Introduction Outline This five page article was written for those involved in the earth sciences who have no background in geophysics. It is intended to explain very briefly how applied geophysics can contribute unique and important information that helps solve a wide range of practical problems in the earth sciences and engineering. The article was adapted from Geophysical Inversion: New Ways of Seeing the Earth's Subsurface, by Francis Jones and Doug Oldenburg, in Innovation, October 1998, Assocation of Professional Engineers and Geoscientists of British Columbia. Importance of Earth's subsurface The surface of the earth has provided the setting for most human endeavours throughout the history of civilization, and these activities have been profoundly affected by the largely invisible characteristics of the immediate subsurface. Human development has depended heavily on resources obtained from both near surface (as in construction materials) and from hundreds to thousands of metres deep (as in metalliferous ores and petroleum based products). We also use water from subsurface aquifers, deposit much of our waste within the near subsurface, and build structures that must interface safely with these shallow regions. Physical properties vs rock type and structure In relation to these activities, subsurface characteristics of particular interest to earth scientists include the location, distribution and structure of rock types, grain size distribution, and material strength, porosity and permeability, to name a few. The earth's inherent complexity can make it difficult or impossible to infer these characteristics from direct observation. Therefore they often must be inferred from the distribution of more fundamental physical properties such as density, electrical conductivity, acoustic impedance and others. These basic properties can be measured via geophysical surveys that record the earth's response to various types of natural or manmade signals. The following table lists physical properties that are most commonly related to geological materials and/or structures, and geophysical survey types that can map variations of these physical properties. Common physical properties Associated geophysical survey techniques Electrical resistivity (or conductivity) DC resistivity, all electromagnetic methods Magnetic susceptibility All magnetic survey methods Density Gravity, and seismic reflection or refraction Acoustic wave velocity Seismic reflection or refraction Other physical properties that can be usefully mapped include chargeability, natural radioactivity, dielectric permitivity, and porosity. Demand for improved modeling Subsurface structures are usually interpreted either in terms of objects, layers, linear features, or complex distributions. This type of information, obtained remotely and non-invasively using geophysical surveys, is routinely used in geotechnical, exploration and environmental activities to characterize geological structures, estimate ore reserves, map contaminant plumes, etc. What is involved in obtaining such information? First, field work is done (Figure 1) which involves making many careful measurements along survey lines on the ground or from aircraft. Traditionally, interpretations of these measurements are often made from graphs or maps of raw or processed data, resulting in qualitative or crudely quantitative information about the locations, depths, and types of materials under ground.
Figure 1: A field crew initializes geophysical acquisition equipment used to conduct a mineral exploration survey at a site near the Iskut River, in west-central British Columbia. In the face of ongoing demand for increasingly quantitative information, however, sophisticated techniques are now being used to numerically estimate the distribution of the earth's physical properties. These modelling procedures give geoscientists a more cost effective, reliable and accurate means of extracting as much information as possible from conventional survey data. They also make it possible to present the rather technical information in more visual and meaningful ways to managers, shareholders, regulatory agencies and other interest groups. After reading this article, it should become evident that the application of geophysics to problems involving earth's subsurface is a non-trivial process. A seven step framework can be used to help understand each aspect of this process. This framework is not referenced often in the article, but there is a one page summary referenced elsewhere which should be examined. pg. 1 of 5. UBC Earth and Ocean Sciences, F. Jones. 04/23/2007 14:14:00
