Updates to the Regional Seismic Travel Time (RSTT) Model: 2. Path-dependent Travel-time Uncertainty

AbstractThe regional seismic travel time (RSTT) model and software were developed to improve travel-time prediction accuracy by accounting for three-dimensional crust and upper mantle structure. Travel-time uncertainty estimates are used in the process of associating seismic phases to events and to accurately calculate location uncertainty bounds (i.e. event location error ellipses). We improve on the current distance-dependent uncertainty parameterization for RSTT using a random effects model to estimate slowness (inverse velocity) uncertainty as a mean squared error for each model parameter. The random effects model separates the error between observed slowness and model predicted slowness into bias and random components. The path-specific travel-time uncertainty is calculated by integrating these mean squared errors along a seismic-phase ray path. We demonstrate that event location error ellipses computed for a 90% coverage ellipse metric (used by the Comprehensive Nuclear-Test-Ban Treaty Organization International Data Centre (IDC)), and using the path-specific travel-time uncertainty approach, are more representative (median 82.5% ellipse percentage) of true location error than error ellipses computed using distance-dependent travel-time uncertainties (median 70.1%). We also demonstrate measurable improvement in location uncertainties using the RSTT method compared to the current station correction approach used at the IDC (median 74.3% coverage ellipse).

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Resampling Methods for Estimating Travel Time Uncertainty: Application of the Gap Bootstrap

Transportation Research Record Journal of the Transportation Research Board ◽

10.1177/0361198118792124 ◽

2018 ◽

Vol 2672 (42) ◽

pp. 137-147 ◽

Cited By ~ 1

Author(s):

Bhaven Naik ◽

Laurence R. Rilett ◽

Justice Appiah ◽

Lubinda F. Walubita

Keyword(s):

Travel Time ◽

Bootstrap Method ◽

Point Estimate ◽

Data Sets ◽

Block Bootstrap ◽

Travel Time Prediction ◽

Resampling Methods ◽

Time Uncertainty ◽

Uncertainty Estimates ◽

Travel Time Uncertainty

To a large extent, methods of forecasting travel time have placed emphasis on the quality of the forecasted value—how close is the forecast point estimate of the mean travel time to its respective field value? However, understanding the reliability or uncertainty margin that exists around the forecasted point estimate is also important. Uncertainty about travel time is a fundamental factor as it leads end-users to change their routes and schedules even when the average travel time is low. Statistical resampling methods have been used previously for uncertainty modeling within the travel time prediction environment. This paper applies a recently developed nonparametric resampling method, the gap bootstrap, to the travel time uncertainty estimation problem, especially as it pertains to large (probe) data sets for which common resampling methods may not be practical because of the possible computational burden and complex patterns of inhomogeneity. The gap bootstrap partitions the original data into smaller groups of approximately uniform data sets and recombines individual group uncertainty estimates into a single estimate of uncertainty. Results of the gap bootstrap uncertainty estimates are compared with those of two popular resampling methods—the traditional bootstrap and the block bootstrap. The results suggest that, for the datasets used in this research, the gap bootstrap adequately captures the dependent structure when compared with the traditional and block bootstrap methods and may thus yield more credible estimates of uncertainty than either the block bootstrap method or the traditional bootstrap method.

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