Fathom Geophysics Newsletter 23
Our Capabilities: True 3D filtering of 3D datasets
INVERSION results and other 3D datasets can now have their internal geological 'plumbing' analyzed in great detail. Explorers can gain a clearer picture of subsurface geological features modeled in their tenements using standard and advanced data-filtering methods that were previously restricted to two-dimensional data grids. This is true 3D filtering of 3D data — and not simply a workaround involving the stacking of separately-processed 2D data slices. A southern Mongolian porphyry copper case study shows how.
Opportunities for explorers to serendipitously stumble over surface outcrops of visible ore or its gossanous remnants have become increasingly rare.
It means a significant part of the mineral exploration game now is to parlay disparate geophysical, geochemical, and geological fieldwork data into a cohesive, comprehensive and realistic analysis of the 3D spatial interrelationships among the various lithological and structural components hosted within an area of interest.  The overall goal is to achieve this before competing explorers learn the lay of the land first.
A detailed three-dimensional interrogation of inversion results and any other 3D datasets available for a given area of interest helps explorers to visualize what is likely to be going on geologically at depth.
We illustrate how by looking at Xanadu Mines' Oyut Ulaan (Red Mountain) porphyry copper-gold project in southern Mongolia.**
Oyut Ulaan (Red Mountain)
Xanadu Mines' Oyut Ulaan project is situated in southern Mongolia's northeast-southwest-striking Gurvansaikhan belt, which in turn is part of the Central Asian Orogenic Belt.
In the project region, fault zones that cross-cut the long axis of preserved paleo-volcanic arcs are thought to have been instrumental in controlling the location of previous magmatic activity and associated porphyry-style mineralization centers. 
Porphyries in the Oyut Ulaan area and its surrounds were considered to have formed in the early Carboniferous as part of an subduction-related island arc accretional tectonic setting.  Debate continues as to the precise nature of accretion in the broader region. For instance, were just one or two long-lived island arcs involved, or did a melange of island arcs, seamounts and microcontinents accumulate?   
Geological maps of Mongolia are still in flux, largely because of a flurry of tectonic evolution-related studies in recent years.
And lithostratigraphically-established subdivision schemes for terranes throughout the country and its surrounds don't seem to match observed regional-scale magnetic and gravity data signatures. Instead, regional magnetic highs seem associated with locales of post-accretion volcanism and plutonism, while regional gravity highs seem associated with areas that have undergone high strain. 
Even so, at the Oyut Ulaan tenement scale, magnetic data are detailed enough that a variety of rock packages and their bounding structures can be distinguished (see Figure 1) and are in good agreement with geological maps of the area. 
Figure 1: Results of band-pass filtering to yield the 7.5m to 800m residual. The procedure used to arrive at the residual was a differential upward continuation. Note that inversion at Oyut Ulaan was carried out on the area's band-pass-filtered total magnetic intensity (TMI) data, which is not supplied in any figures in this write-up. The above figure and subsequent figures involving magnetic data show the area's reduced-to-the-pole (RTP) data, so that anomalies appearing in the data are situated directly over their respective modeled causative bodies. This enables the reader to make meaningful visual comparisons. To view a larger version, click on either the image or this text link.
Before carrying out an inversion on the Oyut Ulaan total magnetic intensity data, we first applied a type of band-pass filter known as a differential upward continuation. We did this to preserve the 'goldilocks' features in the residual data — in other words, to highlight features that were 'just right' in scale. At this particular project, these were the features possessing a wavelength of between 7.5 meters and 800 meters.
This filtering step allowed us to ignore features that weren't salient to the inversion, namely very high frequency noise (i.e., features with a wavelength of less than 7.5 meters) as well as the broad regional magnetic signature (i.e., features with a wavelength exceeding 800 meters).
An inversion is an attempt to find a model — a proposed geological configuration — that's consistent with the measured data that went into the inversion.
The model possesses an explicit depth scale, and features viewable in the model may represent valid geological features. Ideally, a model recreates the data originally employed to a satisfactory degree (a procedure known as forward modeling).
Multiple theoretically-plausible models exist that mathematically honor the inversion's input data. It's similar to how several well-trained geologists will each independently produce different-looking plausible interpreted geological maps and cross sections for the same parcel of ground. 
