Quantitative Magnetization Vector Inversion

Transcription

1 Quantitative Magnetization Vector Inversion I. N. MacLeod, R. G. Ellis 1. Geosoft Inc., Canada, 2. Geosoft Inc., Canada, BIOGRAPHY Ian MacLeod (BSc, Geology, Queen's University, 1978) is the Chief Technologist and founder of Geosoft Inc., Canada. Ian has been involved in the geologic interpretation, modelling and analysis of geophysical data for the purposes of resource exploration for more than 30 years. Dr. Robert Ellis (PhD, Theoretical Physics, University of Melbourne, 1981) is currently Principal Scientist for modelling at Geosoft Inc. Dr. Ellis was a founding member of the University of British Columbia Geophysical Inversion Facility, and subsequently continued to advance and apply geophysical inversion techniques as Principal Geophysicist at BHP Billiton Exploration, joining Geosoft Inc. in SUMMARY Modelling of magnetic rock properties from magnetic field observations has been an important practice in resource exploration for decades. However, the application of this practice has been limited by conventional thinking, which assumes rock magnetization is dominated by induced magnetization such that magnetization direction is aligned with the geomagnetic field. Convention has also accepted that we are unable to model for magnetic remanence without a- priori knowledge of remanence direction and strength. Recent practical successes in directly modelling magnetization vector direction and strength using Magnetization Vector Inversion (MVI) have challenged these conventions, and MVI modelling is proving useful in practical exploration scenarios. The addition of new information, namely the direction and amplitude of magnetization, demands new thinking and approaches to understanding what this information means, and how to use the modelled direction of magnetization in practical situations. This paper presents a new statistical and quantitative approach to define and discriminate different magnetization domains within a full 3D MVI voxel model. Our studies show that modelled vector direction is meaningful even without prior knowledge of remanence (and other) magnetization characteristics. We also demonstrate that reasonable magnetization direction can be recovered from both weakly and strongly magnetized source rocks. Key words: MVI, QMVI, 3D Inversion, Remanence, SOM INTRODUCTION The SAGA 2015 committee challenged us to "Think differently - Do differently". For decades, our approach to modelling magnetic rock properties from magnetic field observations has been bounded by conventional thinking, which includes: The modelling of conventional susceptibility as the primary magnetic rock property on the assumption that magnetization results mostly or entirely from conventional induced magnetization. Our inability to account for remanent magnetization without knowledge of the direction and strength of the remanent component. Both Ellis et al (2012) and Pratt et al (2012) developed methods for direct inversion of the magnetization vector from total magnetic field data. While Pratt pursued the use of a parameterized model, Ellis developed a 3D voxel inversion approach, and both efforts concluded that inversion to a varying direction and intensity of magnetization without prior knowledge of the direction of magnetization was possible and useful. Pratt's parameterized model approach is limited by the assumption of fixed body boundaries with uniform magnetization, and one must initially determine a reasonable geometric boundary for the model. Ellis' full 3D voxel inversion approach allows the magnetization vector to vary in each model cell and relies on a smoothness constraint to limit variation between cells. We consider the voxel inversion to be a more general approach that has the considerable benefit of inverting for different directions of magnetization within the model volume. However, the smoothness of inverted 3D voxel models can make it difficult to identify and classify separate rock units. We approach this challenge in two ways. First, the application of focussing using Iterative Reweighted Inversion (Ellis, 2012), which sharpens boundaries around distinctively anomalous features, and second, by applying Self Organizing Map network analysis (Kohonen, 1982) to classify separate domains of magnetization, which we demonstrate in this paper. Once magnetization domains have been established, we are able to quantify the direction and amplitude of magnetization for an identified anomalous domain using a process we call Quantitative Magnetization Vector Inversion (QMVI). This involves determination of the direction, amplitude and scatter based on Fisher statistic. Scatter provides a measure of the uniformity of magnetization direction within a domain, and this can be used as a measure of confidence. Aside from SOM domain classification, in a study of the Black Hills Norite in South Australia, Extended Abstracts of 14th SAGA Biennial Technical Meeting and Exhibition 2015 Page 1

