A Priori information is often used to refer to "knowledge" about the inversion process and geological problem that is not exactly "data". For example, it may be fair to say that "smooth" models are adequate for modelling the geologic situation. This is A Priori information. See also Prior information.

Anomaly is a term that is used in two ways and therefore it is occasionally confusing. In general, the word means anything that is "not normal". In the context of data, we usually hope that the target or feature of interest will produce a measurable anomaly (variation in the data set) which can then be interpreted in terms of what caused it. In the context of the Earth's subsurface (or the geophysical model), a feature that can be detected or characterized may be referred to as an anomaly or an anomalous zone. For example, a subsurface void is a "density anomaly" that should produce a measurable "gravity anomaly" if a gravity survey is carried out over the void.

This is a discipline that involves making physical measurements above, on the surface, or within the Earth, then applying mathematical and graphical tools to create information about the subsurface physical properties and/or structures. Professionals in environmental, geotechnical engineering or resource exploration often need to know what the Earth is like beneath the surface. It is possible (and common) to dig or drill, but the results are limited to the points that have been directly sampled. Applied geophysics provides a complimentary and non-invasive approach to remotely learning about the subsurface.

An electrical physical property which quantifies how well a material allows electricity to flow. It is the inverse of Resistivity.

The data needed for inversion must be provided in the specified units and are usually the actual data observed in the field. Some processing is required such as reduction of gravity data or diurnal correction of magnetic data. However any normalizations or processing that changes the data cosmetically so that it is easier to display or interpret should be removed or undone prior to inverting the data. Superfluous processing includes: line leveling, normalizing to a time channel, or calculating apparent resistivities and impedances. The practice of gridding data to produce regular data spacing is not recommended as it moves data locations and extrapolates the data values introducing undesirable artifacts. It is generally better to down-sample data sets by removing data rather that resample or grid them.

The location of each datum must be provided as accurately as possible (+/- 1m in most cases but is relative to the scale of the problem being addressed). If the location accuracy is uncertain, forward modeling may be used to determine an appropriate error level or if the data should be discluded from the inversion.

Auxiliary information such as transmitter locations, frequencies of observations, and orientations and intensities of inducing fields are needed as they complete the description of the data.

See also: Standard deviations of data; prior information; topography.

Data are measurements of a physical phenomenon such as a field, or flux, or current, or force, etc. Positions of measurements are important components of all data, and an assessment of the size and nature of all error sources should be included. Examples of physical measurements are: In a magnetic survey, the strength of Earth's magnetic field will be measured. The survey aims to measure how buried susceptible material affects Earth's field at the surface. In a DC resistivity survey, data will include the strength of a current injected into the ground, the voltages measured at other locations, and the position, spacing, and geometry of electrodes used in the survey.

Data misfit describes how close field measurements are to predicted (synthetic or calculated) data. Often we plot the real and synthetic data sets to compare for similarity. Sometimes a plot of the difference between the two data sets is generated to emphasis that variations between the two are small.

Although the earth has a continuous distribution of physical properties we simplify this with a discretization that describes the earth as a model containing a number of cells each having a constant physical property. This model is defined on a 1D, 2D, or 3D grid or mesh. The size of the cells should reflect the resolving power of the survey. If the cells are too large important geologic features may not be adequately modeled. If they are too small it shouldn't adversely affect the inversion outcome but it may slow the process down due to an increase in the size of the system of equations to be solved. The use of padding cells is usually needed either to account for incorrectly removed regional signals in the data or to ensure boundary conditions are met.

"Make into a discrete form". Basically this is a synonym for "digitize". For example the subsurface is a continuous medium, but it must be discretized into a finite number of cells before calculations can be performed to generate data or to estimate models by inversion of measurements.

Any useful model of the Earth recovered by inversion must be capable of causing the data set that was observed. This is tested by comparing the measurements to a synthetic data set generated by forward modelling based upon this recovered model. We say the "model fits the data" if it is capable of generating data that match the field measurements to within a specified degree. The term is a bit confusing because a model can not "fit" a data set - in fact we mean that data caused by a model can "fit" (or match) another data set.

Forward modelling means calculating a data set that would occur if a survey were gathered over a known model of the Earth. This usage of the word "modelling" is essentially the reverse of the definition above, and this often causes confusion for new users of geophysics.

