Sources of uncertainties and artefacts in back-projection results

Back-projecting high-frequency (HF) waves is a common procedure for imaging rupture processes of large earthquakes (i.e. M_w > 7.0). However, obtained back-projection (BP) results could suffer from large uncertainties since high-frequency seismic waveforms are strongly affected by factors like source depth, focal mechanisms, and the Earth's 3-D velocity structures. So far, these uncertainties have not been thoroughly investigated. Here, we use synthetic tests to investigate the influencing factors for which scenarios with various source and/or velocity set-ups are designed, using either Tohoku-Oki (Japan), Kaikoura (New Zealand), Java/Wharton Basin (Indonesia) as test areas. For the scenarios, we generate either 1-D or 3-D teleseismic synthetic data, which are then back-projected using a representative BP method, MUltiple SIgnal Classification (MUSIC). We also analyse corresponding real cases to verify the synthetic test results. The Tohoku-Oki scenario shows that depth phases of a point source can be back-projected as artefacts at their bounce points on the earth's surface, with these artefacts located far away from the epicentre if earthquakes occur at large depths, which could significantly contaminate BP images of large intermediate-depth earthquakes. The Kaikoura scenario shows that for complicated earthquakes, composed of multiple subevents with varying focal mechanisms, BP tends to image subevents emanating large amplitude coherent waveforms, while missing subevents whose P nodal directions point to the arrays, leading to discrepancies either between BP images from different arrays, or between BP images and other source models. Using the Java event, we investigate the impact of 3-D source-side velocity structures. The 3-D bathymetry together with a water layer can generate strong and long-lasting coda waves, which are mirrored as artefacts far from the true source location. Finally, we use a Wharton Basin outer-rise event to show that the wavefields generated by 3-D near trench structures contain frequency-dependent coda waves, leading to frequency-dependent BP results. In summary, our analyses indicate that depth phases, focal mechanism variations and 3-D source-side structures can affect various aspects of BP results. Thus, we suggest that target-oriented synthetic tests, for example, synthetic tests for subduction earthquakes using more realistic 3-D source-side velocity structures, should be conducted to understand the uncertainties and artefacts before we interpret detailed BP images to infer earthquake rupture kinematics and dynamics

Correlations of random classifiers on large data sets

Classification of large data sets by feedforward neural networks is investigated. To deal with unmanageably large sets of classification tasks, a probabilistic model of their relevance is considered. Optimization of networks computing randomly chosen classifiers is studied in terms of correlations of classifiers with network input–output functions. Effects of increasing sizes of sets of data to be classified are analyzed using geometrical properties of high-dimensional spaces. Their consequences on concentrations of values of sufficiently smooth functions of random variables around their mean values are applied. It is shown that the critical factor for suitability of a class of networks for computing randomly chosen classifiers is the maximum of sizes of the mean values of their correlations with network input–output functions. To include cases in which function values are not independent, the method of bounded differences is exploited