A new method for combining gravimetric and geological data

Tecronophysics, 204 ( 1992) 15 1 - 162

Elsevier Science Publishers B.V., Amsterdam

IS1

A new method for combining gravimetric and geological data

C. Castaing a and N. Debeglia h

” Department of Geology, Bureau de Recherches G&logiques et Mini&es, Orthans, France h Department of Geophysics, Bureau de Recherches Gkologiques et Mi&res, O-l&am, France

(Received February 14, 1991; revised version accepted July 23. 1991)

ABSTRACT

Castaing, C. and Debeglia. N.. 1992. A new method for combining gravimetric and geological data. Tectonophysics, 204: 151-162.

Application of the gravity method to structural geology makes it possible to highlight local variations of the gravitational field that are caused by density heterogeneities related to the composition and structure of the crust. These density heterogeneities and their boundaries, which correspond to gravity discontinuities, can be identified using the properties of the vertical and horizontal derivatives of the field.

Gravity data on the Huelgoat granite in the Armorican Massif (France) were subjected to a new two-step geological analysis. First, the gravity discontinuities derived from Bouguer anomaly data were automatically identified; and second these discontinuities were combined with existing geological data.

The first step was made possible by a software program that defines and visualizes the gravity discontinuities through an automatic analysis of the horizontal and vertical gravity gradient functions. The result is a map on which gravity discontinuities separate areas of different densities. The vertical and horizontal derivatives of the field were computed from the gravity data using frequency domain transformations. The second step corresponds to the geological interpretation of the gravity discontinuity map. A petrostructural map is used, which mainly shows the structure and the syntectonic internal fahrie of the area. along with fracture data obtained on the granite and its host rocks. The latter illustrates late brittle def~)rmati~~n.

The petrostructurai map is used to adjust and rearrange the gravity discontinuities in order to obtain a gravity image deduced from the fabric of the rocks, a “fabric/gravity image”. After this, a “fracture/gravity image” is derived by using the fracture data as a filter to obtain priority directions in the gravity discontinuities.

Superimposing the two images provides a structural sketch map that gives a more integrated insight into the ductile and brittle deformation of the area than can be obtained from field observations alone.

Introduction

Whereas quantitative modeling and inversion techniques have been improved considerably in recent years, qualitative geological interpretations of gravity data have until now mostly carried out manually. They help draw structural sketch maps derived from the Bouguer anomalies and their vertical and horizontal gradients and continua- tions. These sketch maps show homogeneous zones of high or low density, which are separated by gravity discontinuities.

In this paper, we present a new approach to the interpretation of gravity data, in this case from the Huelgoat granite massif and its surroundings, in the Armorican Massif, France. Our approach is based on the automatic identification of gravity discontinuities derived from the Bouguer anomalies and, as a second step, on a rearrangement of these d&continuities through correlation with existing geological data.

Automatic identification of elementary gravity features: gravity discontinuities and peaks

Correspondence to: C. Castaing, Departement de Geologic, BRGM, BP 6009 - 45060 Orleans Cedex 02, France.

The gravity method as used in structural geology is based on highlighting the local variations of the gravitational field that are caused by density

~40-~951/92/$05.~ 0 1992 - Elsevier Science Publishers B.V. All rights reserved

152 C. CASTAING AND i-4. DEBEGLIA

irregularities related to the composition and

structure of the crust. A gravity anomaly map shows maxima and minima that are separated by

contour lines of equal gravity. The maxima and minima areas correspond to the central parts of rock masses that have a density which contrasts with that of their surroundings. Above the density boundaries the contour lines will be the most closely spaced. One of the purposes of the geological inte~retation of gravimetric maps is to identify and to locate geological units, their boundaries and their structure. To improve the accuracy of such interpretations, transform functions of the initial field, such as the vertical and horizontal gravity gradients and their continua- tions, may be used.

The gravitational field and the gravity anoma-

lies derive from a scalar potential due to masses located within the Earth’s surface. According to

Gauss’s law, if the gravitational field, g(n. y, 01,

is known everywhere on a closed surface, z = 0, such as that of the Earth, it will be determined

everywhere outside the surface. Its vertical con- tinuation, g(x, y, .z) can be calculated at any point in space, and it is possible to deduce its vertical and horizontal derivatives, and in particu- lar the vertical gradient:

T(x, Y, 2) =%(x7 Y, z)/Qz

and the modulus of the horizontal gradient:

H(.X, Y, z)

The vertical gravity gradient, T, has proved for some time (Gerard and Griveau, 1972; Goguel, 1972) to be effective in showing up local and shallow features. This function is particularly use- ful to resolve the overlapping effects of close

G

-8.01 -

T -.

