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Non-scaled analogue modelling of AMS development during viscous flow: A simulation on diapir-like structures
Tectonophysics 418 (2006) 51 – 61 www.elsevier.com/locate/tecto
Non-scaled analogue modelling of AMS development during viscous flow: A simulation on diapir-like structures Zuzana Kratinová a,d,1 , Prokop Závada a,1 , František Hrouda a,b,⁎, Karel Schulmann c,2 a
c
Institute of Petrology and Structural Geology, Charles University, Prague, Czech Republic b Agico Inc., Ječná 29a, Brno, Czech Republic Centre de Geochimie de la Surface, EOST, Université Louis Pasteur, Strasbourg cedex, France d Geophysical Institute, Czech Academy of Sciences, Bočni II, Prague, Czech Republic
Received 12 May 2005; received in revised form 29 September 2005; accepted 5 December 2005 Available online 28 February 2006
Abstract Development of magnetic fabric within a diapirically ascending columnar body was investigated using non-scaled analogue model made of plaster of Paris containing small amount of fine-grained homogeneously mixed magnetite. The apparatus for the modelling consists of a manual squeezer with calibrated spring and a Perspex container. Set of weak coloured layers at the bottom of the container was forced to intrude overlying fine-grained sand through a hole in a board attached to the squeezer. The development of AMS fabric is correlated with complex flow pattern indicated by coloured and originally horizontal plaster layers. Strongly constrictional and vertical fabric in the base and in the lower domain of the diapir resulting from convergent and upwards flows is overprinted by subhorizontal oblate fabrics due to vertical flattening and initial divergent flow in the apical parts. The measured AMS fabrics are compared with natural examples of magmatic stocks and dykes. © 2006 Elsevier B.V. All rights reserved. Keywords: Analogue modelling; AMS; Diapir; Plaster of Paris
1. Introduction The purpose of analogue modelling of geological processes is to investigate possible mechanisms that contribute to the generation of finally observed structures. Field observation and intuition have inspired geologists to construct analogue models almost two centuries ago (for review see Koyi, 1997). Analogue modelling has ⁎ Corresponding author. František Hrouda, Agico Inc., Ječná 29a, Brno, Czech Republic. Fax: +420 541634328. E-mail addresses: [email protected] (Z. Kratinová), [email protected] (P. Závada), [email protected] (F. Hrouda), [email protected] (K. Schulmann). 1 Fax: +420 21951533. 2 Fax: +33 3 90 24 04 02. 0040-1951/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.tecto.2005.12.013
undergone major progress following the introduction of scaling (Hubbert, 1937) resulted in more realistic models (Koyi, 1997). The majority of models investigated shapes of the modelled bodies (e.g. Parker and McDowell, 1955; Ramberg, 1981; Koyi, 1991, 1993; Schultz-Ela et al., 1993) and only rarely also their internal fabrics (Dixon, 1974; Jackson and Talbot, 1989). Among the latter, the models that use the anisotropy of magnetic susceptibility (AMS) are advantageous, because this method is able to rapidly and precisely investigate the preferred orientation of magnetic minerals in rocks and/or models (the magnetic fabric, for summary, see for instance Tarling and Hrouda, 1993). The first application of AMS in analogue modelling was to investigate the deposition and compaction
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processes in sedimentary rocks (for summary, see Hamilton and Rees, 1970; Rees and Woodall, 1975; Rees, 1983; Tarling and Hrouda, 1993) and in the study of lava flow mechanisms in volcanic rocks (Wing-Fatt and Stacey, 1966). Later, processes of rock deformation were also modelled (Borradaile and Alford, 1987, 1988; Borradaile and Puumala, 1989; Richter, 1990, 1992; Richter et al., 1991; Housen et al., 1993). In all the AMS models, magnetic minerals (magnetite, nickel) were added in small amount into the model material (sand, plaster of Paris, plasticene). Magnetite viscosity cannot be easily controlled and thus all the AMS models used until now are non-scaled. The purpose of the present paper is to investigate the magnetic fabrics within complex diapir-like structure created through analogue modelling, using simple experimental press-like apparatus and plaster of Paris as model material (Figs. 1 and 2). The plaster of Paris was used as an analogue of weak rock, because it can be easily coloured and deformed in the liquid state and transformed to solid state after the experiment. In order to measure the AMS of this model material, small amount of magnetite was added. As the plaster of Paris used in our experiments is diamagnetic, having the
susceptibility about − 5 × 10−6 [SI], our AMS measurements indicate only the magnetite fabric. Even though complex rheological behaviour of the plaster rules out dynamically scaling of our experiments, the results provided by our models can serve as a semi-quantitative map of fabrics throughout similar natural bodies. We show in our experimental work that the AMS can be successfully applied to unravel the directions and shapes of viscous flow/deformation in 3D. However, one has to realize that even though the AMS specimens are relatively small, about 0.63 cm3 in volume, their AMS represents the mean AMS of order-of-magnitude larger volumes in the nature. 2. Analogue material characteristics Experiments were created using the plaster of Paris (commercial name Stuckgips, BPB Formula Company). The properties of plaster were already appreciated in analogue modelling of extensional fault systems (Fossen and Gabrielsen, 1996); the fine grain size of plaster guarantees high resolution of the models and its transition to the solid state is fast. Plaster can be considered as a suspension of plaster grains in water, so
Fig. 1. Experimental apparatus for analogue modelling of diapirism using coloured plaster of Paris and sand. (a) Analogue apparatus. (b) Scheme of the spring segment in detail. (c) Coordinate system used throughout the paper.
