Modelling pitfalls

Modelling of any geophysical data is only as good as the assumptions made when simplifying the complex real- world variations in physical properties into a model that is defined by a manageable number of parameters. We reiterate the points made inSection 2.11.3on the import- ance of accounting for noise levels, choosing an appropri- ate type of model and creating the simplest possible model that matches the observations so as not to imply infor- mation that is not supported by the data. In particular, when modelling potentialfield data, account must also be taken of ambiguity: the unavoidable fact that without con- straints provided by other sources of data, the effects of equivalence and non-uniqueness mean that an infinite number of density or magnetism distributions in the sub- surface can reproduce the observed anomalies.

3.10.6.1 Equivalence

Recall that only relative changes in gravity and magnetic strength are of significance in mineral exploration

geophysics. As shown in Fig. 3.68a, laterally continuous horizontal layers do not cause relative changes in gravity on a surface above them, so the structure of a horizontally layered sequence cannot be determined from measurements made from above. The response is the same as a homogeneous half-space. This is a simpler geometrical form and is, therefore, the equivalent gravity model.

Consider the models inFig. 3.68b. Only lateral changes in density will cause variation in the gravity response. Careful examination of the models shows that in terms of lateral density change these models are equivalent. In all cases there is a lateral density contrast (ρ3– ρ2) which has a

vertical thickness H and depth to top Z.

For the case of spherical density distributions

(Fig. 3.68c), where the mass is distributed radially and

evenly around the centre of the sphere, the gravity effect is the same as if its mass was concentrated at a point at its centre. The same gravity effect is obtained when the mass is distributed homogeneously as a sphere of larger volume and smaller density contrast, or as a spherical shell, or as a multiple spherical density zonation. In all cases the total excess mass (see Section 3.2.1.3) and depth to centre are the same, but the densities and radii varying accordingly. The solid homogeneous sphere, being the simplest form, is the equivalent model for all spherical distributions.

In these three examples the gravity response is identical even though the subsurface density models are different. It goes without saying that the gravity response cannot be used to tell them apart.

3.10.6.2 Non-uniqueness

In Section 2.11.4we described the phenomenon of non-

uniqueness in geophysical modelling, whereby many dif- ferent physical property distributions can produce the same geophysical response, and strategies for dealing with it.

Physical property/geometry ambiguity, as it relates to gravity data, is illustrated inFig. 2.49a. Here, a broad low density feature at shallow depth produces the same gravity response as a range of more compact bodies, of increasing density, at progressively greater depths. They all have the same excess mass (see Section 3.2.1.3). The shallowest, widest and least dense body, and the deepest, smallest and most dense compact body, represent end-members of an infinite number of solutions to the measured response. As shown inSection 3.10.1, amplitude increases when the body is shallower or its density contrast increased, whilst wavelength increases as the body is made deeper or wider. So long as the excess mass of the solutions is the same, the same gravity response will be obtained. Horizontal layering Vertical step Sphere

a) b) c) > 1 1 2 2 2 1 1 1 1 1 2 3 3 2 3 3 3 3 2> 1 2 2 3 r = Background r = Background r = Background Point mass Z H Relative gravity Depth Depth Depth Depth Depth Depth Depth Depth Depth

Depth Depth Depth

Relative gravity Relative gravity r r r r r r r r r _r r r r r r r r r r r r r r

Figure 3.68 Equivalent gravity models for three common geological sections: (a) gravity anomaly, (b) some possible density cross- sections that produce the gravity anomaly, and (c) equivalent model.

For magnetic modelling, there is the additional compli- cation of the direction of the body’s magnetism (see

Sections 3.2.4and3.10.1.2), which can be traded off against changes in its geometry, usually its dip. Different combin- ations of source dip and magnetism direction can produce identical magnetic responses; this type of ambiguity is illustrated inFig. 2.49c. Failure to recognise the presence of remanent magnetism which is not parallel to the present-day Earth’s field will cause the model to be in error, since the assumption of only induced magnetism implies the source’s magnetism to be parallel to the Earth’s field. Even when there is no significant remanent magnet- ism, problems may occur owing to anisotropy of magnetic susceptibility (see Section 3.2.3.7) and, for the case of highly magnetic sources, self-demagnetisation (seeSection

3.2.3.6). Both deflect the induced field away from parallel-

ism with the Earth’s field.

The strategies described in Section 2.11.4.1, of using knowledge of the nature of non-uniqueness to guide the interpretation, can be applied in the analysis of gravity and magnetic data. Of course, some prior knowledge of the geology, and the target, is required in order to identify realistic source geometries. Ideally there is also petrophy- sical data available, but physical properties and especially magnetic properties can vary by large amounts over small distances (Fig. 3.61), so identifying the correct suscepti- bility etc. to use can be equivocal. For these reasons, the interpreter should create several models designed to repre- sent‘end-member’ models of the range of possibilities: for example the deepest possible source, the shallowest pos- sible source etc. In practice, time constraints often mean only one‘preferred’ interpretation is produced.

Figure 3.69 shows three gravity models across the

Bonnet Plume Basin, Yukon Territory, Canada. All are geologically plausible and their responses (not shown)fit the data to an acceptable degree. The particular problem was to determine the extent and thickness of the coal- bearing upper and lower members of the Bonnet Plume Formation. The models represent the maximum and min- imum possible formation thickness, and also what is con- sidered to be the mostly likely form of the underlying geology.

3.11

Examples of gravity and magnetic