Simple Spatial Analysis of Complex Multivariate Airborne Geophysical Data

Ann-Marie Anderson-Mayes
Department of Geographical Sciences and Planning, University of Queensland, Brisbane, Australia
Email: a.anderson@mailbox.uq.edu.au



1. Introduction

Technological advancements of recent decades have driven the development of sophisticated systems for measuring and monitoring the world around us. The information gathered using such systems has improved our understanding of the effect humanity has on Earth, facilitating more informed responses to planning, resource management, and the environment. In particular, our ability to map the subsurface of the earth using airborne geophysical techniques has been one area to benefit significantly from these advances.

Geophysics is "the study of the Earth by quantitative physical methods" (Sheriff, 1984) and in its broadest sense can include investigations from the atmosphere to the Earth's core (Parasnis, 1997). Applied geophysics forms a subset of this broad field of study and uses seismic, gravity, magnetic, electrical, electromagnetic and radioactivity methods to investigate "relatively small-scale and shallow features which are presumed to exist within the Earth's crust" (Parasnis, 1997). The bulk of applied geophysics is concerned with the search for economically viable deposits of oil, gas minerals and water. However, in recent years there has been a trend towards using geophysical techniques for environmental, geotechnical and even archaeological studies.

Geophysical data can be collected by ground-based, shipborne or airborne platforms. The group of geophysical instruments mounted on aircraft, referred to collectively as airborne geophysics, are recognised as providing rapid, inexpensive reconnaissance of large areas with more detailed ground surveys used to follow up specific areas of interest (Parasnis, 1997). In the past one to two decades, GPS (global positioning satellite) navigation systems, digital data recording technology and rapid developments in computer technology have contributed to significant improvements in airborne geophysical data acquisition, processing, visualisation and interpretation. Research efforts in geophysics have focused on using these technologies

The consequence of this research is that in general more data sets are being collected and processed; each data set contains more data than it would have done prior to digital technology; the data is better quality and of higher spatial resolution; and the data is more accurately spatially located. Also, there is a trend towards collecting and using multivariate airborne geophysical data suites, rather than applying just one or perhaps two geophysical techniques. For example, a new airborne system under development in Australia, CERBERUS, will be able to collect magnetic, radiometric, electromagnetic, digital terrain and spectral data on a single airborne platform (CSIRO, 1997).

The single area of applied geophysics that has not been explicitly addressed in this work is the overall process of interpretation. Improved data quality naturally leads to better interpretation products in the hands of a skilled interpreter. Also, computational aspects of interpretation have benefited from improved computer technology, and the map and image products available to interpreters have made some aspects of the interpretation task considerably easier. But, the actual process of interpretation is still largely the domain of the expert interpreter using a manual approach based on a scientific, yet intuitive, assessment of visual cues. Furthermore, this conventional manual approach to interpretation is proving problematic when applied to the emerging generation of multivariate geophysical data sets.

This paper presents the results of simple unsupervised classification applied to a multivariate geophysical data set collected for a dryland salinity study in the southwest of Western Australia. The results show that some aspects of the conventional manual interpretation methodology can be enhanced by using simple spatial analysis techniques, thus improving interpretation outcomes and increasing the value of the data.

2. Interpreting Multivariate Airborne Geophysical Data Sets

The term 'interpretation' is frequently applied to geophysics to describe two different, though related, tasks. 'Computational interpretation' refers to the application of some computational process to translate geophysical measurements into a model of the physical source(s) most likely to have produced those measurements. For example, forward or inverse modelling techniques can be applied to a magnetic anomaly to deduce the probable dimensions, orientation, depth and magnetic susceptibility of the magnetic source(s).

The 'interpretation' of interest in this paper is of the second type, the interpretation of geology from geophysics. It involves extracting information from the data that leads to understanding and knowledge about the subsurface processes and structures relevant to the survey purpose. This is complicated by several factors. First, geophysical data responds to the three-dimensional distribution of multiple sources in the subsurface, so the data is mapping complex phenomena. Second, ground truth data is limited to surface geology, isolated subsurface samples from drill holes, and occasional cross-sections in road cuttings, mine walls, etc., so the data must be interpreted between these validated locations. Finally, geophysics does not normally measure the phenomena of direct relevance to an application problem. For example, aeromagnetics is widely used for groundwater exploration but it does not usually measure the presence or absence of water in the subsurface directly, rather it helps to map the geology of the subsurface so that a skilled interpreter can identify probable water-bearing formations.