0.;

,, (b)

d

- 8.U

(a)

-G

_..__..____.. T

----. ti

Fig. 1. Location of geological units by the method of horizontal and vertical gravity gradients. Theoretical example. (a) Vertical section of the model, the densities being expressed in cgs units. tb) Corresponding gravity anomalies: G = gravity field (mgal); T = vertical gradient (mgal/km); H = modulus of the horizontal gradient tmgal/km). The maxima of the function T correspond to the median axes of the heavy units (plotted as triangles) and its minima to the median axes of the light units (plotted as squares).

The extrema of the function H indicate the position of the boundaries between the geological units of different densities.

A NtW MbTHOD FOR (‘OMBINING GRAVIMETRI<‘ AND GbOLOGICAI. DATA 153

structures, its extreme values being focused above

the bodies that generate the gravity anomalies. The maxima of the function T correspond to bodies with a higher density than that of the surrounding rocks, and the minima correspond to bodies with lower density.

The analysis of the modulus of the horizontal gravity gradient, H, has been used to locate density boundaries (CordeIl and Grauch, 1985; Blakely and Simpson, 1986). The basis of the method is that a vertical density boundary pro- duces an extremum of the function til located at the contact between the geological units (Fig. 1). If the contacts are not vertical, the extremum of the function H may be shifted slightly towards the direction of dip (Grauch and Cord&, 19871. The shift depends on the depth and thickness of the contacts; there is no shift when the contacts are exposed.

The method

The method uses gridded gravity data. The vertical gradient and the components of the horizontal gradient along the two horizontal coordinate axes are first caIculated in the frequency domain by applying appropriate operators to the Fourier transform of the gravity field (Gerard and Griveau, 1972). The inverse Fourier transform leads to both the vertical gravity gradient, T, and the components along the two coordinate axes of the horizontal gravity gradient, from which N can be deduced. This calculation of the gravity gradients must be carried out with care, particularly in the choice of the processing parameters, e.g. spacing of the calculation grid, filtering and periodization, so as to avoid the formation of artefacts. The functions H and 7” are then locally anaIysed by a method adapted from the work of Blakely and Simpson (1986). A search for the location of the extrema of H and T is carried out in the neighbourhood of each grid point along four directions of analysis. If, for a grid node, several extrema are detected along neighbouring directions, the location and magnitude of the extremum are finally obtained by interpolation.

Such a calculation identifies gravity features of two types:

(1) Gravity discontinuities, deduced from the horizontal gravity gradient, characterized by their coordinates, their directions and a parameter proportional to the value of the horizontal gradient at that point; the direction, Q, of the gravity discontinuities is perpendicular to that of the horizontal gradient vectors, and can be deduced from its two components by:

?&,/3X

a = - arctan -

(2) Gravity peaks corresponding to the maxima and minima of the vertical gravity gradient, characterized by their coordinates and a parameter proportional to the vaIue of the vertical gradient at that point.

A~~Iicatio~ to the ~ueigoat granite and its sur-

roundings

The Bouguer anomalies are derived from an interpolation on a 0.5 x 0.5 km2 grid of the available gravity measurements. The density of the gravity stations is about three points per km2 and the accuracy of the measurements is better than 0.6 mGal. The Bouguer anomaly map (Fig. 2) shows negative anomalies above the granite and positive anomalies over the surrounding metasedimentary rocks. This result is explained by the measured densities of the rocks, which are 2.63 for the granites and 2.7 for the metasedimentary rocks. The contacts between the two lithological units generally correspond to high horizontal gradients of the Bouguer anomaly. The map of the vertical gravity gradient of the Bouguer anomaly (Fig. 3) preferentially shows the effects of the shallowest geological structures, and reduces the smoothing between neighbouring anomalies. In- side the granite, sub-units corresponding to local variations of densities are shown on the gravity gradient map. This coincides with the results of density measurements of the granite samples, which yield values ranging from 2.58 to 2.67, as a function of the petrographic facies.

