SUMMARYWe present the first Love-wave group velocity and shear velocity maps of the British Isles obtained from ambient noise interferometry and fully non-linear inversion. We computed interferometric inter-station Green's functions by cross-correlating the transverse component of ambient noise records retrieved by 61 seismic stations across the UK and Ireland. Group velocity measurements along each possible inter-station path were obtained using frequency-time analysis and converted into a series of inter-station traveltime datasets between 4 and 15 seconds period. Traveltime uncertainties estimated from the standard deviation of dispersion curves constructed by stacking randomly-selected subsets of daily cross-correlations, were observed to be too low to allow reasonable data fits to be obtained during tomography. Data uncertainties were therefore estimated again during the inversion as distance-dependent functionals. We produced Love-wave group velocity maps within 8 different period bands using a fully non-linear tomography method which combines the transdimensional reversible-jump Markov chain Monte Carlo (rj-McMC) algorithm with an

Seismic surface wave tomography is a tried and tested method to reveal the subsurface structure of the Earth. However, the conventional 2-step scheme of inverting first for 2-D maps of surface wave phase or group velocity and then inverting for the 3-D spatial velocity structure preserves little information about lateral spatial correlations, and introduces additional uncertainties and errors into the 3-D result. We introduce a 1-step 3-D non-linear surface wave tomography method that removes these effects by inverting for 3-D spatial structure directly from frequencydependent traveltime measurements. We achieve this using the reversible jump Markov chain Monte Carlo (McMC) algorithm with a fully 3-D model parametrization. Synthetic tests show that the method estimates the velocity model and associated uncertainties significantly better than the conventional 2-step McMC method, and that the computational cost seems to be comparable with 2-step McMC methods. The resulting uncertainties are more intuitively reasonable than those from the 2-step method, and provide directly interpretable uncertainty on volumetrics of structures of interest.

Estimating image uncertainty is fundamental to guiding the interpretation of geoscientific tomographic maps. We reveal novel uncertainty topologies (loops) which indicate that while the speeds of both low- and high-velocity anomalies may be well constrained, their locations tend to remain uncertain. The effect is widespread: loops dominate around a third of United Kingdom Love wave tomographic uncertainties, changing the nature of interpretation of the observed anomalies. Loops exist due to 2nd and higher order aspects of wave physics; hence, although such structures must exist in many tomographic studies in the physical sciences and medicine, they are unobservable using standard linearized methods. Higher order methods might fruitfully be adopted.

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