of magnitude and spatial extent, leading to minimal time-lapse differences in seismic amplitude or traveltime. In order to better extract information from the time-lapse data, we show that exploiting the full seismic waveform information can be critical. In this study, we develop and test methods of full waveform inversion that estimate an optimal subsurface model of time-varying elastic properties in order to fit the observed time-lapse seismic data with predicted waveforms based on numerical solutions of the wave equation. Time-lapse full waveform inversion is nonlinear and non-unique, and depends on the knowledge of the baseline velocity model before a change, and (non-) repeatability of earthquake source and sensor parameters, and of ambient and cultural noise. We propose to use repeating earthquake data sets acquired with permanent arrays of seismic sensors to enhance the repeatability of source and sensor parameters. We further develop and test time-lapse parallel, double-difference and bootstrapping inversion strategies to mitigate the dependence on the baseline velocity model. The parallel approach uses a time-invariant full waveform inversion method to estimate velocity models independently of the different source event times. The double-difference approach directly estimates velocity changes from time-lapse waveform differences, requiring excellent repeatability. The bootstrapping approach inverts for velocity models sequentially in time, implicitly constraining the time-lapse inversions, while relaxing an explicit requirement for high data repeatability. We assume that prior to the time-lapse inversion, we can estimate the true source locations and the origin time of the events, and also we can also obtain a reasonably accurate baseline velocity model. Extensive synthetic tests using a realistic velocity model developed from a real project area demonstrate the potential of full waveform inversion to estimate velocity changes from dense surface arrays of seismic stations recording a small number of repeating events. Analysis of sensitivity kernels suggests that positioning sensors at large distances allows for a stable recovery of velocity changes near the event locations by illuminating the inversion area with a wide aperture of angles. We show how full waveform inversion maps the errors in the baseline velocity model and the non-repeatable noise into the estimates of time-lapse velocity changes. Among the three time-lapse inversion methods, parallel inversion is most affected by non-repeatability factors, and is thus the least robust and most contaminated by artefacts. In contrast, the double-difference and bootstrapping methods result in more accurate time-lapse inversions. As the non-repeatability of both sources and noise increases, the bootstrapping method provides more robust and accurate results than the double-difference method.