Bayesian spectral density approach for modal updating using ambient data

The problem of identification of the modal parameters of a structural model using measured ambient response time histories is addressed. A Bayesian spectral density approach (BSDA) for modal updating is presented which uses the statistical properties of a spectral density estimator to obtain not only the optimal values of the updated modal parameters but also their associated uncertainties by calculating the posterior joint probability distribution of these parameters. Calculation of the uncertainties of the identified modal parameters is very important if one plans to proceed with the updating of a theoretical finite element model based on modal estimates. It is found that the updated PDF of the modal parameters can be well approximated by a Gaussian distribution centred at the optimal parameters at which the posterior PDF is maximized. Examples using simulated data are presented to illustrate the proposed method. Copyright © 2001 John Wiley & Sons, Ltd.     

Probabilistic approach for modal identification using non‐stationary noisy response measurements only

This paper addresses the problem of identification of the modal parameters for a structural system using measured non‐stationary response time histories only. A Bayesian time‐domain approach is presented which is based on an approximation of the probability distribution of the response to a non‐stationary stochastic excitation. It allows one to obtain not only the most probable values of the updated modal parameters and stochastic excitation parameters but also their associated uncertainties using only one set of response data. It is found that the updated probability distribution can be well approximated by a Gaussian distribution centred at the most probable values of the parameters. Examples using simulated data are presented to illustrate the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.     

Geophysical Applications of Multidimensional Filtering with Wavelets

--We present imaging results in geophysics based on using multidimensional Gaussian wavelets as a filter in a 2-D Cartesian domain. Besides decomposing the field into various distinct lengthscales, we have also constructed the 2-D maps describing the spatial distributions of the maximum of the wavelet-transformed L₂-norm E_max (x,y) and its corresponding local wavenumber k_max (x,y), where x and y are the Cartesian coordinates. For geoid anomalies, using a wavelet filter extending to 90 degrees, we have discerned the distinct outlines of convergent and divergent tectonic zones and have conducted a quantitative comparison of the short-wavelength gravitational anomalies at those wavelengths between two different geographical locations. We have also compared the wavelet results with a nonlinear bandpass filter in the spectral domain where a Gaussian filter with the logarithm of the degree l acting as the argument has been employed. A wavelet solution, with a length-scale corresponding to 256 degrees, would need a filter with over 400 spherical harmonics centering around l=157 for an optimal spatial fit. The computational effort with the bandpass filter technique greatly exceeds those associated with wavelets. We have also shown the ability of the wavelets to analyze the vastly different scales present in high Rayleigh number convection and the mixing of passive heterogeneities driven by thermal convection. Wavelets will be a useful tool for rapid analyzing of the large multidimensional fields to be captured in many other geophysical endeavors, such as the upcoming gravity satellite missions and satellite radar interferometry images.     

Improved treatments for evaluating horizontal magnetic components through the 3-D FDM in E-polarization induction problems

Introduction The algorithm of the finite difference method (FDM) for solving the 3-D induction problem used by CHEN (1985) is based on the concept suggested by Brewitt-Taylor and Weaver (1976), which assumes the conductivity to be a smoothly-varying function of position. After the comparisons between many model calculations carried out by the author and other methods showed that the vertical components estimated by our method are acceptable in general cases. However, the reliability of the…     

Interactive Statistical Analysis of Complex Mantle Flows with the Web

Up to now, all of the figures in mantle convection literature have been presented in a static manner, where the fields at one scale are shown on a printed page . This is no longer possible with the spatial resolution increasing at an ever rising clip and the appearance of the issue of multi-scale structures. Because of the onslaught of data-flooding and the growing complexity of strongly time-varying physical fields from compressible mantle convection, such as the adiabaticity, and other thermo dynamical heating functions, we can no longer afford to display and look at the results in the same static way as in a book. We have developed a new approach for interrogating data coming out from numerical simulations. This is based on an interactive two-dimensional map which is used over the WEB with a client-server paradigm. We have applied this to investigate mantle convection flows in both two-and three-dimensional situations. The distributions of thermal anomalies found are no longer Gaussian but sometimes have long tails, especially near the edges of plume heads. The same is also found for the distribution of mechanical heating, which can be quite skewed. Our experiences with this new interactive mode of data-query have shown both the educational and scientific importance of using the world wide web media to quiz handily the data taken from large-scale numerical simulations.     

