Instrumental timing and phase errors are a notorious problem in seismic data acquisition and processing. These can be frequency independent, for example due to clock drift, but may also be frequency dependent, for example due to imperfectly known instrument responses. A technique is presented that allows both types of errors to be recovered in a systematic fashion. The methodology relies on the time-symmetry usually inherent in time-averaged cross-correlations of ambient seismic noise: the difference between the arrival time of the direct surface-wave at positive time and the arrival time of the direct surface-wave at negative time is quantified. Doing this for all eligible receiver-receiver pairs of a large-N seismic array, including one or more receivers devoid of instrumental timing errors, the instrumental timing errors of all incorrectly timed receivers can be determined uniquely. Most notably, this is accomplished by means of a weighted least-squares inversion. The weights are based on the receiver-receiver distances and decrease the adverse effect of inhomogeneities in the noise illumination pattern on the recovered instrumental timing errors. Inversion results are furthermore optimized by limiting the inversion to receiver couples that (i) exceed a specific receiver-receiver distance threshold and (ii) whose time-averaged cross-correlations exceed a specific signal-to-noise ratio threshold. Potential frequency dependence of the timing errors is incorporated by means of an iterative, frequency-dependent approach. The proposed methodology is validated using synthetic recordings of ambient seismic surface-wave noise due to an arbitrary non-uniform illumination pattern. The methodology is successfully applied to time-averaged cross-correlations of field recordings of ambient seismic noise on and around the Reykjanes peninsula, SW Iceland.
- Inverse theory
- Seismic instruments
- Seismic interferometry
- Seismic noise
- Surface-waves and free oscillations