A winnowing process takes place, so that the inversion model selected in the end also embodies additional practical considerations (such as geological principles governing the expected relative positioning of rock units present). The final model is going to be as robust and explorationally useful as the various inputs and decisions that went into generating it will permit. 
The Oyut Ulaan inversion results reveal clues about the depth, dip-direction, geometry and morphology characteristics of the area's modeled geological units (see Figure 2, which displays a depth-slice from the full data 'cube', and Figure 3).
Inversion results such as these represent a good launching-off point in that they allow explorers to refine their geological model of the area of interest in situations where there's limited outcrop or poor geological control.
Figure 2a: Oyut Ulaan inversion results depth-sliced at an absolute elevation of 700m. The inversion was performed using the 7.5m to 800m residual of the Oyut Ulaan magnetic data as the input. Pinks and reds indicate higher magnetic susceptibilities, while blues and greens indicate lower magnetic susceptibilities. The yellow line shows where subsequent angled views have been vertically sliced to display depth information. To view a larger version, click on either the image or this text link.
Figure 2b: The same inversion results, this time co-visualized with a grayscale version of the area's band-pass filtered RTP magnetic data (which can be viewed in color in Figure 1). To view a larger version, click on either the image or this text link.
Note that the Oyut Ulaan inversion presented here was performed on the TMI data (not the RTP data) because this usually produces modeled causative bodies possessing more realistic-looking dips. We show the RTP data in the figures of this write-up because we want readers to be able to view magnetic data images in which anomalies are situated over their respective causative bodies. This enables the reader to make meaningful visual comparisons of the 3D filtering results being discussed.
Figure 3 presents an inclined view of the Oyut Ulaan inversion results. The location of the vertical face situated closest to the viewer is given by the yellow line in Figure 2.
Figure 3: The Oyut Ulaan inversion results as shown in Figure 2, but this time viewed from the northwest at an inclination of 30 degrees. To view a larger version, click on either the image or this text link.
We present the same inclined-angle view throughout this write-up for the sake of consistency. But readers should note that each 3D results dataset shown in this case study could have been horizontally and vertically sliced in an endless variety of ways, as required for one's specific viewing purposes — such as plan views, depth slices, cross sections.
This kind of capability gives the data owner an intimate understanding of the connectivity of the various three-dimensional magnetic features modeled in their tenements. It's similar to how a three-dimensional MRI or CAT scan gives a surgeon a thorough understanding of what's going on with their patient's 'plumbing'.
Standard 3D filtering results
Standard filters are ways of transforming geophysical data so that certain features contained in the data stand out more, while other features are downplayed.
Standard filters applied to the Oyut Ulaan inversion results and shown below are:
- The vertical derivative equivalent (VDE) (Figure 4), which is the name we're giving to the three-dimensional-data equivalent of calculating the first vertical derivative (1VD). Results of this transform — which is a high-pass filter that blocks lower-frequency features — pinpoint the locations where there is high-frequency change in modeled source bodies' magnetic susceptibility. When compared to the original inversion results, the VDE accentuates shorter wavelength (more detailed) features at the expense of longer wavelength (more regional) features. The benefit of using the VDE is that it lets you better resolve individual units and their dips.
- The total gradient (TG) (Figure 5), which is the three-dimensional-data equivalent of calculating the horizontal gradient magnitude (HGM). This transform is calculated from the orthogonal x, y, and z derivatives of the data. Results highlight the locations of steep gradients in the data. In other words, results define where marked magnetic susceptibility contrasts occur among the modeled source bodies. These locales are likely to be faults or contacts. The benefit of using the total gradient is that it allows the edges of features to be more readily discernible.
- The 3D tilt angle (Figure 6). The tilt angle filter is defined as the arctangent of the ratio of the VDE to the TG. This transform shows the locations of magnetically susceptible modeled source bodies irrespective of the relative strengths of their susceptibilities. The overall effect of this filter is that it has an equalizing effect on the data. The benefit of using this transform is that features with subtle magnetic signatures become easier to see, and dip directions become clearer.
Figure 4: Vertical derivative equivalent (VDE) produced from the Oyut Ulaan inversion results. The VDE is the 3D-data equivalent of the first vertical derivative (1VD) that's calculated for 2D datasets. The VDE highlights locales possessing high-frequency change in magnetic susceptibility. (Recall that noise is also enhanced in this kind of filter.) These results are being viewed from the northwest at an inclination of 30 degrees. To view a larger version, click on either the image or this text link.