Geophysics primer Geophysical surveys are performed when information about the earth's subsurface is desired but direct sampling through expensive and invasive techniques such as drilling or trenching is insufficient, impractical or ill-advised. A survey may target a whole earth scale, within the top few metres of the subsurface, or anywhere in between. Measuring physical properties During a geophysical survey, energy is put into the earth and responses are recorded at the surface, in the air or in boreholes. Resulting data reveal information about the earth because the behaviour of the energy within the ground is controlled by the distribution of the earth's physical properties. For instance, one basic physical property is magnetic susceptibility, which describes a rock's ability to become magnetized. This physical property provides information on rock type and structures because the rock's magnetic susceptibility relates directly to mineral type, and to the chemical alteration processes involved in its deposition. A second important physical property is electrical conductivity, which quantifies a material's capacity to carry electrical current. Figure 2 illustrates one way that a geophysical survey can be carried out to provide information about the subsurface distribution of electrical conductivity. Figure 2: An example of how the distribution of a physical property (electrical conductivity in this case) can be measured to provide information about geologic materials. Click buttons to reveal corresponding images. 1. The physical properties under this surface are unknown. A geophysical survey - DC resistivity in this case - is used to generate data. 2. Current is injected into the ground, and resulting voltages are measured as electrode geometry varies. In this case, voltages get smaller as electrodes are separated further and further apart. 3. Inversion of this data set produces an estimate of a "layered earth" or 1D model of the relevant physical property - electrical conductivity. 4. Interpretation converts the model into geologic information. Evidently, the application of geophysics to problems involving earth's subsurface is a non-trivial process. A seven step framework can be used to help understand each aspect of this process. This framework is outlined in a one page appendix. Traditional interpretation Traditionally, useful information was extracted from geophysical field results by examining maps or line profiles of raw or filtered survey data. Such images are useful for estimating locations and quantities of buried materials, and to help choose locations for more invasive (and expensive) techniques such as drilling. For example, large scale maps of magnetic of magnetic or gravity data often show geologic structure, or identify an anomalous region that might be associated with a desired target. As an example Figure 3 shows the magnetic data acquired at the Bathurst region of New Brunswick. The major features observed are related to geologic structure.
Figure 3, Tetatouche Antiform - Total Magnetic Field, from "Airborne Geophysical Survey of the Bathurst Mining Camp", Geological Survey of Canada website, http://gdcinfo.agg.nrcan.gc.ca/app/bathmag/tetagouche_e.html (Dec. 2006). Historically, in mineral exploration, the identification of an anomalous region was often the endpoint of the analysis, and the image was used to plan the location of a drill hole. Unfortunately, the success rate was generally poor. At best, data maps provide some information about the lateral extent of a body but little information about what is happening at depth. Quantitative analysis, in particular inversion, is required to obtain 3D information. The mineral exploration example in this article expands on this. Other geoscience professionals also need to obtain quantitative information from data sets that are difficult to interpret without inversion. The geotechnical example in this article illustrates both traditional images of data and quantitative models generated by inversion of this data. Inversion The problem of using recorded data to estimate a reasonable earth model (i.e. a quantitative distribution of one or more physical properties) is known as the geophysical inverse problem. The adjacent cartoon illustrates that the pertinant question being addressed is "what subsurface physical property distribution could have caused the data that were observed at the surface?" Earlier inversion solutions involved characterizing the earth by a few prisms or layers and then numerically finding geometrical and physical properties of these simplified earth models. Due to the earth's extreme complexity, useful models often need to have many parameters, usually more than the number of data. This means that the problem of finding a model (i.e. estimating values for every parameter) is one in which there are more unknowns that data. Such problems do not have unique solutions, and this nonuniqueness is exacerbated when data are noisy or inaccurate. Formal inversion methods address these issues using well defined mathematical techniques. An appendix explains inversion in a little more detail. In the remainder of this article, some benefits of applying rigorous inversion can be seen by comparing the information in 3D and 2D models obtained by inversion, to the traditional map and pseudosection plots of the raw data. pg. 2 of 5. UBC Earth and Ocean Sciences, F. Jones. 04/23/2007 14:14:00
