Arrival-time picking uncertainty: Theoretical estimations and their application to microseismic data

Abstract

<jats:p> Traveltime-based methods depend on the accurate determination of the arrival times of seismic waves. They further benefit from information on the uncertainty with which the arrival times are determined. Among other applications, arrival-time uncertainties are used to weight data in inversion algorithms and to define the resolution of reconstructed velocity models. The most physically meaningful approaches for the estimation of arrival-time uncertainties are based on probabilistic formulations. The two approaches for the assessment of the lower bound of arrival-time uncertainties, the Cramér–Rao Bound (CRB) and the Ziv–Zakai Bound (ZZB), have been reviewed. The CRB determines the minimum-achievable estimation error under the assumption of a high signal-to-noise ratio (S/N) but underestimates said error for small S/N. The ZZB provides a better result for noisy data because it utilizes a priori information. The CRB and ZZB require knowledge of the spectral variance of the signal, which often is hard to determine in seismic experiments. Furthermore, both bounds assume additive white Gaussian noise (AWGN), which does not hold for seismic data. To overcome these problems, alternative expressions have been proposed, which yield comparable estimates as CRB and ZZB but are solely based on the S/N and the dominant period in the data. Moreover, a recipe to correct the S/N and account for the difference between the seismic noise and AWGN has been provided. For a case study of downhole microseismic monitoring, it is determined that the new expressions provide station-dependent arrival-time uncertainties, which are used as weights to improve source location uncertainties. </jats:p>

The sensitivity of seismic refraction velocity models to survey geometry errors, assessed using Monte Carlo analysis

“…Since t e is the most significant source of uncertainty in an output model, field effort should be directed towards maximising SNR -i.e., through the use of more energetic seismic sources and short maximum source-geophone offsets, minimising wind noise on geophones, stacking more sources at any shotpoint, and/or through applying advanced first-break picking techniques (e.g., Zhao et al, 2022). In addition to minimising t e , efforts should be made to obtain accurate estimates of the magnitude of this error to provide realistic estimates of output uncertainties (e.g., Abakumov et al, 2020).…”

Assessment of earthquake localization uncertainties for the design of local seismic networks

“…Picking errors de ne the precision of the hypocenter location since they lead to a relative location scattered around the true earthquake point location (Husen and Hardebeck, 2010). The pick is commonly assumed to be a random variable symmetrically and normally distributed around the true arrival time, even though some authors have demonstrated that the distribution can be highly asymmetrical (Diehl et al 2012, Abakumov et al 2020.…”