Towards 2D Bayesian Tomography of Receiver Functions
Abstract:Receiver function analysis is a powerful tool widely used to isolate and interpret receiver-side structure effects in teleseismic records. The idea is to deconvolve the vertical component from the horizontal components to produce a time series, thus eliminating the influence of the source and distant path effects.
The receiver function is usually migrated and directly interpreted by visual inspection. However, deconvolution is a numerically unstable procedure that needs to be stabilized, and the solution depends on the choice of regularization parameters (e.g. water level and the width of a low pass filter). Since the solution is blurred with multiple reflections from the subsurface that produce apparent discontinuities, qualitative interpretation of receiver functions is subjective. Alternatively, waveforms can be directly inverted for a 1D S-wave velocity model beneath the receiver. An inversion procedure is more quantitative, as a forward model will take into account all possible reflections and conversions. If cast in a Bayesian framework, an inversion also enables one to assess model uncertainties and quantify parameter trade-offs. However, seismologists have preferred migration techniques as they are easier to implement, computationally cheaper, and allow construction of 2D or 3D sections. Inversions have been limited thus far to the 1D case.
In this work we present a method for inversion of converted waveforms measured at a number of aligned stations. The unknown model is a 2D vertical cross section parameterized with a variable number of discontinuities, although the forward model used to compute synthetics under individual stations is 1D. Body waves are inverted jointly with surface wave dispersion measurements to reduce the range of possible solutions. The problem is solved with a fully non linear Bayesian inversion scheme where the posterior velocity distribution is sampled with a Markov Chain Monte Carlo Algorithm. Our approach uses the ‘trans-dimensional’ method that simultaneously samples various models with different numbers of parameters. Not only are we able to assess uncertainty in crustal S velocity, we do so over a range of parameterizations, thus solving the model selection problem. We present preliminary results with synthetic tests that demonstrate the applicability of the method.