Mineral exploration example Large quantities of magnetic field measurements are routinely gathered over mineral and petroleum exploration prospects using airborne techniques. Resulting magnetic anomaly maps can provide information about geological trends because rocks containing higher proportions of the mineral magnetite have a higher magnetic susceptibility, and will affect the local behaviour of the earth's magnetic field. Regional and local magnetic surveys Figure 3 (supplied courtesy of Placer Dome Exploration) provides an example of regional information from an area surrounding the Mt Milligan copper porphyry deposit, located in central British Columbia. Geological trends can be decerned using this type of data, however, exploration for a specific deposit requires more detailed information about local subsurface distributions of rock types. Figure 3b shows anomalous strengths of the earth's magnetic field for a small region of one ore body. Evidently there is a range of different rock types below the surface, but details of location, depth and magnetic susceptibility are difficult to determine directly using conventional methods. a. Figure 3. Total magnetic field strength map for the Mt Milligan region, gathered by airborne magnetic survey techniques. b. Click the button to see a ground based magnetic anomaly map for the small outlined region over one ore body. The large scale regional magnetic field has been removed from this local map to emphasize the signature of anomalous subsurface magnetically susceptible rocks. Inversion to obtain 3D details The goal of inverting this data set was to produce detailed 3D models of magnetic susceptibility to help geologists develop a more complete understanding of the rocks associated with the ore deposit. The first step was to reduce the dense data set from the small region (Figure 3a) to a more manageable 1,029 evenly spaced data points and to divide the model region into 169,000 cells. Then a desirable model type was chosen. In this instance, the process was set up with two criteria; namely to find a model that was (i) as close as possible to a uniform earth with zero susceptibility, and (ii) included structure that was smooth in all three spatial dimensions. In addition, the numerical procedure for finding plausible subsurface models of susceptibility was constrained so that data predicted from the model would match observed field measurements to a degree specified by assuming a noise level (on measurements) of 5%. The resulting model was a 3D volume represented by the 169,000 cells, each with a magnetic susceptibility recovered by the inversion. Visualizing results There are several ways to usefully present volumetric information of this kind. Contour plots of horizontal or vertical slices through the volume, as shown in Figure 4, provide quantitative details at any required location. Alternatively, for a more general impression of the model, a 3D iso-surface image can be created. This is shown in Figure 5, which suggests there is a well defined volume of magnetically susceptible rocks associated with this deposit. This model correlates well with one of the known principal local rock units (MBX monsonite stock) and with locations of mineralization.
Figure 4: The model of magnetic susceptibiility recovered by the inversion of ground-based magnetic data is illustrated by plotting slices from the volume under the survey area. The left panel is a horizontal slice at 80m depth; the right panels are three vertical slices taken along lines at 9600, 9500, and 9400 metres north. Gray lines indicate the slice locations. Corroboration with independent geophysical results Few geophysical surveys are used alone with no other independent information. At Mt Milligan many types geophysical surveys were performed on the ground, from airborne platforms, and from within boreholes. For example, a similar inversion procedure was used to interpret DC electrical measurements gathered over the same area. The 3D iso-surface image of Figure 6 shows a model of the distribution of chargeability (the capacity for material to hold an electrical charge), a physical property related essentially to metal or clay content and grain size. The apparent anti-correlation between magnetic susceptibility and chargeability at Mt Milligan is evident only after careful inversion of two unrelated geophysical data sets. This example illustrates that conducting inversions on multiple types of data sets can provide an enhanced understanding of the surveyed region; in this case it provides insight about subsequent alteration of the rocks that occurred after the initial formation of the mineral deposit. Figure 5: The same magnetic susceptibility distribution model shown in the previous figure is plotted here as a 3D isosurface of constant susceptibility. Any surface between zero and the maximum susceptibility recovered could be chosen for the plot. The best choice for illustrating geologically relevant features depends upon estimating the true susceptibility of rocks, perhaps from borehole or outcropping samples. Figure 6: An isosurface plot of chargeability, which is usually related to the presence of sulphide ores, graphite, or clay minerals. The chargeability model was obtained by carrying out a 3D inversion of induced polarization data collected along parallel survey lines over the deposit region. Comparison with the 3D model of magnetic susceptibility shows that low chargeability is correlated with high susceptibility. Detailed correlation of the two inversion results provided information that contributed to an enhanced understanding of how the ore body was deposited. pg. 3 of 5. UBC Earth and Ocean Sciences, F. Jones. 04/23/2007 14:14:00