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3. Sampling and measurement techniques The coordinate system to which the orientations of the magnetic foliations and lineations are related throughout the paper is defined by the direction of the diapir intrusion and by the edges of the experimental apparatus representing the directions of the model material movements during its manipulation. Namely, the Z direction is the orientation of the axis of the diapir, being the vertical direction in absolute coordinates. The Y direction is left–right horizontal direction from the point of frontal view of the apparatus. The X direction is the horizontal front–rear direction (see Fig. 1c). The diapir was cut into two parts along the YZ plane, passing through the diapir axis. One part was sampled through drilling in a rectangular grid of the edge of 2 cm. The core diameter was 1 cm; the core height was 8 mm to keep the ideal height to diameter ratio (Porath et al., 1966). The cores were fixed into Perspex cylinder of standard size (25 mm in diameter) and their low-field AMS was measured with the KLY-4S Kappabridge (Jelínek and Pokorný, 1997; Pokorný et al., 2004). The AMS data were statistically evaluated using the ANISOFT package of programs (Jelínek, 1978; Hrouda et al., 1990). The mean bulk susceptibility, eccentricity and shape of the AMS ellipsoid can be characterized by the following parameters (Nagata, 1961; Jelínek, 1981): Km ¼ ðk1 þ k2 þ k3 Þ=3 P ¼ k1 =k3 T ¼ ð2 g2 g1 g3 Þ=ðg1 g3 Þ Fig. 2. (a) Vertical section of the diapir. (b) Horizontal section of the diapir 10 cm above the source layer.
its rheology is strongly dependent on the water content. To postpone the solidification reaction a yellow powder called “Retardan” (of unspecified composition) was employed. 1 wt.% of “Retardan” delayed the solidification process of plaster to approximately 2 h, which was sufficient to perform an experiment without any significant rheological changes. Most of the plaster is white, but master layers in our plaster models were coloured with a printing ink (2 vol.%). The material, which the plaster pierces during the experiment and then forms the surrounding support for the evolving diapir, is made by a fine-grained (0.017 mm), almost pure quartz sand. This sand is quarried by the Sklopísek Strelec Company from TUR7/CON1 deltaic formation (see Uličný et al., 2003) in a quarry located close to the town of Sobotka.
where k1 N k2 N k3 are the principal susceptibilities, η1 = lnk1, η2 = lnk2, η3 = lnk3. The value of the mean susceptibility is in our case directly proportional to the content of magnetite in the model material. The parameter P, called the degree of AMS, indicates the intensity of the preferred orientation of magnetite by grain shape in the model material. The parameter T characterizes the symmetry of the AMS ellipsoid. If 0 b T b +1 the AMS ellipsoid is oblate (the magnetic fabric is planar); T = + 1 means that the AMS ellipsoid is rotationally symmetric (uniaxial oblate). If − 1 b T b 0 the AMS ellipsoid is prolate (the magnetic fabric is linear); T = − 1 means that the AMS ellipsoid is uniaxial prolate. If T = 0 the ellipsoid is neutral, on the transition between oblate and prolate. The magnetite that was admixed to plaster is a natural powdered magnetite from the Kiruna mine in Sweden and is processed in P/D Refractories CZ a.s. in Velké Opatovice, Czech Republic. The finest
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Fig. 3. Magnetic characteristics of our analogue model. (a) Total susceptibility vs. low-temperature curve of the magnetite used in our analogue model. (b) Histogram of mean susceptibility (from total 176 specimens measured) of the diapir model.
fraction (grain size b 0.07 mm) was used that is captured in air-filters while the ore is crushed. The low-temperature vs. susceptibility curve of this material, investigated using the CS-L Cryostat Apparatus in cooperation with the KLY-4S Kappabridge, shows conspicuous Verwey transition indicating pure magnetite (Fig. 3a). 4. Experiment apparatus and experimental procedure The analogue apparatus consists of a manual squeezer with a Perspex container mounted on the
bottom of the squeezer (Fig. 1). The cube shaped container 46 cm in inner width has a free upper top side and a removable front. The pressure imposed by the manual squeezer is transferred to the “squeezing board” through a steel construction of a pyramid shape with vertical angles attached at four corners of this pyramid (the stress transmitter in Fig. 1). The squeezing board has a centred circular hole (11 cm in diameter) that determines the width of the plaster column rising during the experiment. The squeezing board slopes down away from the circular hole at an angle of 10° to imitate a bell-shaped source layer below natural
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diapiric bodies. A calibrated spring provides a crude estimate of maximum pressure imposed at the end of the experimental run and relative continuity of the squeezing pressure during the experiment. However, the calibrated spring was used only for technical reasons, to secure repeatability of the process. Keeping in mind complex rheological behaviour of plaster and impossibility in controlling the magnetite viscosity, we had no ambition to use the calibrated spring even for crude scaling. Finally, a Perspex sedimentation trolley is placed on the aluminium rails and powered by accumulator drilling machine. Plaster powder (20 kg) together with 1wt.% of the retarding agent and 0.1 vol.% of magnetite powder was mixed dry manually in a large bucket. The plaster for the experiments was prepared with plaster/water mixing ratio of 2.2. This mixture was then tossed into another bucket with 8.6 l of water and properly homogenised with a stirrer mounted on a drilling machine for at least 5 min. This mixing method has resulted in very homogeneous distribution of magnetite grains in the plaster, which is documented by narrow distribution of the mean susceptibilities measured (see Fig. 3b). One third of this plaster volume was coloured by 100 ml of black printing ink. The plaster/water mixing ratio of the remaining plaster volume was corrected with an appropriate volume of water. Three horizontal layers of plaster (white– black–white) were carefully placed one on another from a rectangular form on the bottom of the lubricated container, while its front was open. This plaster set was covered by a thin lubricated plastic foil stretched on a frame. All walls, the upper and the lower surface surrounding the plaster, are thus characterized as free slip boundaries at the onset of the experiment. Finally, a thin layer (3 cm) of sand was placed on the foil frame and covered by the squeezing board. A stress transmitter was then placed on the squeezing board and an additional 7-cm thick layer of sand was added on the top of the squeezing board. In our axi-symmetric experiments, plaster is squeezed into a vertical cylindrical channel from a horizontal source layer. Manual sedimentation of surrounding sand to the top periphery of the experiment kept pace with the rise of the plaster column, while the plaster plug produced graben structures and radial fault patterns in the thin layer of overlying sand. This incipient topography is immediately levelled by sedimentation from a sedimentation trolley. The experimental run did not last longer than 15 min.
