Optimal resolution tomography with error tracking and the structure of the crust and upper mantle beneath Ireland and Britain

The maximum achievable resolution of a tomographic model varies spatially and depends on the data sampling and errors in the data. The significant and continual measurement-error decreases in seismology and data-redundancy increases have reduced the impact of random errors on tomographic models. Systematic errors, however, are resistant to data redundancy and their effect on the model is difficult to predict; often this results in models dominated by noise if the target resolution is too high. Here, we develop a method for finding the optimal resolving length at every point, implementing it for surface-wave tomography. As in the Backus-Gilbert method, every solution at a point results from an entire-system inversion, and the model error is reduced by increasing the model-parameter averaging. The key advantage of our method consists in its direct, empirical evaluation of the posterior model error at a point.

We first measure interstation phase velocities at simultaneously recording station pairs and compute phase-velocity maps at densely, logarithmically spaced periods. Numerous versions of the maps with varying smoothness are then computed, ranging from very rough to very smooth. Phase-velocity curves extracted from the maps at every point can be inverted for shear-velocity (V_S) profiles. As we show, errors in these phase-velocity curves increase nearly monotonically with the map roughness. We evaluate the error by isolating the roughness of the phase-velocity curve that cannot be explained by any Earth structure and determine the optimal resolving length at a point such that the error of the local phase-velocity curve is below a threshold.

A 3-D V_S model is then computed by the inversion of the composite phase-velocity maps with an optimal resolution at every point. Importantly, the optimal resolving length does not scale with the density of the data coverage: some of the best-sampled locations display relatively low lateral resolution, due to systematic errors in the data.

We apply this method to image the lithosphere and underlying mantle beneath Ireland and Britain. Our very large data produces a total of 11238 inter-station dispersion curves, spanning a very broad total period range (4–500 s), yielding unprecedented data coverage of the area and providing state-of-the-art regional resolution from the crust to the deep asthenosphere. Our tomography reveals pronounced, previously unknown variations in the lithospheric thickness beneath Ireland and Britain, with implications for their Caledonian assembly and for the mechanisms of the British Tertiary Igneous Province magmatism.