Geotechnical example Geotechnical work also requires quantitative, accurately located information about the subsurface. Figure 7a. below shows initial unprocessed results of a DC electrical survey over calcine tailings at the Sullivan Mine in southern BC. Lateral locations of conductive material can be interpreted directly. However, for this application, there was a need to characterize the extent and depth of the calcine material (which has a higher electrical conductivity than host rocks) partly to determine the quantity of calcine and partly to constrain the possible subsurface paths along which ground water could travel. Limitations of standard data presentation The standard form of presentation shown in the top panel of figure 7, known as a pseudosection, distorts the actual distribution of subsurface physical properties. Note that no vertical axis scale is provided. Without formal inversion there is no way to identify the position and value of electrically conductive or resistive materials that gave rise to the observed data. Also, with resistivity surveys it is important to estimate the depth of investigation because the ability to resolve geology at depth depends upon survey geometry and subsurface conductivity as well as the current source power. Traditionally (prior to development of formal inversion techniques), geophysicists used ad-hoc rules to identify the depths at which interpretations became unreliable. Figure 7: a. (top) Raw DC resistivity data from a survey over calcine tailings are plotted in pseudosection format. Resistivity values are apparent rather than true intrinsic resistivities, and the pattern is determined by the plotting convention. Circles indicate plotting points for recorded data values. Lateral surface distribution of highly conductive (i.e. low resistivity) calcine is recognizable, but details of the thickness and geometry of the conductive zone are obscured. b. (Bottom) The conductivity model recovered by 2D inversion of data in the top panel. Each rectangular cell has the value of it's conductivity determined by the inversion algorithm. The location and volume of high conductivity material is clearly defined. The variability at the surface is due to a thin resistive cover of course bouldery fill overlying the area. Portions of the 2D model that are not sensitive to the survey are hatched out. Note that conductivity (which has units of Seimens per metre) is the inverse of resistivity (quoted in units of Ohm-m). Depth of investigation A geophysical survey provides information about a limited volume of the earth. In the inversion our mathematical model usually extends beyond those limits. The value of a physical parameter outside the area of illumination is determined only by parameters in the inversion and does not present reliable information. To prevent over-interpretation of the inversioin results it is best to remove those regions from the final images that are to be displayed. The hatching in Figure 7b accomplishes this goal. It is evident that the geophysical survey provides no information outside of the limits of the survey electrodes and also there is a maximum depth to which the data are sensitive. The maximum depth depends upon the greatest separation of the current and potential electrodes and also upon the level of signal strength compared to noise. Discussion There is a well-defined region of high electrical conductivity (ie low resistivity, in red colours) near the surface and a region of lower conductivity (blues) that appears at the surface. The low conductivity coincides with a known bedrock outcrop and this adds confidence about the interpretability of the image. Interpretation of a precise depth for the interface between conductive material and bedrock would be greatly aided by a single borehole drilled to a depth of roughly 50 metres anywhere within the high conductivity region. This would also help to identify the value of conductivity at which the physical interface should be interpreted. pg. 4 of 5. UBC Earth and Ocean Sciences, F. Jones. 04/23/2007 14:14:00
Conclusions Geophysical surveys are non-invasive techniques for obtaining information about subsurface materials and their distribution or structure. The results of surveys can often be used directly, or after some filtering prior to presentation as graphs or maps. The survey data, perhaps with some filtering, can sometimes be used to answer the question of interest. Generally, however, the information is insufficient and more quantitative analysis is required. The data need to be inverted to generate a distribution of the physical property. The inherent nonuniqueness of the inverse problem is a complicating factor and this has motivated the development of different inversion approaches. Irrespective of details, the application of formal inversion techniques to conventional geophysical data has contributed decisive information in the resolution of mineral exploration and geotechnical problems. Mineral exploration, petroleum, and engineering organizations now routinely apply modern inversion techniques to geophysical surveys, such as gravity, magnetics, resistivity and others. Instead of applying ad-hoc methods to the interpretation of raw or filtered data, geoscientists can now produce a range of acceptable subsurface models based upon rigorous and well defined criteria. The value added through the provision of well constrained, easily visualized 2D and 3D models of subsurface physical properties means that geophysical surveying can be more cost effective, allowing decision makers to act with more confidence in assessing the risks and costs of projects requiring subsurface information. pg. 5 of 5. UBC Earth and Ocean Sciences, F. Jones. 04/23/2007 14:14:00