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5. Results In order to understand the diapiric ascent of plaster the spatial distribution and deformation of coloured plaster was qualitatively evaluated throughout the whole diapiric body. The distribution of coloured plaster in the diapir provided the first order information about the distribution of finite displacements and kinematics of the model. The other important information is the distribution of AMS fabric prior to application of vertical stress and throughout the diapiric model, which yields information about finite strain orientation related to prediapiric fabric pattern and that related to the diapiric material transfer processes. 5.1. Kinematics of diapiric material motions inferred from coloured layered model The experiment described above resulted in a diapiric intrusion of columnar body that is approximately circular in plan view (Fig. 2). The solidified body was cut along the vertical plane passing through the axis of the body. In this way, vertical movements of the model material are well visible due to the fact that the model material consists of three originally horizontal layers that differ in colour, but are identical in mechanical properties. In vertical cross-section, thick subhorizontal colour bands in the base of the model are bent to create a vertical channel that continuously gets wider upwards (the bands diverge slightly). The inner frontiers of the vertical black bands are marked by inward pointing cusps. Thin trails of alternating plaster colours extend from the thick vertical black bands. These structures mark symmetrically both margins of the channel. The outer white band attenuates upward in the model column and shows a thin relict in the apical part. In contrast, the dark band and the inner white band get in turn wider. In the apical part of the body the dark band is relatively thin, too. In the middle of the column, one can observe that the dark band is either doubled (see left side of Fig. 2a) or there are protuberances of the dark band into the outer white band. 5.2. Pre-diapiric magnetic fabric It would be ideal, if the model material possessed isotropic magnetic fabric before starting diapiric ascent, because the magnetic fabric of the diapir could be in this case reasonably considered to have entirely originated through diapiric movements. Unfortunately, we have not been able to prepare such a
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magnetically isotropic material for technical reasons. We are able to create almost homogeneous mixture of plaster of Paris with magnetite that is almost isotropic magnetically provided that the plaster solidifies rapidly. However, for the reasons of making the model material motions visible, we have to use colour layered model. Unfortunately, preparation of such a material (casting the plaster layers in the container and placing three layers one above another) together with necessity
of relatively slow solidifying (providing time for the efficient affecting of gravity field) results in creating model material that is magnetically anisotropic. To estimate this pre-diapiric AMS, we made a special experiment in which the model material was made in an identical way and under the same conditions used in simulating the diapirism, but the model material was not subsequently loaded to initiate the diapirism (Fig. 4a).
Fig. 4. Magnetic fabric in analogue body with pre-diapiric fabric. (a) Vertical cross-section of the model. (b) Orientations of magnetic foliation poles (K3) and magnetic lineations (K1). Equal-area projection on lower hemisphere. (c) Magnetic anisotropy P–T plot.
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The results of this experiment are presented in Fig. 4. The AMS pattern shows relatively homogenous flatlying magnetic foliations and subhorizontal magnetic lineations oriented preferentially along the X coordinate axis (Fig. 4b). The sub-horizontal orientation of magnetic foliation evidently results from the effect of gravity field on magnetite particles in slowly solidifying plaster when the magnetic grains tend to orient their larger surfaces parallel to the horizontal plane. It should be noted that the model material was poured into the experimental apparatus along the X axis direction; the magnetic lineations evidently reflect the direction of the material transport. The shape of AMS ellipsoid,
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characterized by T parameter, is relatively homogenous and mostly oblate (only 10 of 69 samples show very weakly prolate fabric) (Fig. 4c). The degree of AMS, represented by the P parameter, is also relatively homogeneous and relatively strong, mostly ranging from 1.15 to 1.25 (Fig. 4c). 5.3. Diapir magnetic fabric and its origin In the lateral margins of the source layer, the magnetic foliations are virtually horizontal or show only very gentle dips (Fig. 5a). The magnetic lineations are also relatively flat, oriented towards the central hole
Fig. 5. Magnetic fabric in the diapir. (a) Orientation of magnetic foliations in individual specimens. Contoured diagrams of magnetic foliation poles in characteristic domain. (Equal-area projection on lower hemisphere). (b) Orientation of magnetic lineations (arrows denote directions of lineation plunge). Contoured diagrams of magnetic foliation poles in characteristic domain (Equal-area projection on lower hemisphere). (c) Contoured diagram of shape parameter T. (d) Contoured diagram of parameter of the degree of AMS, P. (The parameters P and T were interpolated using the “spline” method in ArcGIS9 environment).
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verging towards the diapir (Fig. 5b). The AMS ellipsoid is neutral to slightly oblate here (Fig. 5c) and the degree of AMS is low to moderate (Fig. 5d). These parts of the model were evidently thinned in vertical direction due to the vertical load (final thickness of the layered model is less than one half of the original thickness on the sides) and the material moved towards the central hole through which it ascended to create a diapir. The subhorizontal orientation of the magnetic foliation was retained, but the magnetic lineation was reoriented from the original parallelism to the X axis (direction of casting of the model material into the apparatus) into the direction pointing towards the central hole. The AMS ellipsoid got a shape of neutral ellipsoid. The degree of AMS is comparable to that of the pre-diapiric model, even though one would expect strengthening of the prediapiric magnetic fabric. Possible explanation of this phenomenon is the assumption of primarily weaker AMS degree than that measured in the model of prediapiric magnetic fabric. Even though the conditions for creating the pre-diapiric and diapiric models were kept as similar as possible, longer time during solidification of the pre-diapiric model in sub-horizontal layers may have resulted in stronger AMS than in the pre-diapiric model. Below the base of the diapiric column in the source layer, the magnetic foliation and lineations are moderately inclined, and becoming progressively vertical in the lower part of the diapir (Fig. 5a,b). The magnetic fabric is clearly linear in this part and the degree of AMS is moderate (Fig. 5c,d). This magnetic fabric evidently originated through vertical channel flow of the model material. In the central part of the diapiric body and in about a half of the height of the experimental diapiric column a transitional zone occurs that is characterized by sudden development of horizontal magnetic foliations and lineations coupled with progressive increase of the degree of oblateness and the decrease of degree of anisotropy. Higher in the column, the foliations and lineations tend to remain subhorizontal, the fabric becomes oblate and the degree of anisotropy increases. In addition, the magnetic foliations and lineations are very steep to upright in the marginal parts of the whole diapir except the apical part (Fig. 5a,b). The magnetic fabric is predominantly oblate with moderate to strong degree of AMS. As the diapir diameter is mostly larger than the diameter of the central orifice, it is obvious that marginal parts of the diapir were affected by the forces pressing them against the outer walls.
