Direct-seismogram inversion for receiver-side structure with uncertain source-time functions

This paper presents direct-seismogram inversion (DSI) for receiver-side structure which treats the source signal incident from below (the effective source-time function-STF) as a vector of unknown parameters in a Bayesian framework. As a result, the DSI method developed here does not require deconvolution by observed seismogram components as typically applied in receiver-function inversion and avoids the problematic issue of choosing subjective tuning parameters in this deconvolution. This results in more meaningful inversion results and uncertainty estimation compared to classic receiver-function inversion. A rigorous derivation is presented of the likelihood function required for unbiased inversion results. The STF is efficiently inferred by a maximum-likelihood closed-form expression that does not require deconvolution by noisy waveforms. Rather, deconvolution is only by predicted impulse responses for the unknown environment (considered to be a 1-D, horizontally stratified medium). For a given realization of the parameter vector which describes the medium below the station, data predictions are computed as the convolution of the impulse response and the maximum-likelihood source estimate for that medium. Therefore, the assumption of a Gaussian pulse with specified parameters, typical for the prediction of receiver functions, is not required. Directly inverting seismogram components has important consequences for the noise on the data. Since the signal processing does not require filtering and deconvolution, data errors are less correlated and more straightforward to model than those for receiver functions. This results in better inversion results (parameter values and uncertainties), since assumptions made in the derivation of the likelihood function are more likely to be met by the inversion process. The DSI method is demonstrated for simulated waveforms and then applied to data for station Hyderabad on the Indian craton. The measured data are inverted with both the new DSI and traditional receiver-function inversion. All inversions are carried out for a trans-dimensional model that treats the number of layers in the model as unknown. Results for DSI are consistent with previous studies for the same location. The DSI has clear advantages in trans-dimensional inversion. Uncertainty estimates appear more realistic (larger) in both model complexity (number of layers) and in terms of seismic velocity profiles. Receiver-function inversion results in more complex profiles (highly-layered structure) and suggests unreasonably small uncertainties. This effect is likely also significant when the parametrization is considered to be fixed but exacerbated for the trans-dimensional model: If hierarchical errors are poorly estimated, trans-dimensional models overestimate the structure which produces unfavourable results for the receiver-function inversion.