Appendix - Inversion Outline The problem of estimating a reasonable earth model (i.e. a quantitative distribution of one or more physical properties based upon recorded data) is known as the geophysical inverse problem. Ever since computers became standard tools for geophysical work, various methodologies for performing geophysical inversion have been developed. There are two broad classes of inversion: "Parametric" methods and "Generalized" inversion methods. Forward modelling: calculating data based upon a known earth model. Inversion: estimating a model based upon measured data and some understanding of the setting. Parametric methods These inversion methods involve finding a model of the earth which is described using only a few parameters. In fact, the solutions require that there be fewer parameters than there are data values so that the problem is formally "over-determined" (see glossary). A few examples of parametric models are: Buried object: parameters could be depth to a sphere (or cylindar), a radius or radius and length, and the physical property contrast between the object and host rocks. Layered earth: parameters are layer thicknesses and physical property values. A buried sheet: parameters might be depth to the top of sheet, it's dip, strike, thickness, and the physical property contrast between the sheet and host rocks. Inversion usually involves searching for the model (i.e. a set of parameters) which generates a data set that best matches the field measurements. The inversion algorithm adjusts model parameters to improve the match between calculated and measured data sets. This is generally an iterative process. Generalized inversion methods This second class of inversion methods allows the earth's model to be more realistically complex, which means that more parameters than data points are permitted. Such problems are mathematically referred to as "under-determined". Most solutions to this more general form of the geophysical inversion problem involve three steps, which can be explained briefely as follows: Represent the earth with many parameters so that complex distributions of physical properties can be simulated. In practice, the earth is divided into many thousands of cells of fixed geometry, each with a constant but unknown value of the relevant physical property. Design an adaptable mathematical function of this earth model called a model objective function. This function's value depends upon the model. Change the model and the function's value changes. The inversion process will involve adjusting parameters making the model in order to produce a minimum value for this objective function. Different types of functions will require different models to produce a minimum value. For example, one sensible model objective function measures how spatially "smooth" the earth's structure is. When the model causing a "minimum" value is found, this will be the "smoothest" model possible. This might be a sensible choice because large scale features of the subsurface are usually more important than fine scale details. How does the geophysical data contribute? The carefully designed model objective function might be minimized using a geologically unreasonable model of the earth. However, an acceptable model must be able to cause the measured field data. This is a second constraint which allows the inversion process to find reasonable models of the earth. So, inversion using optimization methods have two requirements: (i) adjust the model until it's "objective function" takes on a minimum value (ii) subject to the constraint that the model can cause the measured data.
The earth model is a fixed distribution of An acceptible model can cause the data, cells, each with an adjustable value of and simultaneously produces a the physical property. Measured data minimum value for the "model objective are shown on top. function". In practice a number of inversions, with different reasonable objective functions, should be carried out so the interpreter has some insight about the range of earth models that can acceptably reproduce the field data. Error statistics about the data will determine how closely the reproduced data matches the real measured data. The fact that these error statistics are often poorly known is a second good reason for performing several inversions before settling upon a preferred model. Appendix. UBC Earth and Ocean Sciences, F. Jones. 05/25/2007 11:39:30