6. Discussion 6.1. Material transfer processes inferred from coloured plaster layers and AMS fabrics The material transfer during the whole process inferred from the coloured plaster layers and magnetic fabric can be summarized as follows. In the base, the convergent flow induced by vertical squeezing results in radial horizontal motions of the material towards the central hole. This region displays increase of thickness namely of the lowermost white plaster layer coupled with a modification of oblate fabrics in the lateral sides to highly constrictional fabrics extending to the vertical channel. Convergent flow towards the narrow tube in hydrodynamically flowing material is typically related with increasing strain rate resulting in high finite strains and constrictional fabrics (Paterson et al., 1998). The degree of elongation is symmetrical with respect to the vertical flow axis, with the most prolate fabric typical for convergent flows in narrow tubes in the centre. Subsequently, this prolate fabric is being reworked during the upward flow into a subhorizontal oblate fabric. This transition zone is marked by prominently low degree of AMS. The generating flow profile exhibits a symmetrical imbrication pattern of oblate subhorizontal fabrics along the flow axis and the imbrication angle decreases continuously towards the lateral channel boundaries. The transition zone results from superposition of vertical axial flattening superimposed onto constrictional fabric with vertical elongation axis. Progressive axial shortening of constrictional fabric leads to a gradual decrease of prolateness and decrease of the degree of anisotropy. Finally, strong axial flattening leads to entire reworking of the vertical fabric and development of horizontal oblate ellipsoids in the central part of the diapiric column. The whole process of fabric transition is developed in inner white and dark plaster layers in which we observe progressive widening of vertical channel coupled with development of horizontal AMS fabrics. This widening of extrusion channel is certainly associated with divergent type of flow; therefore decrease of strain rate with a natural tendency to development of oblate fabrics (Paterson et al., 1998). At the same time the external parts of dark layer and external white plaster layer show vertical fabrics with oblate ellipsoids. The material in the central part of the column is pushed upwards and it becomes weakly laterally extruded towards the uppermost domain. During this process, limited downward material flow along the margins of the diapir cannot be excluded.
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It is important to consider the stress distribution controlling the transition from vertical to horizontal fabrics in diapirically ascending material. The vertical stress applied on the horizontal plaster layer is pushing the material vertically through a circular hole in a similar manner to natural diapiric systems. In analogue and theoretical models of fabric development during buoyant diapiric rise (e.g. Dixon, 1974; Cruden, 1990), the level of transition of vertical prolate fabrics to subhorizontal oblate fabrics is constrained to the uppermost level of the diapiric head or bulb (Jackson and Talbot, 1989). The bulb at the same time originates after the ascending material reaches the level of neutral buoyancy, which is generally coinciding with the earth surface and results in extrusion like for Zagros salt domes in Iran (Talbot, 1993). However, in our case study, the transition from vertical to horizontal fabric occurs in relatively deeper levels, in the middle of the vertical column. Despite the collapse of our vertical fabric is controlled by experimental conditions, our results imply that in nature the gravity driven collapse of low viscosity materials may occur in greater depths than it might be expected (Rey et al., 2001). 6.2. Correlation of AMS model fabric pattern with natural examples of granitic plugs Among the bodies of granitic rocks, the AMS of those having shapes of steep up to upright granitic stocks has been investigated relatively frequently. It could be interesting to compare the results of this investigation of the natural bodies with the results obtained from our model. In this way, an impression can be obtained how realistic our modelling is. The AMS of granitic stocks was for instance investigated by King (1966), Chlupáčová et al. (1975), Cogné and Perroud (1988) and Hrouda and Lanza (1989). In all the stocks investigated, the magnetic foliations are very steep to upright regardless of the position within the pluton, often conforming in their strikes the shape of the stock outcrop. The magnetic lineations show variable plunges ranging from almost vertical to subhorizontal. The steep magnetic foliations correspond well to the assumed approximately vertical paths of the ascending magma in the stock. However, magnetic lineations indicate that the magma flow is complex giving rise to roughly horizontal magnetic lineations in some parts in contrast to the relatively simple laminar vertical flow in volcanic necks with homogenous vertical magnetic lineations. In our model diapir, the magnetic foliations are steep to upright in the very marginal parts along the entire
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length of the body, while in the central part of the body they show transitions from steep plunges in the lowermost domain to horizontal plunges in the uppermost part. The steep orientations of the magnetic foliations in the marginal portions of the model agree well with those in natural stocks. There is a small difference in the orientation of magnetic foliation in the central portions of the stock. While in natural stocks the magnetic foliations were found steep throughout the stock, including central parts, they are steep only in the lower part of the body in our model. The explanation of this difference is not simple. The possible suggestion is that the erosion levels of the natural stocks investigated are relatively deep and the AMS was measured on specimens coming from the lower part of the body. Alternatively, the overlying rocks of the natural stocks may have been more permeable for magma than was the sand in the model used and the vertical compaction of the magma was effective only in the very apical parts of the stocks. The difference in the orientation of magnetic lineations in our model and in natural stocks is larger. In the model, the flat magnetic lineations correspond to the flat magnetic foliations just as the steep magnetic foliations with the magnetic lineations. In natural stocks, there are numerous and probably even dominating specimens in which the magnetic foliations are steep, but the magnetic lineations are gently inclined, even subhorizontal. This may indicate that the magma flow in natural stock may be more complex than the relatively simple flow of the model material. We speculate that the natural flow comprises also the horizontal flow components that have no equivalents in our model. As the natural stocks often show “tails”, sometimes considered feeder paths for the stocks, horizontal flow from the tail along the circumference of the body may explain generation of relatively numerous flat magnetic lineations and simultaneously steep magnetic foliations. 6.3. Implications for magma movement in dykes Even though our model was primarily constructed to simulate flow in diapiric plutons, its results can be used in solving some problems of generating the AMS in dykes. As magma flow in dykes is often considered to be an important mass transfer within the Earth's crust, the AMS in dykes has been investigated relatively frequently. The AMS in dykes has been classed into four types (for summary see Raposo and Ernesto, 1995). The first and most common type is characterized by approximately parallel orientation of magnetic foliation