The physical Properties of marine sediments as inferred from Wavelet Correlation Analysis

Seismic waves traveling in the water/sediment or sub-bottom sediment interface have been the subject of considerable interest in underwater acoustics in recent years. Some progress has been made in understanding the propagation and attenuation characteristics of interface waves in different geological environments. However, the generating mechanisms are poorly understood. In particular, what is the acoustic-seismic energy conversion process? As seismic waves involve both time and space parameters it should be able to relate directly the propagation characteristics of the ocean bottom interface waves to the shear properties of the sediments over the propagation area. To address these problems we have applied the wavelet correlation method (WCR) to examine the variations of bottom characteristics and their role in coupling waterborne sound into the sea bottom. To confirm the validity of the developed modeling technique, we applied the wavelet correlation analysis for synthetic seismograms and field data. In this discussion paper we present images of the first and second shear modes and the interface wave component as a function of arrival time and frequency. We also discuss the possibility of inverting phase and group velocity information directly from the wavelet cross-correlation function and propose the way of using the WCR method to predict physical dynamic parameters of marine sediments.     

Stability of the oceanic lithosphere with variable viscosity: an initial-value approach

We have studied the problem concerning the onset of convective instabilities below the oceanic lithosphere. A system of linear partial differential equations, in which the background temperature field is time-dependent, is integrated in time to monitor the evolution of incipient disturbances. Two types of rheologies have been examined. One depends strongly on temperature. The other involves a viscosity which is both temperature- and pressure-dependent. The results from this initial-value approach, in which the viscosity profiles migrate downward with time, reveal the importance of considering temperature- and pressure-dependent rheology in issues regarding the development of local instabilities in upper mantle convection. For temperature-dependent viscosity, viscosities of 0(10²⁰P) are required to produce instabilities with growth-rates of 0(.1/Ma). In contrast, these same growth rates can be attained for a temperature- and pressure-dependent viscosity profile with a mean value close to 0(10²⁰P) in the upper mantle, owing to the presence of a low viscosity zone, 0(10²⁰P), existing right below the lithosphere. Unlike the results of temperature-dependent viscosity, whose growth-rates increase with time, the amplification of disturbances in a fluid medium with temperature- and pressure-dependent rheology reaches a maximum at an early age, < 50 Ma, and decreases thereafter with time. This suggests the potential importance played by initial disturbances in the evolution of the oceanic lithosphere.     

Volume rendering visualization of 3D spherical mantle convection with an unstructured mesh

We propose a new approach to utilize the algorithm of hardware-assisted visibility sorting (HAVS) in the 3D volume rendering of spherical mantle convection simulation results over unstructured grid configurations. We will also share our experience in using three different spherical convection codes and then taking full advantages of the enhanced efficiency of visualization techniques, which are based on the HAVS techniques and related transfer functions. The transfer function is a powerful tool designed specifically for editing and exploring large-scale datasets coming from numerical computation for a given environmental setting, and generates hierarchical data structures, which will be used in the future for fast access of GPU visualization facilities. This method will meet the coming urgent needs of real-time visualization of 3D mantle convection, by avoiding the demands of huge amount of I/O space and intensive network traffic over distributed parallel terascale or petascale architecture.     

Visualization of time-dependent dynamics of postglacial rebound

Postglacial rebound is a major geological process which plays an important role in many areas in the earth sciences. Up to now, most of the images derived from studies of the glacial isostatic adjustment phenomenon have been concerned with surface signatures, such as the uplift and gravity anomalies and not much attention has been paid on the dynamical responses in the mantle. We will make use of the 3D visualization package Amira to depict both the external and internal deformation histories of the transient viscoelastic flow inside the mantle induced by postglacial uplift. Of particularly great interest are the transient displacement fields and shear heating inside the mantle. This same visualization technology can be brought to bear in the future for visualizing tsunami waves in ocean basins excited by earthquakes, volcanic eruptions and InSAR images. We have also integrated the visualization results into the Google Earth virtual globe by combining this scheme with the Amira package to provide a better geographical and dynamical context. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.