The gradient analysis program has been ap- plied to the Huelgoat area gravity data and has provided a map showing both gravity discontinuities and peaks (Fig. 4). The elementary gravity

154 C. CASTAING AND N DEBEGLIA

160

0 2 4 6km

Fig. 2. Bouguer gravity anomaly map of the Huelgoat granite. Contour interval = 1 mGal.

0 1 I 6km

Fig. 3. Vertical gravity gradient map of the Huelgoat granite. Contour interval = 0.5 mGal/km.

A NEW METHOD FOR COMBINING GRAVIMETRIC AND GEOLOGICAL DATA 155

0 POULLROUFN

_ ~

Al l 2 -3 0 2 A 6km L ,

Fig. 4. Map of the gravity features of the Huelgoat granite. I = maxima of the vertical gradient (positive peaks); 2 = minima

vertical gradient (negative peaks); 3 = gravity discontinuities.

of the

discontinuities are represented by bars with a constant length function of the spacing of the calculation grid. The thickness of these bars is proportional to the value of the horizontal gravity gradient at this point. The peaks are plotted using triangles for the maxima and squares for the minima, their size being proportional to the vertical gravity gradient. This map illustrates the shallow geological structure of the area much more distinctly than the Bouguer anomaly map or that of its vertical gradient.

The gravity features have only a local significance due to their mode of definition, in this case a local search for the extrema of the gradient functions. In fact, this method identifies all the extrema, even the most isolated, that have an amplitude higher than a given threshold. As this detection is not dependent upon the geometric organization of the extrema, the coherence of the map of the gravity feature (Fig. 4) depends on the accuracy of the basic data and on the quality of the data processing. This objective document

needs to be interpreted through the geological knowledge of the area in question.

Images defined by the combination of gravity and

geological data

Available data

Map of the gravity features (Fig. 4) The automatic identification of the gravity dis-

continuities and peaks was the first step in the geological interpretation of the gravity data of the Huelgoat area.

Petrostructural map (Fig. 5) The petrostructural map shows the envelopes

of the various facies of the Huelgoat granite, the main shear zones including those passing through the Monts d’ArrCe, and the fabric components, which here are the traces of flow foliation, schistosity and cleavage in the granite and its host rocks (Georget, 1986).

156 C’. CASI‘AING AN11 N. DEBECiLIA

Fig. 5. Petrostructural map of the Hueigoat granite. I = envelopes of the various facies of the granite; 2 = shear zones; 3 = fabric

planes (flow foliation, schistosity or cleavage); 4 = contact-metamorphism aureole; A, 8, C, D = various facies of the Huelgoat granite; E = Plouneour granite; MA = Monts d’Arr6e; PT = “Triple point” areas formed by the schistosity planes.

The syntectonic diapiric intrusion of the granite is characterized by synkinemati~ contact metamorphism of the metasedimentary rocks and by mylonitization on the northern margin of the pluton at the contact with the Monts d’ArrCe shear zone (Darboux, 1981; Castaing et al., 1987). The syntectonic intrusion is also shown in the geometrical reIationships that exist between the petrofabric of the pluton and that of the country rocks. At the contact, the schistosity planes of the metasedimentary rocks are moulded into the bow-foliation planes of the granite, which show an helicoidal arrangement in the centre of the pluton (Ledru and Brun, 1977). Furthermore, the schistosity pIanes form “triple point” areas on

each side of the major axis of the pluton (Brun and Pons, 1981).

Fracture data (Fig. 6)

The Iate-tectonic evoIution of the area in- volved intense fracturing of the granite and its host rocks. The fracture data are plotted as directional histograms of the fractures measured on the ground (Fig. 6a) or interpreted from SPOT spatial imagery (Fig. 6b). Three distinct episodes of brittle deformation have been identified (Castaing et al., 1989): a NW-SE compressions shown by the NlOO-130”E set of fractures most commonly acting as dextral strike-slip faults; a N-S compression inducing conjugate strike-slip


Fig. 6. Directional histograms of fractures in the Huelgoat granite: (a) measured on the ground; (b) interpreted from

SPOT satellite imagery.

faults trending NO-30”E (sinistral) and N150- 170”E (dextral); a NE-SW extension reworking the NlOO-130”E- and the N150-170”E-trending faults as normal faults.