A geophysical model is a simplified concept of how one physical property is distributed within the Earth. Geophysical models are generally either an object, a halfspace, 1D, 2D, or 3D . Note that a "model of the Earth" can mean either a geological model in which the subsurface is described in terms of rock types, structures, fluids, etc., or a geophysical model defined here. Often a geologist and geophysicist must work together to reconcile these two ways of understanding the Earth.

A discipline of science which uses the tools of mathematics and physics to answer questions about the Earth.

A volume in which half is "air" and the other half is a constant value. Geophysicists consider the earth to be a "halfspace" when the whole volume that is visible has only a constant value of the relevant physical property.

This term is used both to refer to a phenomenon and to the type of field survey that measure this phenomenon. Electric charges in the ground, and the way in which they interact with surfaces of mineral grains, are affected by application of an electric field. The effects can be measured by recording dynamic time or frequency behaviour of potentials caused by the application of the field.

Interpretation of geophysical data involves two steps. First the data must be interpreted in terms of a causative distribution of the relevant physical property. Then this "model" can be interpreted in terms of geology (structures, minerals, rock type alteration, etc). Geophysical interpretation may be carried out in many ways, ranging from simple data inspection to sophisticated inversion and modelling.

Inversion (or inverse modelling) is the process of mathematically estimating one or more models of subsurface physical property distributions that could explain a data set that was gathered in the field.

Misfit is a measure of how close one data set is to another. See also "Fitting the data".

Modelling usually means the process of developing models of the Earth based upon measured geophysical data. It may be as simple as recognizing that an anomaly is likely caused by a buried pipe, or it may involve sophisticated data processing and/or inversion to mathematically build a range of plausible models.

A problem is said to be "non-unique" when there is no possibility of obtaining a single unique solution. See also "under-determined.

Norm is basically another word for "size". There are various types of norms. A system can be "measured" by calculating a norm. One common type is a "sum of squares", or "L2" norm.

A branch of mathematics related to determining the best or optimum choice from a large (possibly infinite) range of possibilities.

are physical characteristics of the ground being investigated, such as density, electrical conductivity, and others. More details are given in section 1.2.2.

Also referred do as A Priori information. Additional information of the earth such as a known background or reference model, an expected structure or geometry, and known specific physical properties that can be assigned to cells can also be included in an inversion. These data can be used to constrain and guide the inversion. See also A Priori information.

The data a finite number of inaccurate observations, therefore there are many more model parameters (or cells) than data and we don't want to produce a model that will exactly reproduce the data. As a result the data don't uniquely constrain all of the model parameters and there are an infinite number of models that, when forward modeled, will reproduce the data to within the specified standard deviations.

This inherent instability is regularized through the introduction of a model objective function which enables us to choose the type of model recovered. In this function a priori information can be applied in the form of constraints. In the absence of any a priori information the smallest or smoothest models are recovered. Flexibility of this function through control parameters (alpha coefficients and weighting matrices) ensures that most geologic scenarios can be achieved.

There is a trade-off between the degree to which the data are fit and the influence of the model objective function. This means that if the data predicted from the model closely reproduces the observed data, noise in the data maybe manifested as spurious features in the model. Whereas if the predicted data does not reproduce the observations well the model assumes the characteristics of the a priori information. These situations are termed over-fitting and under-fitting the data respectively.

This trade-off is generally manipulated with the Chi-factor which controls the degree to which the data is fit. If it is assumed the data have errors that are Gaussian in nature, have zero mean and are non-correlative in nature, when the errors have been appropriately assigned a data misfit equal to the number of data would produce the best result. The Chi-factor is the ratio of data-misfit to number of data; a Chi-factor of less than one would over-fit the data while a Chi-factor of greater than one would under-fit the data. Convergance of an inversion is obtained when a model is determined that XXXXXXX while fitting the data to the predescribed degree.

An electrical physical property which quantifies how well a material prevents electricity to flow. It is the inverse of Conductivity.

Standard deviations represent the uncertainty of, or error in, the data and are an integral part of the survey. They have to be provided for each datum in order to determine the degree to which the model will reproduce, or fit, the data.

If topography is being included then it should be provided for the whole area being considered and with a data density appropriate for the scale of discretization (i.e.. at least one value per mesh cell).

A problem is said to be "under-determined" when there are more unkowns than data. There are not enough equations to obtain a unique solution. Under-determined problems are inherently "non-unique".