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to the dyke plane with the magnetic lineation subparallel to the direction of flow of magma in a dyke. During magma flow, the larger surfaces of magnetic minerals orient approximately parallel to the dyke, while the longer dimensions orient parallel to the magma flow direction. The second type is characterized by approximately perpendicular orientation of magnetic foliation to the dyke plane and magnetic lineation parallel to the dyke. It is presumed that this orientation originates through a compaction of a static magma column along the dyke when the magnetic minerals are re-oriented with their larger surfaces perpendicular to the flow direction (Park et al., 1988; Raposo and Ernesto, 1995). The third type is rare, being characterized by horizontal magnetic foliation and also horizontal magnetic lineation perpendicular to the dyke; this magnetic fabric may be attributed to secondary processes such as hydrothermalism (Rochette et al., 1991). The fourth type shows almost random orientation of magnetic foliations and lineations, which may result from very complex flow pattern or from severe post-magmatic changes of the magnetic minerals (Hrouda, 1985). In addition, another secondary aligning processes following initial emplacement (or very late stage processes) can affect the magnetic fabric in dykes, but these are out of scope of this paper. The results of our modelling support the hypothesis by Park et al. (1988) and Raposo and Ernesto (1995) concerning the mechanism of the generation of the preferred orientation of magnetic minerals in the type two. In the upper domain of our diapir the magnetic foliations and magnetic lineations are flat, perpendicular to the material motion. This orientation is evidently due to the pressure of already ascended material by the portions of coming material in one continuous process. If similar mechanical conditions are at work in the Earth's crust, the type two magnetic fabrics in dykes can quite well originate as suggested by Park et al. (1988) and Raposo and Ernesto (1995). 7. Conclusions The experimental results highlight a strong correlation between the AMS fabric and bulk flow pattern inferred from the geometry of the colour banding. The analogue models of AMS give the constraints to the flow regimes operating in different parts of the diapiric bodies that reflect the changing boundary conditions (Jackson and Talbot, 1989). In the base of the model, the flow is described by the radial stretching field verging to the narrow constrictional channel. The lower part of the vertical channel is
dominated by relict (or inherited) prolate vertical fabrics due to convergent flow. The upper part displays symmetrical imbrication profile of subhorizontal oblate fabrics marked by low degree of AMS, which corresponds to a zone of superposition of axial flattening on vertical constrictional fabrics in the centre of the plug associated with widening of the plug and divergent flow. High shear strain on the lateral margins of the active channel associated with viscous drag of vertically ascending plaster led to the development of zones of intense deformation. The transition from vertical to horizontal fabric in the centre of the plug is interpreted in terms of gravity collapse of plaster column thanks to the weight of the overlying plaster and pressure of overburden. The AMS fabric of the model is correlated with fabrics in natural granite plugs and dykes and it is proposed that the vertical pressure driven by weight of overburden is a leading factor controlling the fabric transition observed in the modelled example. Our non-scaled analogue modelling of AMS provides interesting insights and helps to unravel the internal strain pattern during ascent of non-linear viscous materials. Plaster served as a convenient analogue medium, which has a potential to model structures in natural magmatic systems or salt diapirs, while it reproduces both shear zones and folding in a ductile regime. 8. Uncited reference Borradaile and Jackson, 2004 Acknowledgement Dr. Chris Talbot is thanked for fruitful discussions concerning the topic and for friendly reviewing the draft of the manuscript. We are grateful to Ing. Bomberová of P/D Refractories CZ a.s. for providing us with magnetite powder and to Ing. Josef Záruba for his help with designing the analogue apparatus. We appreciate the help of Mgr. Veronika Kopačková of Czech Geological Survey in the ArcView GIS presentation of our results. This research was supported financially by the Ministry of Education of the Czech Republic (FRVS 2850/2003) and by the Grant Agency of the Czech Republic (GACR 205/03/0204). References Borradaile, G.J., Alford, C., 1987. Relationship between magmatic susceptibility and strain in laboratory experiments. Tectonophysics 133, 121–135.
Z. Kratinová et al. / Tectonophysics 418 (2006) 51–61 Borradaile, G.J., Alford, C., 1988. Experimental shear zones and magnetic fabrics. J. Struct. Geol. 10 (8), 895–904. Borradaile, G.J, Jackson, M.P.A., 2004. Anisotropy of magnetic susceptibility (AMS): magnetic petrofabrics of deformed rocks. In: Martin-Hernandez, F., Luneburg, C.M., Aubourg, C., Jackson, M. (Eds.), Magnetic Fabric: Methods and ApplicationsGeol. Soc., London, Special Publications, vol. 238, pp. 299–360. Borradaile, G.J., Puumala, M.A., 1989. Synthetic magnetic fabrics in a plasticene medium. Tectonophysics 194, 73–78. Chlupácová, M., Hrouda, F., Janák, F., Rejl, L., 1975. The fabric, genesis, and relative-age relationship of the granitic rocks of the Čistá-Jesenice massif, as studied by magnetic anisotropy. Gerlands Beitr. Geophys. 84, 487–500. Cogne, J.-P., Perroud, H., 1988. Anisotropy of magnetic susceptibility as a strain gauge in the Flamanville granite, NW France. Phys. Earth Planet. Inter. 51, 264–270. Cruden, A.R., 1990. Flow and fabric development during the diapiric rise of magma. J. Geol. 98 (5), 681–698. Dixon, J.M., 1974. A new method of determining finite strain in models of geological structures. Tectonophysics 24, 99–114. Fossen, H., Gabrielsen, R.H., 1996. Experimental modelling of extensional fault systems by use of plaster. J. Struct. Geol. 18 (5), 673–687. Hamilton, N., Rees, A.I., 1970. Magnetic fabric of sediments from the shelf at la Jolla (California). Mar. Geol. 9, M6–M11. Housen, B.A., Richter, C., Pluijm, B.A., Van der, 1993. Composite magnetic anisotropy fabrics: experiments, numerical models, and implications for the quantification of rock fabrics. Tectonophysics 220, 1–12. Hrouda, F., 1985. The magnetic fabric in the Brno massif. Sbor. Geol. Ved, UG, pp. 89–112. Hrouda, F., Lanza, R., 1989. Magnetic anisotropy in the Biella and Traversella stocks (Periadriatic Line): implications for the emplacement mode. Phys. Earth Planet. Inter. 56, 337–348. Hrouda, F., Jelínek, V., Hrušková, L., 1990. A package of programs for statistical evaluation of magnetic anisotropy data using IBM-PC computers. EOS Trans. AGU. Fall Meeting. Hubbert, M.K., 1937. Theory of scale models as applied to the study of geologic structures. Geol. Soc. Amer. Bull. 48, 1459–1520. Jackson, M.P.A., Talbot, C.J., 1989. Anatomy of mushroom-shaped diapirs. J. Struct. Geol. 11 (1/2), 211–230. Jelínek, V., 1978. Statistical processing of anisotropy of magnetic susceptibility measured on groups of specimens. Stud. Geophys. Geod. 22, 50–62. Jelínek, V., 1981. Characterisation of magnetic fabric of rocks. Tectonophysics 79, 63–67. Jelínek, V., Pokorný, J., 1997. Some new concepts in technology of transformer bridges for measuring susceptibility anisotropy of rocks. Phys. Chem. Earth 22, 179–181. King, R.F., 1966. The magnetic fabric of some Irish granites. Geol. J. 5, 43–66. Koyi, H., 1991. Mushroom diapirs penetrating overburdens with high effective viscosities. Geology 19 (12), 1229–1233. Koyi, H., 1997. Analogue modelling: from a qualitative to a quantitative technique—a historical outline. J. Pet. Geol. 20 (2), 223–238. Koyi, H., Talbot, C.J., Torudbakken, B.O., 1993. Salt diapirs of the southwest Nordkapp Basin: analogue modelling. Tectonophysics 228, 167–187.
