Separation of deterministic signals using independent component analysis (ICA)

Independent Component Analysis (ICA) represents a higher-order statistical technique that is often used to separate mixtures of stochastic random signals into statistically independent sources. Its benefit is that it only relies on the information contained in the observations, i.e. no parametric a-priori models are prescribed to extract the source signals. The mathematical foundation of ICA, however, is rooted in the theory of random signals. This has led to questions whether the application of ICA to deterministic signals can be justified at all? In this context, the possibility of using ICA to separate deterministic signals such as complex sinusoidal cycles has been subjected to previous studies. In many geophysical and geodetic applications, however, understanding long-term trend in the presence of periodical components of an observed phenomenon is desirable. In this study, therefore, we extend the previous studies with mathematically proving that the ICA algorithm with diagonalizing the 4th order cumulant tensor, through the rotation of experimental orthogonal functions, will indeed perfectly separate an unknown mixture of trend and sinusoidal signals in the data, provided that the length of the data set is infinite. In other words, we justify the application of ICA to those deterministic signals that are most relevant in geodetic and geophysical applications.     

Probabilistic Assessment of Tsunami Recurrence in the Indian Ocean

The Indian Ocean is one of the most tsunamigenic regions of the world and recently experienced a mega-tsunami in the Sumatra region on 26 December 2004 (M _W 9.2 earthquake) with tsunami intensity I (Soloviev-Imamura intensity scale) equal to 4.5, causing heavy destruction of lives and property in the Indian Ocean rim countries. In this study, probabilities of occurrences of large tsunamis with tsunami intensities I ≥ 2.0 and I ≥ 3.0 (average wave heights H ≥ 2.83 m and H ≥ 5.66 m, respectively) during a specified time interval were calculated using three stochastic models, namely, Weibull, gamma and lognormal. Tsunami recurrence was calculated for the whole Indian Ocean and the special case of the Andaman-Sumatra-Java (ASJ) region, excluding the 1945 Makran event from the main data set. For this purpose, a reliable, homogeneous and complete tsunami catalogue with I ≥ 2.0 during the period 1797–2006 was used. The tsunami hazard parameters were estimated using the method of maximum likelihood. The logarithm of likelihood function (ln L) was estimated and used to test the suitability of models in the examined region. The Weibull model was observed to be the most suitable model to estimate tsunami recurrence in the region. The sample mean intervals of occurrences of tsunamis with intensity I ≥ 2.0 and I ≥ 3.0 were calculated for the observed data as well as for the Weibull, gamma and lognormal models. The estimated cumulative and conditional probabilities in the whole Indian Ocean region show recurrence periods of about 27–30 years (2033–2036) and 35–36 years (2039–2040) for tsunami intensities I ≥ 2.0 and I ≥ 3.0, respectively, while it is about 31–35 years (2037–2041) and 41–42 years (2045–2046) for a tsunami of intensity I ≥ 2.0 and I ≥ 3.0, respectively, in the ASJ region. A high probability (>0.9) of occurrence of large tsunamis with I ≥ 2.0 in the next 30–40 years in the Indian Ocean region was revealed.     

Determining the location of buried plastic water pipes from measurements of ground surface vibration

‘Mapping the Underworld’ is a UK-based project, which aims to create a multi-sensor device that combines complementary technologies for remote buried utility service detection and location. One of the technologies to be incorporated in the device is low-frequency vibro-acoustics, and techniques for detecting buried infrastructure, in particular plastic water pipes, are being investigated. One of the proposed techniques involves excitation of the pipe at some known location with concurrent vibrational mapping of the ground surface in order to infer the location of the remainder of the pipe. In this paper, measurements made on a dedicated pipe rig are reported. Frequency response measurements relating vibrational velocity on the ground to the input excitation were acquired. Contour plots of the unwrapped phase revealed the location of the pipe to within 0.1-0.2 m. Magnitude contour plots revealed the excitation point and also the location of the pipe end. By examining the unwrapped phase gradients along a line above the pipe, it was possible to identify the wave-type within the pipe responsible for the ground surface vibration. Furthermore, changes in the ground surface phase speed computed using this method enabled the location of the end of the pipe to be confirmed.     

Thermomechanical properties of deep argillaceous formations

A difficulty in the interpretation of mechanical and thermo-mechanical tests on specimens drawn from large argillaceous formations is the strong inhomogeneity of void ratio, clay minerals and carbonates content.

In this paper a relationship is developed to link strength and the maximum preconsolidation stress to the initial void ratio and carbonate content. Compressibility is also correlated to carbonates.

Thermal strains in drained and undrained conditions for a Spanish, a belgian and an Italian natural clay are compared. In the elastic state strains are comparable, while in the plastic range thermal strains are highest for the Belgian clay, lower in the Spanish cemented clay and lowest in the Italian clay, very stiff and cemented.     

Evidence for a sunspot in A.D. 939 in an Arabian Source

It is the purpose of this paper to present evidence concerning the appearance of a sunspot in A.D. 939 observed by Arabs from the Iberian Peninsula. The sunspot record appears in the Arab source known as al-Muqtabis V.     

Seasonal change in the deep atmosphere of Uranus

We present high-resolution radio maps of Uranus, made from data collected in 1994 at wavelengths of 2 and 6 cm, which show large-scale changes occurring deep and rapidly in the troposphere. Brightness features in these maps are significantly different from those observed throughout the 1980's. These differences are not due to the changing viewing geometry, but result from atmospheric changes in the 5 to 50 bar region. All the observations show strong latitudinal variations in absorber abundance and/or temperature, causing the South Pole to appear brighter than lower latitudes. The transition between bright pole and darker latitudes is always near −45°, but between 1989 and 1994 the contrast between the regions increased significantly. This suggests that the large-scale circulation in the upper 50 bars of the uranian Southern Hemisphere changed. Older, disk-averaged microwave observations have suggested that seasonal variability occurs, but these new maps are the first to provide detailed timing and location information which can be used to test dynamical models.