Nonsymmetric Sources Research Articles

Hypothesis tests on Rayleigh wave radiation pattern shapes: a theoretical assessment of idealized source screening

SUMMARYShallow seismic sources excite Rayleigh wave ground motion with azimuthally dependent radiation patterns. We place binary hypothesis tests on theoretical models of such radiation patterns to screen cylindrically symmetric sources (like explosions) from non-symmetric sources (like non-vertical dip-slip or non-VDS faults). These models for data include sources with several unknown parameters, contaminated by Gaussian noise and embedded in a layered half-space. The generalized maximum likelihood ratio tests that we derive from these data models produce screening statistics and decision rules that depend on measured, noisy ground motion at discrete sensor locations. We explicitly quantify how the screening power of these statistics increase with the size of any dip-slip and strike-slip components of the source, relative to noise (faulting signal strength) and how they vary with network geometry. As applications of our theory, we apply these tests to (1) find optimal sensor locations that maximize the probability of screening non-circular radiation patterns and (2) invert for the largest non-VDS faulting signal that could be mistakenly attributed to an explosion with damage, at a particular attribution probability. Finally, we quantify how certain errors that are sourced by opening cracks increase screening rate errors. While such theoretical solutions are ideal and require future validation, they remain important in underground explosion monitoring scenarios because they provide fundamental physical limits on the discrimination power of tests that screen explosive from non-VDS faulting sources.

Radiation of twisted whistler waves from a crossed-loop antenna in a magnetoplasma

A study is made of the radiation of whistler waves with helical phase fronts from nonsymmetric sources immersed in a homogeneous cold magnetoplasma. The emphasis is placed on calculating the radiation resistance of an antenna in the form of two orthogonally crossed circular loops with quadrature-phased currents using an approach that is based on an eigenfunction expansion representation of the excited field. Analytical and numerical results are reported for the radiation characteristics of such an antenna in the whistler range and differences in the behavior of the radiation resistance below and above the lower hybrid resonance frequency are revealed. The results obtained can be useful in understanding the basic features of excitation of twisted whistler waves in a magnetoplasma.

Estimation for Two-Dimensional Nonsymmetric Coherently Distributed Source in L-Shaped Arrays

We explore the estimation of a two-dimensional (2D) nonsymmetric coherently distributed (CD) source using L-shaped arrays. Compared with a symmetric source, the modeling and estimation of a nonsymmetric source are more practical. A nonsymmetric CD source is established through modeling the deterministic angular signal distribution function as a summation of Gaussian probability density functions. Parameter estimation of the nonsymmetric distributed source is proposed under an expectation maximization (EM) framework. The proposed EM iterative calculation contains three steps in each cycle. Firstly, the nominal azimuth angles and nominal elevation angles of Gaussian components in the nonsymmetric source are obtained from the relationship of rotational invariance matrices. Then, angular spreads can be solved through one-dimensional (1D) searching based on nominal angles. Finally, the powers of Gaussian components are obtained by solving least-squares estimators. Simulations are conducted to verify the effectiveness of the nonsymmetric CD model and estimation technique.

Recovery of a space-dependent vector source in anisotropic thermoelastic systems

We investigate the theoretical and numerical determination of a space-dependent vector source (load) in an anisotropic thermoelastic system of type-III from the knowledge of an additional final time measurement. The uniqueness of a solution to this inverse source problem is proved for various assumptions made on the convolution kernel. A convergent and stable iterative algorithm is proposed for the recovery of the unknown vector source in the linear case and, at the same time, a stopping criterion is also given. Three numerical experiments are considered to validate the properties of the proposed iterative procedure and the regularizing/stabilizing character of the corresponding stopping criterion. The numerical experiments carried out showed that it exists a certain limitation of the method with respect to the recovery of non-symmetric sources.

Nonsymmetric sources and optimum signal selection

There are some applications where the information source is nonsymmetric. Here, it is shown that differential pulse code modulation (DPCM) of video signals results in a nonsymmetric source. Previous works on 2-D signal design have been focused around equally likely sources. In this paper, an iterative algorithm for minimum error signal design subject to average power (or peak power) constraint is presented. Then, design of minimum cost signal sets is addressed, and application to a DPCM system for picture transmission is developed. Comparisons are made between the nonsymmetric and symmetric signal design in one case and between minimum error signal design and minimum cost signal selection in the other case, for the transmission of DPCM-coded signals. It is seen that nonsymmetric signal design gains significant improvements over the equally likely signal selection when the channel is noisy. Minimum cost signal design also demonstrated some improvement relative to minimum error signal selection over noisy channels.

On the evil effects arising from the use of dolomitic lime in building brick walls

We investigate the theoretical and numerical determination of a space-dependent vector source (load) in an anisotropic thermoelastic system of type-III from the knowledge of an additional final time measurement. The uniqueness of a solution to this inverse source problem is proved for various assumptions made on the convolution kernel. A convergent and stable iterative algorithm is proposed for the recovery of the unknown vector source in the linear case and, at the same time, a stopping criterion is also given. Three numerical experiments are considered to validate the properties of the proposed iterative procedure and the regularizing/stabilizing character of the corresponding stopping criterion. The numerical experiments carried out showed that it exists a certain limitation of the method with respect to the recovery of non-symmetric sources.