Despite these intrinsic difficulties, the sheer quantity of geophysical data that has been collected and geologically interpreted successfully is testimony to the value of the technology. Furthermore, the conventional interpretation methodology, based largely on manual information extraction triggered by visual cues, has been sufficient. However, interpreting the new generation of multivariate data is proving problematic using the conventional methodology. The sheer quantity of data makes it difficult to effectively and efficiently extract information. Anderson-Mayes (1997) discussed this interpretation problem and proposed a new interpretation methodology to address this problem. This paper deals with one aspect of that new interpretation methodology - using exploratory data analysis techniques to examine relationships between variables. The exploratory analysis technique used is unsupervised classification and it is applied to a dryland salinity case study in the southwest of Western Australia.

3. A Dryland Salinity Case Study

Dryland salinity occurs when salts (principally sodium chloride) stored in the subsurface are remobilised by rising groundwater tables and deposited at the surface or in the root zone of agricultural plants (Peck and Williamson, 1987). The major contributor to rising groundwater tables is the replacement of deep rooted, native vegetation with shallow rooted pastures and crops resulting in decreased evapotranspiration and consequently increased groundwater recharge (McFarlane et al., 1993).

The spatial distribution of surface salt degradation is governed by a complex interaction of geology and surface topography. Mapping the extent of surface salt degradation can be achieved using remote sensing techniques (Wheaton et al., 1994; Evans et al., 1996). However, appropriate remediation measures can only be implemented if the specific subsurface causes of salt degradation in a study area are understood. This subsurface information must be obtained using geophysical techniques. Engel et al. (1987a, 1987b) showed that ground-based magnetic techniques identified geological controls on groundwater movement and electromagnetic techniques helped map the distribution of salt storage. A number of subsequent studies have proved that airborne geophysical data is equally successful in these two mapping tasks (see for example: Street and Anderson (1993), Street and Duncan (1992), Odins et al. (1995)). Furthermore, electromagnetic and radiometric techniques provide valuable information about the regolith which further improves our understanding of salt degradation. Therefore, a comprehensive geophysical study of salinity should include magnetic, electromagnetic and radiometric data combined with all relevant surface information.

The case study for this paper comes from the Broomehill district in the southwest of Western Australia (see Figure 1). A full interpretation report by Leeming et al. (1994) gives details of the background to the study. These details are briefly summarised here.

Figure 1: Location diagram for Broomehill case study

Figure 2: The extent of surface salt degradation at Broomehill

In late 1993, Broomehill was surveyed using two airborne geophysical aircraft. The electromagnetic system was SALTMAP, a new system designed specifically to map near surface electrical conductivity variations for salinity studies (Duncan et al., 1992). Lines were flown north-south at a spacing of 200 metres and a nominal survey height of 120 metres, with the towed bird receiver deployed approximately 95 metres behind the plane and 60 metres below it. Magnetic and radiometric data were collected simultaneously at a nominal survey height of 70 metres and a line spacing of 200 metres. Digital elevation data along line was recovered using the aircraft radar and barometric altimeters.

The purpose of the geophysical survey was to

The interpreters reported that application of their conventional, manual interpretation methodology to the multivariate data suite presented them with some difficulties. In particular, the number of geophysical and non-geophysical variables made it likely that potentially important relationships between data sets were not being identified (Anderson-Mayes, 1997) and thus the full value of the data was not being realised. This paper shows that a simple unsupervised classification can help to alleviate this problem.

4. Exploratory Spatial Analysis with Unsupervised Classification

Unsupervised classification, such as that commonly applied to remotely sensed imagery, has been chosen as the exploratory analysis technique for this study. The choice of unsupervised classification in preference to supervised classification is based on two factors. First, the purpose of the analysis is to determine what information is contained in the data. Interpreters will probably use this approach near the beginning of the interpretation process to help understand and represent the spatial correlations between the available geophysical and non-geophysical variables. Therefore, they are unlikely to have sufficient training data on which to base a supervised classification. Second, selection of the appropriate training data is difficult when dealing with geophysical data. Since the data is dealing with subsurface phenomena, there is rarely a large amount of reliable ground truth data, except where a study area is already at an advanced stage of study. Even if a good geological map exists, it will often contain a strong element of interpreted information (Reynolds, 1997), and this interpretation could bias the results of a supervised classification.