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Nagata, T., 1961. Rock Magnetism. Maruzen, Tokyo. Park, J.K., Tanczyk, E.I., Desbarats, A., 1988. Magnetic fabric and its significance in the 400 Ma Mealy diabase dykes of Labrador, Canada. J. Geophys. Res. 93, 13689–13704. Parker, T.J., McDowell, A.N., 1955. Model studies of salt-dome tectonics. Bull. Am. Assoc. Pet. Geol. 54, 207–250. Paterson, S.R., Fowler, T.K., Schmidt, K.L., Yoshinobu, A.S., Yuan, E. S., Miller, R.B., 1998. Interpreting magmatic fabric patterns in plutons. Lithos 44, 53–82. Pokorný, J., Suza, P., Hrouda, F., 2004. Anisotropy of magnetic susceptibility of rocks measured in variable weak magnetic fields using the KLY-4S Kappabridge. In: Martin-Hernandez, F., Luneburg, C.M., Aubourg, C., Jackson, M. (Eds.), Magnetic Fabric: Methods and Applications. Geol. Soc., London, Special Publications, vol. 238, pp. 69–76. Porath, H., Stacey, F.D., Cheam, A.S., 1966. The choice of specimen shape for magnetic anisotropy measurements on rocks. Earth Planet. Sci. Lett. 1, 92. Ramberg, H., 1981. Gravity, Deformation and the Earth's Crust, 2ed edition. Academic Press, New York. 452 pp. Raposo, M., Ernesto, M., 1995. Anisotropy of magnetic susceptibility in the Ponta-Grossa dyke swarm (Brazil) and its relationship with magma flow direction. Phys. Earth Planet. Inter. 87 (3–4), 183–196. Rees, A.I., 1983. Experiments on the productions of transverse grain alignment in a sheared dispersion. Sedimentology 30, 437–448. Rees, A.I., Woodall, W.A., 1975. The magnetic fabric of some laboratory-deposited sediments. Earth Planet. Sci. Lett. 25, 121–130. Rey, P., Vanderhaeghe, O., Teyssier, C., 2001. Gravitational collapse of the continental crust: definition, regimes and modes. Tectonophysics 342 (3–4), 435–449. Richter, C., 1990. The anisotropy of magnetic susceptibility— numerical models, deformation experiments, and practical application in structural geology. Tüb. Geowiss. Arb., Ser. A 8, 123. Richter, C., 1992. Particle motion and the modelling of strain response in magnetic fabrics. Geophys. J. Int. 110, 451–464. Richter, C., Fritsch, W., Ratschbacher, W., Schwarz, H.-U., 1991. The magnetic fabrics of experimentally deformed artificial clay-water dispersions. Tectonophysics 200, 143–155. Rochette, P., Jenatton, L., Dupuy, C., Boudier, F., Reuber, I., 1991. Diabase dikes emplacement in the Oman ophiolite: a magnetic fabric study with refernce to geochemistry. In: Peters, et al. (Eds.), Ophiolite Genesis and Evolution of the Oceanic Lithosphere. Kluwer, pp. 55–82. Schultz-Ela, D.D., Jackson, M.P., Vendeville, B.C., 1993. Mechanics of active salt diapirism. Tectonophysics 228 (3–4), 275–312. Talbot, C.J., 1993. Spreading of salt structures in the Gulf of Mexico. Tectonophysics 228 (3–4), 151–166. Tarling, D.H., Hrouda, F., 1993. The Magnetic Anisotropy of Rocks. Chapman and Hall, London. Uličný, D., Čech, S., Grygar, R., 2003. Tectonic and depositional systems of A Shallow-marine, Intra-Continental Strike-Slip Basin: exposures of the Ceský Ráj Region, Bohemian Cretaceous Basin. Geolines-Proceeding of the 8thMeeting of the Czech Tectonic Studies Group, pp. 133–148. Wing-Fatt, L., Stacey, F.D., 1966. Magnetic anisotropy of laboratory materials in which magma flow is simulated. Pure Appl. Geophys. 64, 78–80.
Non-scaled analogue modelling of AMS development during viscous flow: A simulation on diapir-like structures Zuzana Kratinová a,d,1 , Prokop Závada a,1 , František Hrouda a,b,⁎, Karel Schulmann c,2 a
c
Institute of Petrology and Structural Geology, Charles University, Prague, Czech Republic b Agico Inc., Ječná 29a, Brno, Czech Republic Centre de Geochimie de la Surface, EOST, Université Louis Pasteur, Strasbourg cedex, France d Geophysical Institute, Czech Academy of Sciences, Bočni II, Prague, Czech Republic
Received 12 May 2005; received in revised form 29 September 2005; accepted 5 December 2005 Available online 28 February 2006
Abstract Development of magnetic fabric within a diapirically ascending columnar body was investigated using non-scaled analogue model made of plaster of Paris containing small amount of fine-grained homogeneously mixed magnetite. The apparatus for the modelling consists of a manual squeezer with calibrated spring and a Perspex container. Set of weak coloured layers at the bottom of the container was forced to intrude overlying fine-grained sand through a hole in a board attached to the squeezer. The development of AMS fabric is correlated with complex flow pattern indicated by coloured and originally horizontal plaster layers. Strongly constrictional and vertical fabric in the base and in the lower domain of the diapir resulting from convergent and upwards flows is overprinted by subhorizontal oblate fabrics due to vertical flattening and initial divergent flow in the apical parts. The measured AMS fabrics are compared with natural examples of magmatic stocks and dykes. © 2006 Elsevier B.V. All rights reserved. Keywords: Analogue modelling; AMS; Diapir; Plaster of Paris
1. Introduction The purpose of analogue modelling of geological processes is to investigate possible mechanisms that contribute to the generation of finally observed structures. Field observation and intuition have inspired geologists to construct analogue models almost two centuries ago (for review see Koyi, 1997). Analogue modelling has ⁎ Corresponding author. František Hrouda, Agico Inc., Ječná 29a, Brno, Czech Republic. Fax: +420 541634328. E-mail addresses: [email protected] (Z. Kratinová), [email protected] (P. Závada), [email protected] (F. Hrouda), [email protected] (K. Schulmann). 1 Fax: +420 21951533. 2 Fax: +33 3 90 24 04 02. 0040-1951/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.tecto.2005.12.013
undergone major progress following the introduction of scaling (Hubbert, 1937) resulted in more realistic models (Koyi, 1997). The majority of models investigated shapes of the modelled bodies (e.g. Parker and McDowell, 1955; Ramberg, 1981; Koyi, 1991, 1993; Schultz-Ela et al., 1993) and only rarely also their internal fabrics (Dixon, 1974; Jackson and Talbot, 1989). Among the latter, the models that use the anisotropy of magnetic susceptibility (AMS) are advantageous, because this method is able to rapidly and precisely investigate the preferred orientation of magnetic minerals in rocks and/or models (the magnetic fabric, for summary, see for instance Tarling and Hrouda, 1993). The first application of AMS in analogue modelling was to investigate the deposition and compaction
