Bias in seismic estimates of crustal properties

Abstract

SUMMARY It has come to our attention that the least-squares estimator we proposed in a recent paper to recover bulk crustal P velocity, VP, and P velocity/S velocity ratio, R, of the crust from traveltimes of scattered teleseismic phases, is inconsistent. That is, in the presence of errors, estimates of R will be biased downwards and estimates of VP will be biased upwards from their true values. In this note we supply bias corrections for both quantities that depend upon an estimate of the variance in a ratio of traveltime sums, and demonstrate their validity through comparison with estimates based on a two-parameter grid search. Application to station HYB yields R = 1.756 ± 0.005, VP = 6.2 ± 0.1 km s −1 , after correction of a systematic traveltime picking error that had affected our previous results. In addition, we provide an alternative waveform-stacking approach that involves a 2-D grid search over R and VP followed by a 1-D line search over crustal thickness H. An estimate of the direct Ps conversion time is required, and results from station HYB are consistent with those produced using traveltimes alone.