Creating a gravity image representative of the fabric of the massif

We consider in this case that the gravity discontinuities can correspond to geological struc-

tures such as lithological contacts, fabric-plane

alignments and shear zones, all of which are structures that always develop along a certain length, as is shown on the petrostructural map (Fig. 5). The superimposition of the map of the gravity features (Fig. 4) on to the petrostructural map (Fig. 5) makes it possible to determine the gravity discontinuities which underline (according to their location and direction) the geological structures. It is thus possible to emphasize these discontinuities, extending the bars by a variable length which is function of a “geological weight” attributed to the underlined geological structures.

In the present case (Fig. 51, we consider that the direction of the main shear zones takes priority wherever they exist: N70-85”E in the Monts d’ArrCe; approximately N100”E between Saint- Rivoal and Loqueffret; etc. At the contact zones between the granite and its country rocks, the orientation of the contact plane is regarded as having priority if there is no shear zone. Outside the shear zones and the lithological contact zones, the directional priority is given by the characteris- tics of the planar fabric, such as flow foliation, schistosity and cleavage.

For each of the sectors considered, we give priority, in a step-wise procedure, to the discontinuities which are progressively closer to the direction of the dominant geological structures. Each gravity discontinuity extended in this way will stop against a discontinuity of a higher order, avoiding any intersection. In this manner; a gravity image of the structure and fabric of the area is derived from both the gravity and the petrostructural data, and is called a “fabric/gravity image” (Fig. 7). Until now, this operation has been carried out by hand, by combining the automatically mapped gravity discontinuities (Fig. 4) with the petrostructural map (Fig. 5). The petrostructural map can be regarded as an “image guide” through which the gravity discontinuities are ranked and extrapolated.

In fact, the fabric/gravity image makes it possible to optimize the geological data shown on the petrostructural map. Not only does this image emphasize the internal structure of the pluton, but it also demonstrates its syntectonic intrusion through the existence of “triple point” areas

158 C. CASTAING AND N. DEBEGLIA

60

130 160

0 2 4 FJkm L, ’ I

Fig. 7. Fabric/gravity image of the Huelgoat granite showing the “fabric/gravity discontinuities” network. MA = Monts d’Arr&; BE = eastern boundary of the pluton; PT = “triple point” areas formed by the “fabric/gravity discontinuities”.

formed by the extrapolated gravity discontinuities (Fig. 71, which are similar to those formed by the cleavage planes and shown on the petrostructural map (Fig. 5). Furthermore, the major shear structures are clearly shown on the fabric/gravi~ image, including the dextral character of those of the Monts d’ArrCe.

Creating a gravity image representatiue of the fracturing of the ~a~~~f

Earlier, we considered that the gravity discontinuities (Fig. 4) might correspond to lithological contacts, fabric planes or shear zones, but they may also correspond to faults and other major fractures. As before, the initial image corresponds to the map of the gravity features (Fig. 41, but the final image is intended to show the later

brittle deformation rather than the syntectonic penetrative deformation.

The “image guide” that corresponds to the petrostructural map is replaced by the fracture system summarized by the directional histograms (Fig. 6). These data will serve to filter the elementary gravity discontinuities, as a function of a directional classification drawn up on the basis of the statistical, kinematic and chronological stud- ies carried out on fracture patterns.

This classification brings out four orders of priority: a first order, covering a range of directions from NlOO” to N130”E corresponding to the set of fractures best expressed by the first episode of faulting; a second order, covering a range of directions from N-S to N30”E corresponding to the sinistral strike-slip faults of the second episode of faulting; a third order, covering a range of

A NEW .?viETHOD FOR COMBINING GRAVIMETRIC AND GEOLOGICAL DATA 159

directions from N150” to N170”E corresponding to the dextral strike-slip faults of the second episode of faulting; a fourth order, covering a range of directions from NW’ to N80”E repre- senting the set of faults that are less accurately expressed but which strike along the major regional structures (Fig. 5).

The sorting method used is a manual scanning of the map of the gravity discontinuities (Fig. 41, which are filtered as a function of the priority directions defined above. This scanning allows the identification of groups of discontinuities the neighbouring features of which have the same range of direction and are distant by a value less than a given threshold. To each group is allocated a segment, centred on the gravity centre of the group, the size of which is determined by the envelope of the group along its mean directions.

The network of segments is completed by indicating the offsets of these segments and the offsets of all positive or negative gravity axes. The offset zones are then underlined by segments the

directions of which are consistent with those of

fracturing. In this way, a gravity image of the fracturing of the area is derived from both the

gravity and the fracture data, and is called a “fracture/ gravity image” (Fig. 8).