2 (2013) demonstrated that voxel inversion for the direction of magnetization does indeed recover the true direction of magnetization. In this paper we expand that work to identify additional magnetic domains and use the method of QMVI to quantify notably different magnetic units. METHOD AND RESULTS (2013) demonstrated that the peak magnetization within a strong magnetization swarm does accurately indicate the magnetization direction. In order to further test the sensitivity of MVI modelling to multiple magnetization directions and intensity of magnetization, we first consider a synthetic example in which we place 4 weakly magnetized (0.01 SI) prismatic bodies with orthogonally different directions of magnetization around a more strongly magnetized body (1.0 SI). This synthetic model is measured in the presence of a geomagnetic field with declination 1.2 degrees and inclination -56 degrees, and illustrated in Figure 1. Notable is the weakness of the response from the low susceptibility bodies relative to the dominant anomaly from the 100 times more magnetic body at the centre of the model. Figure 2 shows the VOXI MVI result of the synthetic model response in comparison to the true model. MVI is able to identify all 5 bodies with reasonable fidelity. We show the MVI vectors for the Southwest prism, which demonstrate reasonable alignment with the true model. Figure 3 shows the average direction of magnetization determined from MVI modelling for all 4 weakly magnetized bodies, and these have generally good agreement with the expected magnetization. On the strength of these synthetic tests, we have developed the Quantitative Magnetization Vector Inversion (QMVI) method for application to real data. QMVI has the following 4 steps: VOXI MVI (Magnetization Vector Inversion) inversion, focussed with two passes of Iterative Reweighted Inversion (IRI Ellis, 2012). Identification of anomalous magnetization by the application of Self Organizing Maps (SOM) to the magnetization amplitude K, and vector components (Kx,Ky,Kz) to automatically identify magnetization domains that are distinct from above background responses. Further SOM classification of the normalized direction of magnetization, Norm(Kx,Ky,Kz), to identify separate magnetization domains based on direction. Quantification of direction and amplitude within each domain to determine average MVI susceptibility, dominant direction, and Fisher statistic estimate of the scatter of direction. Black Hills Norite As noted previously, the authors used the direction of magnetization at the peak amplitude of an MVI model of the Black Hills Norite to demonstrate the accuracy of MVI with regard to magnetization direction. Here we revisit that work and apply the QMVI technique more broadly. Figure 4 shows the total magnetic intensity in an area enclosing the Black Hills Norite in South Australia. The Norite intrusive complex is represented by prominent asymmetric magnetic anomalies A, B and C, and the more symmetric anomaly D. Prior studies have focussed on Anomaly C as the magnetic properties of the source rock at this location are well established in the literature. In this work we broaden our analysis to the other anomalous areas, and in particular consider Anomaly D, which shows a very different anomaly shape that would suggest a different direction of magnetization. The first step in the analysis involves inverting for magnetization direction using VOXI MVI. The voxel model comprised 239 x 224 horizontal cells 100m square; 30 cells in depth, 50m thick at surface, with thickness increasing with depth to a total model thickness of 3.2 km. Figure 5 shows a VOXI MVI model magnetization amplitude slice at a plan depth of 1200 m. The voxel approach to inversion produces smoothly varying results, as demonstrated in Figure 5. Some sharpening of contrast is possible with focussing, and in this case we have applied two passes of Iterative Reweighted Inversion focussing, in which the output of an inversion is used as a weighting function in successive iterations to encourage anomalous features to become more focussed. While magnetization in nature may indeed be smoothly varying, conceptual models of geology benefit from