Figure 5: The total gradient (TG) produced from the Oyut Ulaan inversion results. The TG is the 3D-data equivalent of the horizontal gradient magnitude (HGM) that's calculated for 2D datasets. The TG highlights locales where pronounced step-changes occur in absolute magnetic-susceptibility values, and hence highlights modeled magnetic features' edges. Note that structure detection results (shown in Figure 8) provide more depth-related information than the TG. This is because structure detection produces results that are independent of magnetic features' amplitudes (that is, structure detection results aren't based on the absolute size of features' susceptibility values). Inversions inherently produce less contrast at depth, because the act of producing an inversion means only a relatively narrow range of magnetic susceptibility values is found at depth. It means the values of the TG are necessarily smaller there, hence the petering out effect seen in the above figure the deeper one goes in the resulting data 'cube'. These results are being viewed from the northwest at an inclination angle of 30 degrees. To view a larger version, click on either the image or this text link.
Figure 6: The 3D tilt angle (3DTA) produced from the Oyut Ulaan inversion results. The 3DTA is the angle between the vertical derivative equivalent (shown in Figure 4) and the total gradient (shown in Figure 5). The 3DTA produces a version of the data that is equalized. That is, the act of calculating the 3DTA pulls down big 'mountains' in magnetic susceptibility values seen across the dataset and gives a boost to areas that have middling and small values. It means the 3DTA clarifies modeled dip directions and highlights modeled units possessing a more subtle magnetic signature. These results are being viewed from the northwest at an inclination angle of 30 degrees. To view a larger version, click on either the image or this text link.
Advanced 3D filtering: Structure detection results
The structural characteristics of a region are important to know for the purposes of mineral exploration. 
When it's calculated properly and used appropriately, structure-detection analysis can be a powerful tool, to help get a geological handle on one's exploration area and help identify sub-areas of particular interest.
The structure detection filter is a feature-detection algorithm used to highlight the locations of ridges, valleys and edges in gridded data.
Edges found in the data highlight locales where modeled lithological contacts and faults may be situated.
The algorithm looks for discontinuities in the data, and it does this in a way that is independent of the absolute size of the data values involved in the step change. It means that step changes in areas of low contrast in the data are highlighted equally as well as step changes in areas of high contrast. All that matters to the algorithm is whether step changes possess the frequency being sought.
Structure detection results highlight the layout of the intricate 3D network of modeled structures occurring in the area of interest (see Figure 7 and Figure 8).
Because structure detection analysis can now be run as a true 3D filter, data owners can interrogate results fully according to not only latitude and longitude but also depth. This permits them to better understand the interconnectivity — or, conversely, the isolatedness — of individual modeled structures, and to determine the modeled structures' deep-seatedness.
Figure 7a: 3D structure detection results produced from the Oyut Ulaan inversion results. This structural analysis allows data owners to visualize and interrogate in a 3D manner the degree of interconnectivity among modeled structures situated in the area of interest. This analysis was done on the inversion of the TMI data and was completed in an amplitude-independent manner, using a wavelength of 100 meters. High values (pinks and reds) indicate the edges of modeled features, and those edges represent modeled lithological contacts and faults. To view a larger version, click on either the image or this text link.
Figure 7b: The same structure detection results, this time co-visualized with a grayscale version of the area's band-pass filtered RTP magnetic data (which can be viewed in color in Figure 1). To view a larger version, click on either the image or this text link.
Figure 8: 3D structure detection results produced from the Oyut Ulaan inversion results, viewed from the northwest at an inclination angle of 30 degrees. To view a larger version, click on either the image or this text link.
Advanced 3D filtering: Complexity analysis results
Geologically complex areas tend to receive close attention from mineral explorers because they're thought to represent paleo-environments conducive to ore-deposit formation.
The thinking is that if a network of geological structures possesses the appropriate degree of complexity, the network may have acted as a high-volume highway for hydrothermal fluids, and may have hosted sites suitable for the precipitation of economic amounts of ore metals.
When applied to the output of an inversion, the use of geological complexity mapping allows explorers to highlight areas spatially rich in modeled geological features such as folds, faults and lithological contacts.