This fracture/ gravity image is characterized by the preponderance of NlOO-130”E and N50- 80”E directions. The former, mainly located on the northeast and southwest sides of the pluton, corresponds to the major faults (Fig. 6). The latter direction is found over the whole area and particularly in the Monts d’Arree (Fig. 81, and emphasizes the gravity anomalies induced by the regional syntectonic structures (Figs. 1, 2 and 5) rather than those indicating the N50-80”E fracture set.

Furthermore, it is obvious that the N50-80”E gravity discontinuities are earlier than the other sets, because they are clearly offset by the NlOO- 130”E and N150-170”E sets working as dextral strike-slip faults (Fig. 81, in full agreement with the kinematics of fracturing as explained above.

-1 -2 1-w- 3 0 , 1 I 6km t

Fig. 8. Fracture/ gravity image of the Huelgoat granite showing the “fracture/gravity discontinuities” network. 2 = NIOO-130”E; 2 = NOOO-030”E; 3 = N050-080%

160 C. CASTAING AND N. DEBEGLlA

The fracture/gravi~ image thus confirms the

logic of the fracture patterns, and illustrates the fundamental network of brittle discontinuities which can create density heterogeneities.

Discussion and conclusions

The classical interpretation of gravity data usu- ally contains a subjective element which is diffi- cult to identify. The approach set out in this paper makes it possibIe to separate the objective and easily quantifiable part of the analysis from the more subjective part which corresponds to the combination of the gravity and geological

data. This is achieved first by the automatic anal-

ysis of the gravity data, which provides a map of gravity discontinuities separating uniform zones of different densities. As a second step, this map is interpreted by reference to selected geological data presented as a petrostructural map (indicating the structure and the syntectonic internal fabric), or by comparison with brittle deformation data illustrating later faulting.

The petrostructura1 map is regarded as an “image guide” that helps to rank and extrapolate the gravity discontinuities so as to visualize the penetrative deformation by drawing a network of fabric/ gravity discontinuities (Fig. 7). This di-

I 16

0

-1 -2

160

3 0 2 6km 1-w-

4

Fig. 9. Structural sketch map of the Huelgoat massif. I, 2, 3 = “Fracture/gravity discontinuities”; 4 = “Fabric/gravity discontinu ities”.


vides the map into several gravimetrically homogeneous polygonal areas: the length and arrangement of the sides varies as a function of the “image guide” data, but the directions are defined by the Bouguer anomaly data.

In order to illustrate later faulting, the gravity discontinuities are initially filtered as a function of priority directions according to the statistics and kinematics of faulting, after which they are grouped spatially into larger segments. The network is then completed by drawing in the offsets of these segments. It is thus possible to visualize the brittie deformation by drawing a network of fracture/ gravity discontinuities (Fig. 8).

In the first step, all the elementary gravity discontinuities are recorded, to some extent, in the fabric/gravity image. This image, which is fairly compiex, is representative of the syntectonic penetrative deformation of the region. In the second step, the filtering and grouping of the elementary gravity discontinuities leads to a smaller number of fracture/gravity discontinuities, giving an image that is simpler but representative of the regional late-tectonic fauIting. The two approaches are thus complemental, and the superimposition of the two images leads to a structural sketch map of the Huelgoat area (Fig.

91. Automating the method of obtaining such

structural sketch maps now seems to be of pri- mary importance. Such automation would make it much easier to vary the “image guides” and the “geological filters” rapidly, so as to examine the gravitational representativeness of each of them and to explain the significance of the gravity discontinuities better. It would also open the way to using data of an entirely different nature, such as satellite imagery or magnetic data.

The final gravity images obtained by our method retain their initial specificity, but can bring out new subsurface information not shown by the initial data on gravity and geology. In the case of the Huelgoat granite, the interpreted gravity images provide a more integrated insight into the regionaf ductiIe deformation and the late brittle tectonics than can be obtained simply by studying the outcrops.

Acknowledgements

We wish to thank J.L. Bles, H.M. Kluyver and S. Lallier for their helpful criticism of the manuscript. The software used in this study has been developed at BRGM within the framework of a joint BRGM and TOTAL research pro- gramme. covering developments in the GMI_ PACK software for processing and inter- preting potential fields.

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