DATA INTEGRATION USING THE IMAGE GRAND TOUR

Introduction

Geoscience, like many disciplines, is experiencing an overabundance of data. A geoscientist often has access to a large variety of data including gravity anomalies, magnetic anomalies, digital elevation grids, laser altimetry, multispectral imagery, geological maps, and seismic velocity images. The challenge is then to take these varied and often disparate sources and to integrate them together in a manner that increases knowledge and understanding of the underlying structures and processes in the Earth.

This integration problem is inherently difficult in visualization related to the high dimensionality of the data. When visualizing the data as an image, there are a number of different color models that will support the display of multidimensional spatial data with the most common being Red-Green-Blue (RGB). However, it is generally the case that these methods will at most allow for the display of three different components. While there has been work in visualizing more than three dimensions of spatial information, these approaches generally add only a few additional dimensions. Furthermore, the increased ability to visualize dimensions comes at a cost of increased complexity and difficulty in analysis and understanding.

Dimensionality Reduction

A common way to deal with the difficulties of visualizing multidimensional data is to first reduce the dimensionality by methods such as linear projections. Perhaps the most popular method of doing this is Principal Component Analysis (PCA). PCA is a common technique in remote sensing, often being applied to multispectral imagery. Guo et al (2006) applied it to spectral decomposition of seismic data with excellent results. However, PCA has some serious limitations as its goal is to maintain the maximum variance in the projected data. The reliance upon variance is troubling in many remote sensing applications since the feature of interest may only be a small portion of the data set. In such a case, the variance of the overall data set is likely to be dominated by the background or noise. As such, PCA may be optimally wrong in that it may maximize the noise. Additionally, the global nature of PCA means that local dependencies are generally ignored in favor of global trends. The most interesting limitation is the lack of involvement of the implied spatial nature of structure in spatial data. Organization of the data in the spatial view of the data is not considered in PCA.

Image Grand Tour

The Image Grand Tour (IGT) is an interactive method for doing dimensionality reduction when the data is spatial in nature and can be visualized as an image. The IGT involves defining a smooth trajectory in the set of all possibly linear projections. This trajectory may be chosen according to a number of criteria including denseness or maximum coverage in a finite time. The idea is then to view the data as projected in image form in a smooth manner, creating a form of data movie. The geoscientist can then visualize the data from ‘all possible angles' and look interactively for interesting views that offer insight into the data. The IGT has been applied to a number of areas including medical imaging, land mine detection, and multispectral imaging. Wallet and Marfurt (2008) demonstrated the value of applying the IGT to interpreting spectral decomposition information from seismic data. They demonstrated that the IGT yielded information that was not readily apparent using PCA alone. In doing this, they constructed single, grayscale views of the data that showed data features that increased understanding of the data.

Application

We illustrate the grand tour technique by applying it to a land seismic survey acquired over south Texas, USA. Spectral decomposition was run on the volume resulting in 85 spectral components, ranging from 5 Hz to 90 Hz. We recognized a horizon containing a fluvial- deltaic system and flattened each data volume. We then applied PCA to these 85 images to reduce them to the eight highest PCA images (Figure 1). We note that several channel features can be seen in the first six principal components or eigenspectra, while only random noise (either geological or seismic) can be seen in eigenspectra 7 and 8.

FIGURE 1 NEAR HERE

Examining other eigenspectra revealed that significant information appeared outside the first three images (Figure 1). However, by the time we reach the seventh eigenspectrum, little information appears visible. We thus chose to run the IGT using the first six eigenspectrum since they appear to capture all of the value in the data set.

Running the IGT revealed structure that was not readily apparent when examining just the first three eigenspectra. We stop our tour any time we identify a feature of geologic interest. The top of Figure 2 shows the six coefficients applied to each eigenspectra at the current tour location. Several small channels appear that were difficult to see in Figure 1. Figure 2a presents various meandering channels, several of which were not clearly visible or in the first three eigenspectra. Figure 2b clearly shows a distinct view of a single meandering channel. While this channel was visible in previous images, this view provides tighter localization. This illustrates the value of combining information gathered from multiple tour projections.

FIGURE 2 NEAR HERE

Conclusions

The IGT is a valuable method for integrating multiple data sources interactively. Since the geoscientist controls the projections, the process is geared towards views that are interesting from a domain specific definition rather than predefined criteria related to variance. Using the IGT, it is possible to construct views of data that reveal insight that is not apparent using other methods.

Acknowledgments

We thank Anadarko Petroleum for permission to use its seismic data in this study. This study was partly supported by the U.S. National Science Foundation via the GEON project.

References Cited

Guo, H., K. J. Marfurt, J. Liu, and Q. Dou, 2006, Principal components analysis of spectral components: 76th Annual International Meeting, SEG, Expanded Abstracts, 988-992.

Wallet, B. C. and K. J. Marfurt, 2006, A grand tour of multispectral components: A tutorial: The Leading Edge, 27, 334-341.

Figure Captions

Figure 1: The first eight eigenspectra (principal components) representing the vast majority of the energy in the 85 spectral components. Note that different channel features appear stronger in different components. Eigenspectra V7 and V8 show very little channel information. Eigenspectra V2 and V3 are quite sensitive to the NS-trending acquisition footprint.

Figure 2: (a) A IGT projection that illuminates very narrow meandering channels (yellow arrows) and a NW-trending major channel that corresponds to deeper valley fill (magenta arrow). (b) An IGT projection that is in general featureless, except for the channel indicated by the green arrow.

Acronyms

• IGT – Image Grand Tour

• PCA – Principal Component Analysis