The unsupervised classification applied in this study is a two-step process. First, the classes are built using the iterative self-organising method, applied in ARC/INFO using the GRID routine, ISOCLUSTER. Second, each grid cell of the survey area is classified using the maximum likelihood classifier, implemented as MLCLASSIFY in ARC/INFO. A good description of the theory behind these two processes is given in Jensen (1996). The geophysical and terrain variables used in this study are all measured on different scales, so a normalisation process is applied to ensure that each variable is treated equally in the classification analysis. The normalisation process (suggested by Bailey (1995)) subtracts the mean from each data value and divides by the standard deviation.

In the Broomehill study, a selection of normalised geophysical and terrain variables are classified and then compared with the distribution of surface salt degradation. They are

Radiometric data responds to the upper 30cm of the Earth's surface and allows mapping of both broad lithological changes and local regolith effects (e.g. weathering) (Dickson and Scott, 1997). In this study, it provides information about the regolith materials in the study area. SALTMAP data maps near surface electrical conductivity variations (Duncan et al., 1992) and this yields information about the probable distribution of saline groundwater. Terrain data characterises the position of the regolith materials (from radiometrics) and salt storage (from electromagnetics) in the landscape. These three data sources can be logically combined in a classification because they all represent surface to near-surface geological variations. Magnetics is not included because it includes information about deeper geological features that may confuse this near surface picture.

A number of different sets of variables from the above list were classified. Trial and error determined that approximately ten classes represented the variability in the data sufficiently without making interpretation of those classes too complicated. A final set of classifications were created with a starting number of 12 classes, but a threshold of 150 sample points for the smallest class usually resulted in one or two fewer classes than this being created. For each classification, the distribution of surface salinity was compared with the distribution of classes. The results are described in the following section.

5. Comparison of Classification Results with Surface Salinity

The main purpose of the unsupervised classification at Broomehill is to determine if there is any link between the derived geophysical units and surface salinity. If such a link exists, then this can be used to aid in

Surface salinity was compared with the derived geophysical units for a number of different unsupervised classifications, and the percentage area of each class affected by salinity was calculated for four examples. Figure 3 tabulates the results for the best combination of variables with regard to salinity discrimination, and Figures 4,5 and 6 are results from classifications of subsets of these variables. The tables show results for comparison of the classes with both the SPOT and Landsat degradation maps (see Figure 2), but as these results show similar trends, only the SPOT results will be discussed in the following.

Figure 3 relates to an unsupervised classification of five normalised variables: potassium, thorium, total count, log10 of channel 10 conductivity and terrain slope. Eleven classes were identified and Class 4 (highlighted as red text in Figure 3) stands out as being significantly more salinity prone than any other class with 36.8% of it classed salt degraded according to the SPOT map. This class covers only 11.3% of the survey area, yet includes 51.7% of the SPOT salt degradation. Classes that are not salinity prone are also evident. Classes 6, 9 and 11 (highlighted in dark blue in Figure 3) are all less than 1.0% salinity and classes 2, 7 and 8 (highlighted in light blue in Figure 3) are all less than 2.5% salinity. Combined these six classes cover 47.8% of the total area and include only 10.9% of the SPOT salt degradation. So, clearly seven classes can be identified as either strongly salinity prone or not salinity prone.Figure 3: Results from Classification of Potassium, Thorium, Total Count, Terrain Slope, Conductivity

Figures 4 - 6 show results from classifications of subsets of these five variables to demonstrate that the five variable analysis does indeed give the best results in terms of salinity discrimination. Figure 4 shows the results for a three variable classification of normalised potassium, thorium and total count. This is a radiometrics only classification and no single class emerges as being strongly salinity prone, although Class 4 is moderately saline. The three classes 5, 8 and 9 are not prone to salinity, but combined they only cover 14.9% of the total survey area. So, clearly conductivity and slope are important contributors to the salinity discrimination seen in Figure 3.Figure 4: Results from Classification of Potassium, Thorium, Total Count

Figure 5 results from a three variable analysis of potassium, thorium and log10 of channel 10 conductivity, thus excluding slope. Class 8 is the most salinity prone class with 39% of it classed salt degraded according to the SPOT map. This makes it slightly more salt degraded than Class 4 in the five variable classification (Figure 3). A moderately salt degraded class is also evident - Class 9. However, this three variable classification is less effective than the five variable classification in identifying non-saline classes. Classes 2, 6 and 11 are the three significantly non-saline classes but combined they only cover 29.6% of the survey area.Figure 5: Results from Classification of Potassium, Thorium, Conductivity

