HR: 1340h
AN: SF13A-0709    [Abstracts]
TI: Tensor Field Visualization in Geomechanics Applications
AU: * Hotz, I
EM: ihotz@ucdavis.edu
AF: Institute for Data Analysis and Visualization (IDAV), Dept. of Computer Science, University of California, Davis, CA 95616 United States
AU: Feng, L
EM: zfeng@ucdavis.edu
AF: Institute for Data Analysis and Visualization (IDAV), Dept. of Computer Science, University of California, Davis, CA 95616 United States
AU: Hamann, B
EM: hamann@cs.ucdavis.edu
AF: Institute for Data Analysis and Visualization (IDAV), Dept. of Computer Science, University of California, Davis, CA 95616 United States
AU: Joy, K
EM: joy@cs.ucdavis.edu
AF: Institute for Data Analysis and Visualization (IDAV), Dept. of Computer Science, University of California, Davis, CA 95616 United States
AU: Manaker, D
EM: manaker@geology.ucdavis.edu
AF: Geology Dept., University of California, Davis, CA 95616 United States
AU: Billen, M I
EM: billen@geology.ucdavis.edu
AF: Geology Dept., University of California, Davis, CA 95616 United States
AU: Kellogg, L H
EM: kellogg@geology.ucdavis.edu
AF: Geology Dept., University of California, Davis, CA 95616 United States
AB: Scalar and vector fields, and especially tensor fields like stress and strain tensor fields, play an important role in the study of geophysics, including earthquakes. For example, time-varying tensor data result from modeling the behavior of bending plates. Application areas we focus on are concerned with a better understanding of bending phenomena in rocks, in the Earth's lithosphere, and in subducting slabs. The associated mathematical models and numerical simulations generate stress and strain data that are tensors. Tensors contain so much information and related components in each point that it is not easy to capture and visualize all information. Typically, researchers plot cross-sections or maps of individual components, which do not allow a view of all the information included in models or observational data. Therefore, it is important to provide scientists with an overview of an entire tensor field. We have developed a tensor field visualization method tailored specifically to the class of tensor fields exhibiting properties similar to stress and strain tensors, which are commonly encountered in geophysics/geomechanics. These tensor fields are characterized by the property that they have positive and negative eigenvalues. The sign of the eigenvalues indicates regions of expansion and compression. To understand field behavior visually, it is important to express these features in an intuitive way. Our technique is a global method providing an overview of an entire tensor field by using a continuous representation. The main idea it to represent a tensor field as a ``texture-deforming operator,'' which resembles deforming a piece of fabric to express the characteristic properties of a tensor field. The texture is stretched or compressed and bended according to the physical meaning of the tensor field. Large positive eigenvalues, which indicate tension, are illustrated by a texture with low density or a stretched piece of fabric. For negative eigenvalues, indicating compression, we obtain a dense compressed texture. By animating the various parameters of our technique, the impression of stretching, compressing and bending can be enhanced, or used to represent time-varying data sets. The method is based on two steps: first, we define a positive definite metric with the same topological structure as the tensor field; second, we visualize the resulting metric. Every principal direction is represented using line-integral convolution (LIC). Here, a white-noise texture is blurred according to the tensor field, resulting in a high correlation of pixels along the principal lines, whereas almost no correlation appears in directions perpendicular to these lines. The resulting visualizations are highly effective depictions of the principal direction behavior over the entire field. In each LIC image, the eigenvalues of every eigenvector field are used to define the free parameters of the underlaying noise image (density, spot size) and the convolution (length of a filter kernel). In addition to these three ``structural'' parameters, color intensity can be used to enhance the impression of compression and stretching. We use a continuous color mapping, ranging from red for the smallest negative eigenvalues, white for zero eigenvalues, to green for largest positive eigenvalues. Finally, the resulting LIC images are overlaid to generate the fabric-like texture.
DE: 8159 Rheology--crust and lithosphere
DE: 8162 Rheology--mantle
DE: 8164 Stresses--crust and lithosphere
DE: 8166 Stresses--deep-seated
DE: 8168 Stresses--general
SC: Special Focus: Advances in Data Acquisition, Management, Analysis and Display [SF]
MN: 2004 AGU Fall Meeting