thinking about magnetization as a rock property that is somewhat uniform across a geologic unit of interest. It is common practice for an interpreter to create a susceptibility amplitude isosurface, which is presented as a "shell" to visually represent an interpreted feature of interest. However, this approach only deals with one scalar parameter (MVI susceptibility), and is unable to consider direction of magnetization. Furthermore, the choice of value is arbitrary and generally not well justified. Li and Sun (2014) show how clustering might be incorporated into the inversion to enforce uniformity within a single body. Our approach is to use a Self- Organizing Map (SOM) to classify the resulting VOXI MVI inversion based on direction and amplitude and thus identify anomalous domains with characteristic magnetization direction and MVI susceptibility amplitude. Given VOXI MVI model, we separate truly anomalous and distinctive magnetic zones from background by Extended Abstracts of 14th SAGA Biennial Technical Meeting and Exhibition 2015 Page 2

3 creating a (SOM) classification (after Fraser and Dickenson, 2007) of just 4 background classes based on the VOXI MVI susceptibility amplitude K and direction vector (Kx,Ky,Kz). We then create a set of new "anomalous" classes from the 2% of data that least fit the background classes. All voxel cells are then assigned to either a background class or an anomalous class based on Euclidean distance between the cell value (K,Kx,Ky,Kz) and the class centroid. Although only the most anomalous 2% of data are used to define anomalous classes, the reclassification process will generally assign more than 2% of the cells into the anomalous classes. In our experiments we have found this process to be remarkably robust, and thus provides an objective way to identify the boundary of magnetic domains in a way that is able to consider amplitude and direction of magnetization. Figure 6 shows the automatically identified anomalous domain for the Black Hills study area. Only cells that lie within these anomalous classes are considered for further analysis. It is worth distinguishing between a "class" and a magnetic "domain". In this paper, we refer to a class as a statistical classification that comes from an automatic SOM analysis. An interpreter must decide if a class represents a geologically meaningful domain of magnetization. The interpreter may also choose to combine two or more classes into a single domain that is meaningful to the interpretation. Our interest now is to separate just the anomalous data into separate magnetization domains based on direction of magnetization. To do this we again turn to SOM analysis, but now we use only the normalized magnetic vector directions Norm(Kx,Ky,Kz). In this step the interpreter decides the number of domains expected and chooses an appropriate number of SOM classes. Figure 7 shows a 3D perspective of the final colour-coded direction-classified model. This clearly shows three distinct magnetization domains. Notably, the red domain that gives rise to anomaly D is clearly distinguished from the other domains. We also see that the source for anomalies A, B and C (the blue domain) is consistently defined, as is a third possibly interesting domain that aligns with magnetization on the Northeast side of the interpreted intrusive bodies. The final step in the QMVI process is to quantify and report the magnetization amplitude, direction and scatter based on the Fisher statistic. Our 2013 work demonstrated that magnetization tends to align with the true magnetization at the magnetic peak in an MVI model, with vectors straying away from this alignment with distance from the peak and relative to the size of the magnetic feature. Based on this observation we use the most magnetic 20% of cells within a domain to calculate an average magnetization amplitude (MVI susceptibility), magnetization direction and scatter. The result of this analysis for the Black Hills Norite study area is shown in Figure 7 together with the colour-coded domains. Our choice of 20% is somewhat arbitrary, though we suggest that using this metric in QMVI reporting will provide a consistent measurement by which to compare future estimates of magnetization direction within QMVI derived domains. Once a geologically meaningful set of magnetization domains have been established over a particular geologic region, it would be convenient to then use these domains to classify MVI results in other parts of a study area. Such a process would involve first separating anomalous magnetization from background, and then assigning