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processes in sedimentary rocks (for summary, see Hamilton and Rees, 1970; Rees and Woodall, 1975; Rees, 1983; Tarling and Hrouda, 1993) and in the study of lava flow mechanisms in volcanic rocks (Wing-Fatt and Stacey, 1966). Later, processes of rock deformation were also modelled (Borradaile and Alford, 1987, 1988; Borradaile and Puumala, 1989; Richter, 1990, 1992; Richter et al., 1991; Housen et al., 1993). In all the AMS models, magnetic minerals (magnetite, nickel) were added in small amount into the model material (sand, plaster of Paris, plasticene). Magnetite viscosity cannot be easily controlled and thus all the AMS models used until now are non-scaled. The purpose of the present paper is to investigate the magnetic fabrics within complex diapir-like structure created through analogue modelling, using simple experimental press-like apparatus and plaster of Paris as model material (Figs. 1 and 2). The plaster of Paris was used as an analogue of weak rock, because it can be easily coloured and deformed in the liquid state and transformed to solid state after the experiment. In order to measure the AMS of this model material, small amount of magnetite was added. As the plaster of Paris used in our experiments is diamagnetic, having the
susceptibility about − 5 × 10−6 [SI], our AMS measurements indicate only the magnetite fabric. Even though complex rheological behaviour of the plaster rules out dynamically scaling of our experiments, the results provided by our models can serve as a semi-quantitative map of fabrics throughout similar natural bodies. We show in our experimental work that the AMS can be successfully applied to unravel the directions and shapes of viscous flow/deformation in 3D. However, one has to realize that even though the AMS specimens are relatively small, about 0.63 cm3 in volume, their AMS represents the mean AMS of order-of-magnitude larger volumes in the nature. 2. Analogue material characteristics Experiments were created using the plaster of Paris (commercial name Stuckgips, BPB Formula Company). The properties of plaster were already appreciated in analogue modelling of extensional fault systems (Fossen and Gabrielsen, 1996); the fine grain size of plaster guarantees high resolution of the models and its transition to the solid state is fast. Plaster can be considered as a suspension of plaster grains in water, so
Fig. 1. Experimental apparatus for analogue modelling of diapirism using coloured plaster of Paris and sand. (a) Analogue apparatus. (b) Scheme of the spring segment in detail. (c) Coordinate system used throughout the paper.
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3. Sampling and measurement techniques The coordinate system to which the orientations of the magnetic foliations and lineations are related throughout the paper is defined by the direction of the diapir intrusion and by the edges of the experimental apparatus representing the directions of the model material movements during its manipulation. Namely, the Z direction is the orientation of the axis of the diapir, being the vertical direction in absolute coordinates. The Y direction is left–right horizontal direction from the point of frontal view of the apparatus. The X direction is the horizontal front–rear direction (see Fig. 1c). The diapir was cut into two parts along the YZ plane, passing through the diapir axis. One part was sampled through drilling in a rectangular grid of the edge of 2 cm. The core diameter was 1 cm; the core height was 8 mm to keep the ideal height to diameter ratio (Porath et al., 1966). The cores were fixed into Perspex cylinder of standard size (25 mm in diameter) and their low-field AMS was measured with the KLY-4S Kappabridge (Jelínek and Pokorný, 1997; Pokorný et al., 2004). The AMS data were statistically evaluated using the ANISOFT package of programs (Jelínek, 1978; Hrouda et al., 1990). The mean bulk susceptibility, eccentricity and shape of the AMS ellipsoid can be characterized by the following parameters (Nagata, 1961; Jelínek, 1981): Km ¼ ðk1 þ k2 þ k3 Þ=3 P ¼ k1 =k3 T ¼ ð2 g2 g1 g3 Þ=ðg1 g3 Þ Fig. 2. (a) Vertical section of the diapir. (b) Horizontal section of the diapir 10 cm above the source layer.
its rheology is strongly dependent on the water content. To postpone the solidification reaction a yellow powder called “Retardan” (of unspecified composition) was employed. 1 wt.% of “Retardan” delayed the solidification process of plaster to approximately 2 h, which was sufficient to perform an experiment without any significant rheological changes. Most of the plaster is white, but master layers in our plaster models were coloured with a printing ink (2 vol.%). The material, which the plaster pierces during the experiment and then forms the surrounding support for the evolving diapir, is made by a fine-grained (0.017 mm), almost pure quartz sand. This sand is quarried by the Sklopísek Strelec Company from TUR7/CON1 deltaic formation (see Uličný et al., 2003) in a quarry located close to the town of Sobotka.
where k1 N k2 N k3 are the principal susceptibilities, η1 = lnk1, η2 = lnk2, η3 = lnk3. The value of the mean susceptibility is in our case directly proportional to the content of magnetite in the model material. The parameter P, called the degree of AMS, indicates the intensity of the preferred orientation of magnetite by grain shape in the model material. The parameter T characterizes the symmetry of the AMS ellipsoid. If 0 b T b +1 the AMS ellipsoid is oblate (the magnetic fabric is planar); T = + 1 means that the AMS ellipsoid is rotationally symmetric (uniaxial oblate). If − 1 b T b 0 the AMS ellipsoid is prolate (the magnetic fabric is linear); T = − 1 means that the AMS ellipsoid is uniaxial prolate. If T = 0 the ellipsoid is neutral, on the transition between oblate and prolate. The magnetite that was admixed to plaster is a natural powdered magnetite from the Kiruna mine in Sweden and is processed in P/D Refractories CZ a.s. in Velké Opatovice, Czech Republic. The finest
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Fig. 3. Magnetic characteristics of our analogue model. (a) Total susceptibility vs. low-temperature curve of the magnetite used in our analogue model. (b) Histogram of mean susceptibility (from total 176 specimens measured) of the diapir model.
