aglo

Inversion concepts:  
Suitable problems for geophysical inversion
 

For those making use of geophysical inversion for the first time, it is natural to ask "will inversion contribute towards my problem?" This page provides a ten-point outline of criteria to consider when answering this question.

The range of problems requiring inversion

If your geoscience question can be answered without knowing the values and distributions of physical properties within the ground, then rigorous inversion may not be necessary. One example is an object search question (such as locating underground storage tanks) for which a simple map of a geophysical anomaly might provide a clear indication of where the desired object is located.

Inversion is essentially a processing step that attempts to find the cause for a set of measurements. Therefore inversion can contribute to geoscience problems at any scale. See the sidebar for examples of inversion being used at all scales of problems, from studying the structure of a whole planet, down to characterizing features at the scale of only a few cubic meters.

Ten aspects affecting suitability of problems for inversion

As the needs of exploration, engineering, environmental, and other industries become more sophisticated, so too do the requirements for inexpensive, non-invasive acquisition of detailed quantitative information about subsurface materials. In the image to the right, the value of density throughout the volume of interest has been estimated by inversion of ground-based gravity data set, in order to characterize an ore deposit as quantitatively as possible.

The question now is, "what aspects of a problem affect its suitability for inversion?" The following ten points below should be considered - click numbers to jump to corresponding details below.

1. Physical property contrast 2. Illumination energy 3. Problem size 4. Consistent data & model type 5. Topography
6. Permissible locations of buried features 7. Consistency with prior knowledge 8. Accurate, clearly understood data 9. Well-characterized data errors 10. Consistency between discretization & data

1. Physical property contrast: There must be a physical property contrast corresponding to the geological problem. This is true for all geophysical work, and it is true for inversion. If the data contain no response related to the target, inversion will recover nothing.

  • Example: In the Century Deposit case history (in Chapter 9), the model of electrical conductivity obtained by inversion of DC resistivity data did not show where the ore body was, although other structural information was obtained. However, the chargeability model did include zones of chargeable material corresponding with economic ore. A table of physical property values obtained by drilling confirms that the ore body's electrical conductivity is similar to host rocks, while it's chargeability is significantly different from surrounding geologic materials.

2. Illumination energy: Data should be gathered with source energy interacting with the target in as many different ways as possible. When the source energy cannot be moved, some prior knowledge about how material is likely to be distributed can be incorporated into the inversion. This is done for potential fields data - see chapters on inverting magnetic and gravity data.

  • Example: One variety of DC resistivity survey (a so-called 'gradient array' survey) involves using only a single location for source electrodes. This type of data is hard to invert successfully and techniques similar to inverting magnetic or gravity data may be necessary. More discussion can be found in the San Nicolas case history of Chapter 9, in section 3, "Regional scale geophysics", under "Chargeability".

3. Problem size: What is meant by problem size? This issue is covered in detail throughout the CD-ROM, but there are two essential aspects: the number of cells used to discretize the Earth (referred to as N), and the number of data values (referred to as M). The numerical implementation of inversion schemes will involve working with matrix calculations that are as big as N x M.

  • Example: How serious is this? Imagine a normal airborne survey covering an area 4km by 4km, involving survey lines spaced 100m apart and measurement spacing along the lines of 5m (represented by the lines with dots in the cartoon to the right). For this survey, N = 32,000. If we want the subsurface model to include cells that are 10x10x5m down to a depth of 4km, then our volume includes 400 x 400 x 400 = 64,000,00 cells (represented by the volume of cubes under the survey area in our cartoon). Even for this seemingly reasonable situation, N x M is too large for normally available computing tools. A compromise will be necessary. The size of each cell must be increased (reducing spacial resolution), and the number of data values can be reduced so there are only a few data points for each cell at the model's surface.

4. Consistent data and model type: Inversion for 1D or 2D models (see the model types summary page in the "Foundations" chapter) can only produce sensible results if the measurements are unaffected by geologic conditions that change in the "missing" direction. In addition, if the data do not contain information about variations in all 3 dimesions, then full 3D inversions are not likely to be successful. In other words, the data set and the choice of inversion methodology must be consistent.

  • Example: DC resistivity and IP surveys are commonly gathered along survey lines. To cover large areas, several lines may be used. These lines are usually rather far apart compared to the measurement spacing along the lines. Individual 2D inversions are recommended for each data set gathered along a line. Fully 3D inversions using many lines will likely be successfull only if the survey line spacing is less than the maximum electrode spacing along the lines. An example of the latter situation is given in the Cluny, Mt. Isa case history of chapter 9.

5.Topography: 2D and 3D inversions must have good topography data available. Many types of data are affected by topography, so these affects will be explained by erroneous structrues if topography is not correct in the inversion model.

  • Example: The 2D synthetic model shown to the right has some variations in electrical conductivity under a mountain and a valley. Synthetic DC resistivity data generated over this model have been inverted with and without proper topography. Click the following buttons to see the two resulting models of the earth's distribution of electrical conductivity:

    True model; first inversion result; second inversion result.

6.Permissible locations of buried features: If there are geologic features affecting the data which do NOT lie within the volume encompassed by the model, then the inversion will be forced to place erroneous features within the model in order to account for those components of the data. This is very important, especially for magnetic and gravity surveys.

7. Consistency with prior knowledge: If a process is designed to generate "smooth" models, you should expect to interpret the recovered models in terms of smooth variations of the physical property. This is not necessarily a problem if the "smooth" models can be interpreted in terms of structures expected. The point here is that interpretations can be effective only when the inversion process being used is properly understood.

  • Example: The figures to the right show how a discrete block of conductive material may be revealed by inversion using a process that returns smooth models. Move your mouse over the figure to see the inversion result. This issue is much clearer with a good understanding of why inversion procedures do what they do.

8. Accurate, clearly understood data: It should be obvious that inversion results can be only as good as the input data. In addition to having accurate data, it is necessary to know exactly what the physical measurements were, and how the input data were generated from those measurements. Predicted data cannot be produced properly, and therefore a successfull inversion outcome cannot be expected if all the relevant details are consistent with the forward modelling procedure used in the inversion.

  • More details: For the outline of this point, see Decision number 1: fitting the data, in Chapter 3, " Inversion Concepts".

9. Well characterized data errors: In addition to understanding exactly where the original data come from, there must be an estimate of the errors that are associated with each data value. It is not common for quantitative statistics to be available, so assumptions often must be made about the errors associated with data.

10. Consistency between discretization and data: The size of cells used in the model should be smaller than the size of all features that will affect the measurements. In other words, data must NOT contain information caused by features that are smaller than the cell size.

  • More details: To meet this demand with magnetic or gravity data, it may be necessary to calculate an equivalent data set that would have been gathered some distance from the surface. The relevant data processing step is called upward continuation.
  • More details: For other types of data it may be necessary to increase the errors assigned to data if geologic features exist which are very small and/or close to the measurement location.