anomalous cells to the meaningful magnetization domains based on normalized direction, or normalized direction and amplitude should amplitude difference be a distinguishing attribute. One could evaluate the degree of fit based on the Fisher statistic of scatter. We have not done this in the current study, but this is a logical extension of the QMVI technique. Of course, we leave it to the interpreter and the purposes of a particular study to decide the significance or usefulness of QMVI discriminated domains, though our view is that such analysis can be helpful in any situation where varying directions of magnetization exist. CONCLUSIONS Extending prior work, we have shown that MVI voxel inversion models can accurately determine direction of magnetization when multiple directions exist in the same model area. We have also shown that the MVI inversion method is able to distinguish quite variable levels of magnetic intensity within the same model. And finally, we propose and demonstrate a method to use SOM classification to automatically distinguish magnetic source rocks from less magnetic background, and to then classify different magnetization domains based on direction. ACKNOWLEDGMENTS The authors acknowledge the support of Geosoft Inc, and the many colleagues at Geosoft who actively work on advancing the practical application of geophysical inversion technologies. RGE also wishes to acknowledge the unpublished pioneering work done on the application of SOM methods in geophysics by Barry DeWet at BHP Billiton. REFERENCES Ellis, R. G., de Wet, B., Macleod, I. N., 2012, Inversion of magnetic data for remanent and induced sources. ASEG Extended Abstracts 2012: 22nd Geophysical Conference: pp Extended Abstracts of 14th SAGA Biennial Technical Meeting and Exhibition 2015 Page 3

4 Ellis, R. G., 2012, Iterative Reweighted Inversion. Geosoft Technical Note, MacLeod, I. N., Ellis, R. G. 2013, Magnetic Vector Inversion, a simple approach to the challenge of varying direction of rock magnetization. ASEG Forum on the Application of Remanent Magnetization, 2013 ASEG general meeting. Fisher, R.A., Dispersion on a sphere. Proceedings of the Royal Society of London, Series A, 217: Fraser, S. J, and Dickson, B. L., 2007, A New Method for Data Integration and Integrated Data Interpolation: Self- Organizing Maps. In "Proceedings of Exploration 07: Fifth Decennial International Conference on Mineral Exploration" edited by B. Milkereit, p Kohonen, T., 1982, Self-Organization of Topologically Correct Feature Maps. Biological Cybernetics, 43, Li, Y., Sun, J., 2014, Total magnetization vector inversion using guided fuzzy c-means clustering. SEG Technical Program Expanded Abstracts 2014: pp Pratt, D. A., McKenzie, K. B., and White, A. S., 2012, The remote determination of magnetic remanence. ASEG Extended Abstracts 2012: 22nd Geophysical Conference: pp FIGURES Figure 2. Magnetization amplitude > from VOXI MVI inversion of synthetic field in Figure 1. The MVI magnetization vector directions are shown for the indicated body, with true vectors in grey. Earth Field D: 1.3 I: -56 Figure 1. 3D representation of 5 magnetized prisms (top), showing direction of magnetization and coloured by intensity. The lower map shows the synthetic total magnetic intensity at surface with the plan outline of the lower susceptibility prisms. Figure 3. QMVI modelled direction of magnetization relative to the synthetic model. Synthetic model directions are indicated by the green arrows and the large cones in each body are the QMVI directions determined from the MVI inversion. Extended Abstracts of 14th SAGA Biennial Technical Meeting and Exhibition 2015 Page 4

5 C B D A Earth Field D: 8.4 I: km Figure 4. TMI over the Black Hills Norite complex in South Australia. Norite anomalies are indicated by A, B and C. Anomaly D is interpreted to represent a different domain of magnetization. Figure 6. 3D view from the South of magnetically anomalous cells based on SOM classification. SOM analysis considers both amplitude and direction of the MVI magnetization vector. C B D A Domain K mvi (SI) Declination Inclination Scatter Blue Red Green Figure 5. VOXI MVI susceptibility amplitude depth slice at 1200m. Pink represents high MVI susceptibility in the model (>0.02 S SI). Figure 7. SOM analysed anomalous domains based on direction of magnetization. QMVI measures of magnetization are presented in the table. The Scatter is the Fisher statistic of direction variability for the strongest 20% of samples in each domain. Extended Abstracts of 14th SAGA Biennial Technical Meeting and Exhibition 2015 Page 5