And because complexity analysis can now be run on datasets as a true 3D filter, data owners can interrogate results fully according to latitude, longitude, and depth (see Figure 9 and Figure 10).
Figure 9a: 3D complexity analysis results calculated using the Oyut Ulaan structure detection results. Higher values (pinks and reds) indicate a higher density of modeled structural intersections and therefore a higher degree of geological complexity. This 3D complexity analysis was completed in an amplitude-independent manner, using a wavelength of 100 meters. To view a larger version, click on either the image or this text link.
Figure 9b: The same complexity analysis results, this time co-visualized with a grayscale version of the area's band-pass filtered RTP magnetic data (which can be viewed in color in Figure 1). To view a larger version, click on either the image or this text link.
Figure 10: 3D complexity analysis results calculated using the Oyut Ulaan structure detection results, viewed from the northwest at an inclination angle of 30 degrees. Hover your mouse pointer over the image to also see the shaded areas representing regions containing modeled causative bodies with relatively low magnetic susceptibilities. To view a larger version, click on either the image or this text link.
Advanced 3D filtering: Intrusion detection results
Areas hosting intrusive geological bodies are important to mineral explorers who focus on intrusion-hosted ore deposits, or intrusion-associated ore deposits, or both.
The geological bodies of interest here include stocks, batholiths, alteration haloes, skarns, kimberlites, steep-plunging mineral lenses, and breccia pipes.
When applied to the output of an inversion, the use of geological intrusion mapping allows explorers to highlight areas rich in modeled intrusives.
The intrusion detection filter being used highlights round features, as opposed to linear features, in the data. Such round features have a higher likelihood (than surrounding locales) of being intrusive bodies or discrete alteration zones. Radially symmetric highs are likely to represent the thicker portions of the dikes and sills, or the locations of underlying intrusions. Radially symmetric magnetic lows can also be sought out using this filter, and can represent areas that have undergone fluid-infiltration-related demagnetization.
And because intrusion detection analysis can now be run on datasets as a true 3D filter, data owners can interrogate results fully according to latitude, longitude, and depth (see Figure 11 and Figure 12).
Figure 11a: 3D intrusion detection analysis results produced from the Oyut Ulaan inversion results. Higher values (reds and oranges) indicate locales in which equant, magnetically-susceptible features reside. This 3D intrusion detection analysis was completed in an amplitude-independent manner, using a base radius of 200 meters. Note that the filter applied looks for features with a radius of between this base radius and two times this base radius. Also note that the filter won't locate features that are significantly larger or smaller than this range. To view a larger version, click on either the image or this text link.
Figure 11b: The same intrusion detection results, this time co-visualized with a grayscale version of the area's band-pass filtered RTP magnetic data (which can be viewed in color in Figure 1). To view a larger version, click on either the image or this text link.
Figure 12: 3D intrusion detection analysis results produced from the Oyut Ulaan inversion results, viewed from the northwest at an inclination angle of 30 degrees. To view a larger version, click on either the image or this text link.
True 3D filtering
Algorithms implemented in 2D should be regarded as being of limited usefulness when the objective is to analyze 3D data 'cubes'.
Arguably, the stacking of separately-processed 2D data slices is trivial. But what is not trivial is finding a way to legitimately handle the multitude of processing-induced seams that arise when abutting adjacent 2D-filtered data slices together. It's better to avoid generating the seams in the first place.
A true 3D approach to analyzing exploration data is not only a mercifully-seamless approach that prevents needless butchering of results during post-data-processing steps, but also offers the intrinsic advantage that data adjacent in all directions from any given single data point is being factored into the filter's algorithm decisions and hence improves the quality of the data-filtering results.
All else being equal, results obtained from true 3D filtering is going to supply better information about the continuity and interrelationships of geological features detected in the 3D dataset.
What else is possible?
The Oyut Ulaan inversion case-study presented above is an example of an unconstrained inversion applied to magnetic data. Constrained inversions honoring additional relevant data, such as drilling-derived information, can also be done.
The full gamut of 3D filtering can be applied to other types of three-dimensional datasets too — such as 3D seismic data, 3D geochemical data, gravity inversion results, and 3D induced polarization (also known as IP) data.
