Obtaining free USArray data by multi-dimensional seismic reconstruction

USArray, a pioneering project for the dense acquisition of earthquake data, provides a semi-uniform sampling of the seismic wavefield beneath its footprint and greatly advances the understanding of the structure and dynamics of Earth. Despite continuing efforts in improving the acquisition design, network irregularity still causes spatial sampling alias and incomplete, noisy data, which imposes major challenges in array-based data analysis and seismic imaging. Here we employ an iterative rank-reduction method to simultaneously reconstruct the missing traces and suppress noise, i.e., obtaining free USArray recordings as well as enhancing the existing data. This method exploits the spatial coherency of three-dimensional data and recovers the missing elements via the principal components of the incomplete data. We examine its merits using simulated and real teleseismic earthquake recordings. The reconstructed P wavefield enhances the spatial coherency and accuracy of tomographic travel time measurements, which demonstrates great potential to benefit seismic investigations based on array techniques.

Object tracking via dual fuzzy low-rank approximation

For the object loss problem in the tracking process caused by illumination, occlusion, pose variation, and motion blur, the tracking method based on dual fuzzy low-rank approximation in a particle filter framework is proposed in this paper. Firstly, multiple constraint regions are built to filter insignificant samples, and more distinguished candidate samples are selected. Secondly, dual fuzzy observation function of each candidate sample is created based on the designed low-rank approximation representations of object and background. Then the generalized tracking results are obtained by computing membership degrees of dual fuzzy observation functions. Finally, based on the spatial coherency principle, the final tracking result is determined from the generalized results by measuring similarities of consecutive objects. The proposed method shows good performance as compared with several state-of-the-art trackers on challenging benchmark sequences.

Optimal biased Kriging: Homeogram tapering and applications to geoid undulations in Korea

This article studies the Optimal Biased Kriging (OBK) approach which is an alternative geostatistical method that gives up the unbiasedness condition of Ordinary Kriging (OK) to gain an improved Mean Squared Prediction Error (MSPE). The system of equations for the optimal linear biased Kriging predictor is derived and itsMSPE is compared with that of Ordinary Kriging. A major impediment in implementing this system of equations and performing Kriging interpolation with massive datasets is the inversion of the spatial coherency matrix. This problem is investigated and a novel method, called “homeogram tapering”, which exploits spatial sorting techniques to create sparse matrices for efficient matrix inversion, is described. Finally, as an application, results from experiments performed on a geoid undulation dataset from Korea are presented. A precise geoid is usually the indispensable basis for meaningful hydrological studies over wide areas. These experiments use the theory presented here along with a relatively new spatial coherency measure, called the homeogram, also known as the non-centered covariance function.

Extreme 1-day rainfall distributions: Analysing change in the Western Cape

Severe floods in the Western Cape Province of South Africa have caused significant damage to property and infrastructure over the past decade (2003–2014). The hydrological design criteria for exposed structures and design flood calculations are based mostly on the implicit assumption of stationarity, which holds that natural systems vary within an envelope of variability that does not change with time. This assumption was tested by examining the changes in extreme 1-day rainfall high percentiles (95th and 98th) and both the 20- and 50-year return period rainfall, comparing the period 1950–1979 against that of 1980–2009 across the province. A generalised Pareto distribution and a peaks-over-threshold sampling approach was applied to 76 rainfall stations across the province. Of these stations, 48 (63%) showed an increase in the 50-year return period 1-day rainfall and 28 (37%) showed a decrease in the 1980–2009 period at the 95th percentile peaks-over-threshold. At the 98th percentile peaks-over-threshold, 49 stations (64%) observed an increase and 27 (36%) a decrease for the later period. The change in the number of 3-day storms from the first to the second period is negligible, evaluated at 0.9% and 0.5% at the 95th and 98th percentile peaks-over-threshold levels, using cluster analysis. While there is no clear spatial coherency to the results, the general trend indicates an increase in frequency of intense rainfalls in the latter half of the 20th and early 21st centuries. These results bring into question assumptions of stationarity commonly used in design rainfall.