CG72A-01

Distributed Geocomputations and Web Collaboration

* Blais, J (blais@ucalgary.ca), University of Calgary, Geomatics Engineering 2500 University Drive N.W., Calgary, AB T2N 1N4, Canada

With the new Cyberinfrastructure available to the scientific community, advanced geocomputations are often distributed and with Virtual Globes, Observatories and HUBs, the environment is most conducive to web collaboration. Remote sensors can be networked using the web facilities and observational data analyzed from the desks of scientists in practically any location around the world. This is especially important in such fields as astronomy, geophysics and environmental science which have observatories and sensor instrumentation most often in remote locations. Examples of web networks will be described with some of the computational challenges for geoscientists. In particular, the Turtle Mountain Monitoring Project and Field Laboratory in South-Western Alberta will be briefly discussed. With the semantic web and related developments, scientific knowledge is going to benefit from such web collaboration in ways unheard of only a few years ago.

CG72A-02

3-D Finite-Element Modelling of Magnetotelluric Data With a Static Divergence Correction

* Farquharson, C G (cgfarquh@mun.ca), Memorial University of Newfoundland, Department of Earth Sciences, St. John's, NL A1B 3X5, Canada

In the magnetotelluric method measurements are made of the electric and magnetic fields that are generated by electric currents induced in the Earth's subsurface by the naturally occurring time variations of the Earth's magnetic field. The induced currents, and hence the measured electric and magnetic fields, depend on the electrical conductivities of the geological structures in the subsurface. The most common technique for computing magnetotelluric data for a given 3-D Earth model is the finite-difference method. This has been applied to the second-order partial differential equations for the E-field and the H-field. In both cases it was found that a static divergence correction term greatly increased the efficiency of the solution procedure. Recently the finite-element method has been receiving attention as a means of modelling magnetotelluric data. The usual implementation of this method involves a discretization of the E-field in terms of edge-element basis functions. Because these basis functions preserve the continuity of the tangential component of the E- field between cells, it was thought that a static divergence correction like that for the finite-difference method was not necessary. However, this is not the case. A static divergence correction term, which is the gradient of a scalar potential calculated by solving a finite-element discretization of the direct-current resistivity differential equation, and which is the finite-element equivalent of the correction term developed for the finite-difference solution procedures, significantly accelerates 3-D finite-element magnetotelluric modelling.

CG72A-03

The Role of Multi-Dimensional Wavelet Approximation in Geodetic Applications: De- Noising, Compression and Analysis Tool

* Elhabiby, M (mmelhabi@ucalgary.ca), Senior Research Engineer, Department of Geomatics Engineering, University of Calgary, 2500 University Dr. N.W., Calgary, AB T3B2V3, Canada
Sideris, M G (sideris@ucalgary.ca

El-Sheimy, N (elsheimy@ucalgary.ca) AB: Multi-resolution wavelet transform representation of signals is a very powerful tool for geodetic applications. The focus of this paper is to evaluate and explore the role of wavelets in different multi-dimensional geodetic applications and on different approximation levels, using planar, torus and spherical implementations. Four different wavelet properties will be numerically evaluated, namely de-noising, de-trending, compression and analysis. (1) De-noising, de-trending and analysis are applied for the removal of the GPS long wavelength carrier-phase multipath error in the measurement domain. (2) Analysis and compression are introduced through the implementation of a wavelet transform algorithm combined with a conjugate gradient method for the inversion of airborne gravimetry integral (downward continuation). In this application we introduce the power of wavelets in performing three-dimensional inversions, using the two-dimensional wavelet transform. For global multi-resolution analysis, an approximation is introduced on (3) the torus and (4) the sphere. The former is a combined two-dimensional wavelet-torus technique for the multi-resolution analysis of time- variable global gravity field recovery, using first generation wavelets. This combined algorithm is used for the analysis of GRACE time variable changes at all different levels of decomposition and is compared to the spherical wavelet transform. Conclusions and recommendations are given with respect to the suitability, accuracy and efficiency of the wavelet transform as a powerful mathematical tool that can be used in numerous geodetic applications.

CG72A-04

The Singular Spectrum Analysis Approach in the Analysis of Weekly GRACE and Hydrology Models Water Mass Anomalies Information

* Rangelova, E (evrangel@ucalgary.ca), Department of Geomatics Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada
Kim, J W (jw.kim@ucalgary.ca), Department of Geomatics Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada

We use the method of singular spectrum analysis to extract short- and long-term periodic water mass anomaly signals from a time series of the recently publicly available GFZ weekly GRACE solutions. We analyze time- lagged continuous time series (from February 2004 to May 2008) of GRACE spherical harmonic coefficients of maximum degree and order 30. One of the main advantages of performing the analysis in the spectral domain instead of in the spatial domain is the reduction of the computational load because a much smaller number of coefficients than spatial pixels are analyzed. Furthermore, no de-striping and isotropic smoothing filters are necessary because our filtering technique is able to smooth significantly the GRACE random errors and to reduce largely the correlated errors besides extracting all significant periodic signals. Moreover, the removal of part of geophysical signals together with the correlated GRACE errors and the reduction of the GRACE-derived water mass anomaly amplitudes are avoided. We demonstrate that our filtering technique effectively reduces the average RMS of water mass variability over the oceans when all but annual, semi-annual and long-term global variations in the spherical harmonic coefficients are filtered out. On land, we compare the filtered weekly GRACE-derived water mass anomalies with the weekly-averaged GLDAS mass anomalies for Amazon, Congo, Ob and Mississippi basins. The GRACE-derived trends agree well with the GLDAS model trends in all of the studied basins. Our results also demonstrate that the singular spectrum analysis approach is a powerful tool for extracting any short- and long-term signals as well as phase shifts and amplitude variations of the periodic water mass anomalies.