And additional powerful data-interrogation techniques can be used in conjunction with 3D filtering, such as intersection analysis and isosurfacing derived from thresholding procedures. (We're refraining from providing details here, though, for article-length reasons.)
Finally, just as inversions are applicable outside of the porphyry copper exploration arena, so too 3D filtering can be applied to datasets involving any ore deposit type.
** Acknowledgement: Fathom Geophysics gratefully acknowledges Mat Brown of Xanadu Mines for permission to discuss the Oyut Ulaan (Red Mountain) case study and to present some results of 3D filtering of Oyut Ulaan inversion results.
 J. McGaughey (2007) "Geological models, rock properties, and the 3D inversion of geophysical data", Paper 30, Advances in Geophysical Inversion and Modeling, In: B. Milkereit (2007) "Proceedings of Exploration 07: Fifth Decennial International Conference on Mineral Exploration", 473-483.
 Xanadu Mines corporate presentation (October 2017) Slide number 7, www.xanadumines.com.
 A. Vigar (2014) "Valuation report on the Kharmagtai Project, Mongolia", www.xanadumines.com. Note that this description of Oyut Ulaan's regional geology appeared in this valuation report within a quotation of prior work that was authored or compiled by Ivanhoe Mines Mongolia Inc.
 J.H.S. Blight (2006) "The geological evolution of the Saykhandulaan Inlier, Mongolia: A window into the Paleozoic growth of the South Gobi mineral belt", PhD Thesis, University of Leicester, 205 pages.
 A. Kroner, V. Kovach, E. Belousova, E. Hegner, R. Armstrong, A. Dolgopolova, R. Seltmann, D.V. Alexeiev, J.E. Hoffmann, J. Wong, M. Sun, K. Cai, T. Wang, Y. Tong, S.A. Wilde, K.E. Degtyarev and E. Rytsk (2014) "Reassessment of continental growth during the accretionary history of the Central Asian Orogenic Belt", Gondwana Research, 25, 1, 103-125.
 B.F. Windley, D. Alexeiev, W. Xiao, A. Kroner and G. Badarch (2006) "Tectonic models for accretion of the Central Asian Orogenic Belt", Journal of the Geological Society, 164, 31-47.
 A. Guy, K. Schulmann, M. Munschy, J.-M. Miehe, J.B. Edel, O. Lexa and D. Fairhead (2014) "Geophysical constraints for terrane boundaries in southern Mongolia", Journal of Geophysical Research: Solid Earth, 119, 7966-7991.
 See, for example: Xanadu Mines corporate presentation (March 2017) Slide number 28, geological map of Oyut Ulaan, www.xanadumines.com.
 J.A. Scales, M.L. Smith and S. Treitel (2001) "Introductory geophysical inverse theory", Samizdat Press, 193 pages.
 R.W. Saltus and R.J. Blakely (2011) "Unique geologic insights from 'non-unique' gravity and magnetic interpretation", GSA Today, 21, 12, 4-11.
 See, for example, discussion and cited work in: S. Micklethwaite, H.A. Sheldon and T. Baker (2010) "Active fault and shear processes and their implications for mineral deposit formation and discovery", Journal of Structural Geology, 32, 151-165. They said: "Geological structure has a first-order spatial relationship with hydrothermal ore deposits."
About Fathom Geophysics
In early 2008, Amanda Buckingham and Daniel Core teamed up to start Fathom Geophysics. With their complementary skills and experience, Buckingham and Core bring with them fresh ideas, a solid background in geophysics theory and programming, and a thorough understanding of the limitations of data and the practicalities of mineral exploration.
Fathom Geophysics provides geophysical and geoscience data processing and targeting services to the minerals and petroleum exploration industries, from the regional scale through to the near-mine deposit scale. Among the data types we work on are: potential field data (gravity and magnetics), electrical data (induced polarization and electromagnetics), topographic data, seismic data, geochemical data, precipitation and lake-level time-lapse environmental data, and remotely-sensed (satellite) data such as Landsat and ASTER.
We offer automated data processing, automated exploration targeting, and the ability to tailor-make data processing applications. Our automated processing is augmented by expert geoscience knowledge drawn from in-house staff and from details relayed to us by the project client. We also offer standard geophysical data filtering, manual geological interpretations, and a range of other exploration campaign-related services, such as arranging surveys and looking after survey-data quality control.