Finally, Figure 6 is the same as Figure 5 except conductivity is replaced with terrain slope. Once again, two strongly salinity prone classes emerge - classes 1 and 2. Class 2 is the most salt degraded class, but at only 25.8% salinity according to SPOT it is significantly less salt degraded than the most saline classes in Figures 3 and 5. From this result we conclude that conductivity information is important in successfully dividing the landscape into units related to surface salt degradation.Figure 6: Results from Classification of Potassium, Thorium, Terrain Slope

Clearly, the five variable classification gives the best discrimination into both saline and non-saline classes. The results in Figure 5 suggest that conductivity is important for identifying the saline prone classes, since terrain slope is not included in that analysis. Figure 7 shows that the spatial distribution of the saline prone classes from these two classifications is highly correlated. However, the only good identification of non-saline classes is seen in the five variable classification, suggesting that the combination of variables yields important information.Figure 7: Distribution of salt degraded classes from Figures 3 and 5

Figure 8 is a final map of the five variable classification with SPOT salinity overlaid. The classes are shaded according to their level of salt degradation - very low, low, average or high. Clearly, the large areas of high salinity are mostly found on Class 4 as shown in the above analysis. The stream marked 'A' on the map is of particular interest. This is the only major stream in the study area which is not significantly salt affected. Clearly, it is also the only major stream which does not have a large area classified as Class 4. This indicates that this creek is geologically different from other major creeks in the catchment, an observation that might help explain the relatively non-saline status of this creek.Figure 8: Map of five variable unsupervised classification

Figure 9 shows the histograms for each class by variable for the five variable classification. It is clear that each class has a unique geophysical signature, further demonstrated in Figure 10 which tabulates the means and standard deviations for each variable in each class. Thorium and total count distributions are quite highly spatially correlated in this case study, so it might be asserted that using both is inappropriate since a class that has low total count values usually has low thorium values. However, classes 3, 7 and 8 do not conform to this norm because in all three the total count component is relatively higher than the thorium component, proving that including both adds valuable discrimination of the landscape.Figure 9: Histograms of each variable in each class for five variable classification

Figure 10: Means and standard deviations of each variable in each class

The histogram analysis in Figure 9 effectively represents the geophysical properties of the various classes. Class 4, the most salt-affected class, covers the lowest slopes, the highest conductivities, low to moderate potassium, low total count and low thorium. This makes sense since it is already well known that most of the surface salinity is found adjacent to the streams in the lowest parts of the landscape. The non-saline classes (2, 6, 7, 8, 9 and 11) include the full range of slope values (although mostly higher slope values); the full range of conductivity values (although mostly lower conductivity values); the full range of potassium and thorium values; and the full range of total count values (although mostly higher total count values). Although, the general trends here are as expected (i.e. high slopes and low conductivities), the full range of values is represented in all five variables, confirming again that it is the combination of geophysical signatures in each class which is giving discrimination of these non-saline units.

6. Conclusions

This paper has clearly demonstrated that an unsupervised classification of combined geophysical and terrain variables can divide the landscape into regions that are meaningful in terms of surface salt distribution. It is significant that an unbiased classification of the data correlates so well with an independently determined map of surface salinity. This proves that

  1. information relevant to salinity development is contained within the geophysical data; and,
  2. the information can be efficiently interrogated and represented using simple unsupervised classification techniques.

Furthermore, this is not an isolated result. In a related study, Clarke et al. (1998) report excellent correlation between mapped Tertiary sediments and an unsupervised classification of geophysical and terrain data. Again, there is useful information in the combination of variables that can readily be extracted using a simple spatial analysis technique.

In terms of improving interpretation of multivariate airborne geophysical data, these are important results. The conventional, manual interpretation methodology would simply not be able to divide the landscape into meaningful units so efficiently and effectively. This paper demonstrates that a very simple spatial analysis technique can yield useful information, replacing the cumbersome and ineffective manual overlay approach to spatial correlations. Adherents to the conventional interpretation approach are justly cautious about 'automatic' interpretation techniques, but use of techniques such as classification help to alleviate the labour intensive tasks of interpretation, freeing the interpreter to concentrate on the knowledge intensive tasks.

It is probable, even in the near future, that more complex spatial analysis techniques being developed in the field of geocomputation will enable more sophisticated analysis of multivariate geophysical data. However, in the meantime, it is important to demonstrate that even very simple (and readily applied) spatial analysis techniques can improve interpretation outcomes.

Acknowledgements

I would like to acknowledge World Geoscience Corporation Limited who have supported this research project through provision of data, funding and expertise. Also, special thanks to Dr Pramod Sharma and Mr Greg Street for their invaluable guidance and advice.

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