CG72A-05

On Monte Carlo Methods and Applications in Geoscience

* Zhang, Z (zhanzhan@ucalgary.ca), University of Calgary, Geomatics Engineering 2500 University Drive N.W., Calgary, AB T2N 1N4, Canada
Blais, J (blais@ucalgary.ca), University of Calgary, Geomatics Engineering 2500 University Drive N.W., Calgary, AB T2N 1N4, Canada

Monte Carlo methods are designed to study various deterministic problems using probabilistic approaches, and with computer simulations to explore much wider possibilities for the different algorithms. Pseudo- Random Number Generators (PRNGs) are based on linear congruences of some large prime numbers, while Quasi-Random Number Generators (QRNGs) provide low discrepancy sequences, both of which giving uniformly distributed numbers in (0,1). Chaotic Random Number Generators (CRNGs) give sequences of 'random numbers' satisfying some prescribed probabilistic density, often denser around the two corners of interval (0,1), but transforming this type of density to a uniform one is usually possible. Markov Chain Monte Carlo (MCMC), as indicated by its name, is associated with Markov Chain simulations. Basic descriptions of these random number generators will be given, and a comparative analysis of these four methods will be included based on their efficiencies and other characteristics. Some applications in geoscience using Monte Carlo simulations will be described, and a comparison of these algorithms will also be included with some concluding remarks.

CG72A-06

Evaluation of Interpolators for Void Filling of Geophysical data sets

* Taghvakish, S (staghvak@ucalgary.ca), PHD Student, Dept of Geomatics Engineering, University of Calgary, 2500 University Drive N.W., Calgary, AB T2N 1N4, Canada
Braun, A (braun@ucalgary.ca) AB: In every physical observation there can be data voids due to no-continuous observation, instrument or operator errors or environmental obstacles. Thus, the lack of continuous data is a very common side effect especially in earth observation disciplines . One way to fill data voids is to use interpolators to re-establish the continuity. This study is devoted to evaluate different numerical interpolators including Thin Plate Splines, Kriging, Projection onto convex sets, with a focus on their behavior with respect to data roughness. In order to systematically analyze the performance of the interpolators, synthetic data sets were produced using an Autocorrelation function and a correlation length. By doing this, almost any type of data roughness can be simulated, which allows for a systematic analysis of the roughness vs. interpolator performance parameter space. The roughness parameter can be calculated with different means, which is also considered in the analysis. Eventually, the results allow for the determination of the optimal interpolator for any arbitrary geophysical data set, once its roughness has been determined. Data sets considered include geopotential models, gravity anomalies and topographic data. The methodology can be easily adopted for additional interpolation algorithms.

CG72A-07

The use of Wavelets in GPS Error Analysis with Emphasis to Singularity Detection and Multipath Removal.

* El-Ghazouly, A (aaelghaz@ucalgary.ca), Mobile Multi-Sensor Systems (MMSS) Research Group, Department of Geomatics Engineering, the University of Calgary., 2500 University Dr. N.W., Calgary, AB T2N 1N4, Canada
Elhabiby, M (mmelhabi@ucalgary.ca

El-Sheimy, N (naser@geomatics.ucalgary.ca) AB: GPS errors such as cycle slip and multipath are contaminated with GPS data measurements and degrade the position accuracy and stability. Cycle slip error is defined as singularity points of sharp variation in a data series. The cycle slip error must be detected and removed. The multipath error is a combination of medium/low frequencies that are contaminated with GPS measurements. To achieve a high accurate position solution cycle slip should be detected and removed and multipath error should be reduced or removed if applicable. The ability of wavelet to transform the data to the frequency domain with high resolution in both time and frequency domains helps in localizing different error types, which leads to an innovative technique that could be used for error mitigation. In this paper, the ability of wavelet multi-resolution analysis to tackle both cycle slip and multipath errors in the carrier phase measurement domain is introduced. Wavelet-based singularity detection and removal is introduced under different situations for cycle slip especially when small signal to noise ratio exists. Also, this paper presents wavelet-based trend extraction for multipath mitigation in carrier phase measurements domain using wavelet multi-resolution analysis. Systematic errors (mainly multipath) are isolated and extracted from GPS double difference residuals using wavelet multi-resolution analysis by the application of new trend detection methodology. The proposed wavelet-based singularity detection will lead to reliable cycle slip detection and removal even under small signal to noise ratio. Also, the wavelet-based trend extraction will lead to the removal of multipath signal especially low frequency multipath error.

Authors (2009), Title, Eos Trans. AGU, 90(22), Jt. Assem. Suppl., Abstract xxxxx-xx