fraction (grain size b 0.07 mm) was used that is captured in air-filters while the ore is crushed. The low-temperature vs. susceptibility curve of this material, investigated using the CS-L Cryostat Apparatus in cooperation with the KLY-4S Kappabridge, shows conspicuous Verwey transition indicating pure magnetite (Fig. 3a). 4. Experiment apparatus and experimental procedure The analogue apparatus consists of a manual squeezer with a Perspex container mounted on the
bottom of the squeezer (Fig. 1). The cube shaped container 46 cm in inner width has a free upper top side and a removable front. The pressure imposed by the manual squeezer is transferred to the “squeezing board” through a steel construction of a pyramid shape with vertical angles attached at four corners of this pyramid (the stress transmitter in Fig. 1). The squeezing board has a centred circular hole (11 cm in diameter) that determines the width of the plaster column rising during the experiment. The squeezing board slopes down away from the circular hole at an angle of 10° to imitate a bell-shaped source layer below natural
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diapiric bodies. A calibrated spring provides a crude estimate of maximum pressure imposed at the end of the experimental run and relative continuity of the squeezing pressure during the experiment. However, the calibrated spring was used only for technical reasons, to secure repeatability of the process. Keeping in mind complex rheological behaviour of plaster and impossibility in controlling the magnetite viscosity, we had no ambition to use the calibrated spring even for crude scaling. Finally, a Perspex sedimentation trolley is placed on the aluminium rails and powered by accumulator drilling machine. Plaster powder (20 kg) together with 1wt.% of the retarding agent and 0.1 vol.% of magnetite powder was mixed dry manually in a large bucket. The plaster for the experiments was prepared with plaster/water mixing ratio of 2.2. This mixture was then tossed into another bucket with 8.6 l of water and properly homogenised with a stirrer mounted on a drilling machine for at least 5 min. This mixing method has resulted in very homogeneous distribution of magnetite grains in the plaster, which is documented by narrow distribution of the mean susceptibilities measured (see Fig. 3b). One third of this plaster volume was coloured by 100 ml of black printing ink. The plaster/water mixing ratio of the remaining plaster volume was corrected with an appropriate volume of water. Three horizontal layers of plaster (white– black–white) were carefully placed one on another from a rectangular form on the bottom of the lubricated container, while its front was open. This plaster set was covered by a thin lubricated plastic foil stretched on a frame. All walls, the upper and the lower surface surrounding the plaster, are thus characterized as free slip boundaries at the onset of the experiment. Finally, a thin layer (3 cm) of sand was placed on the foil frame and covered by the squeezing board. A stress transmitter was then placed on the squeezing board and an additional 7-cm thick layer of sand was added on the top of the squeezing board. In our axi-symmetric experiments, plaster is squeezed into a vertical cylindrical channel from a horizontal source layer. Manual sedimentation of surrounding sand to the top periphery of the experiment kept pace with the rise of the plaster column, while the plaster plug produced graben structures and radial fault patterns in the thin layer of overlying sand. This incipient topography is immediately levelled by sedimentation from a sedimentation trolley. The experimental run did not last longer than 15 min.
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5. Results In order to understand the diapiric ascent of plaster the spatial distribution and deformation of coloured plaster was qualitatively evaluated throughout the whole diapiric body. The distribution of coloured plaster in the diapir provided the first order information about the distribution of finite displacements and kinematics of the model. The other important information is the distribution of AMS fabric prior to application of vertical stress and throughout the diapiric model, which yields information about finite strain orientation related to prediapiric fabric pattern and that related to the diapiric material transfer processes. 5.1. Kinematics of diapiric material motions inferred from coloured layered model The experiment described above resulted in a diapiric intrusion of columnar body that is approximately circular in plan view (Fig. 2). The solidified body was cut along the vertical plane passing through the axis of the body. In this way, vertical movements of the model material are well visible due to the fact that the model material consists of three originally horizontal layers that differ in colour, but are identical in mechanical properties. In vertical cross-section, thick subhorizontal colour bands in the base of the model are bent to create a vertical channel that continuously gets wider upwards (the bands diverge slightly). The inner frontiers of the vertical black bands are marked by inward pointing cusps. Thin trails of alternating plaster colours extend from the thick vertical black bands. These structures mark symmetrically both margins of the channel. The outer white band attenuates upward in the model column and shows a thin relict in the apical part. In contrast, the dark band and the inner white band get in turn wider. In the apical part of the body the dark band is relatively thin, too. In the middle of the column, one can observe that the dark band is either doubled (see left side of Fig. 2a) or there are protuberances of the dark band into the outer white band. 5.2. Pre-diapiric magnetic fabric It would be ideal, if the model material possessed isotropic magnetic fabric before starting diapiric ascent, because the magnetic fabric of the diapir could be in this case reasonably considered to have entirely originated through diapiric movements. Unfortunately, we have not been able to prepare such a
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magnetically isotropic material for technical reasons. We are able to create almost homogeneous mixture of plaster of Paris with magnetite that is almost isotropic magnetically provided that the plaster solidifies rapidly. However, for the reasons of making the model material motions visible, we have to use colour layered model. Unfortunately, preparation of such a material (casting the plaster layers in the container and placing three layers one above another) together with necessity
of relatively slow solidifying (providing time for the efficient affecting of gravity field) results in creating model material that is magnetically anisotropic. To estimate this pre-diapiric AMS, we made a special experiment in which the model material was made in an identical way and under the same conditions used in simulating the diapirism, but the model material was not subsequently loaded to initiate the diapirism (Fig. 4a).
Fig. 4. Magnetic fabric in analogue body with pre-diapiric fabric. (a) Vertical cross-section of the model. (b) Orientations of magnetic foliation poles (K3) and magnetic lineations (K1). Equal-area projection on lower hemisphere. (c) Magnetic anisotropy P–T plot.
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The results of this experiment are presented in Fig. 4. The AMS pattern shows relatively homogenous flatlying magnetic foliations and subhorizontal magnetic lineations oriented preferentially along the X coordinate axis (Fig. 4b). The sub-horizontal orientation of magnetic foliation evidently results from the effect of gravity field on magnetite particles in slowly solidifying plaster when the magnetic grains tend to orient their larger surfaces parallel to the horizontal plane. It should be noted that the model material was poured into the experimental apparatus along the X axis direction; the magnetic lineations evidently reflect the direction of the material transport. The shape of AMS ellipsoid,
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characterized by T parameter, is relatively homogenous and mostly oblate (only 10 of 69 samples show very weakly prolate fabric) (Fig. 4c). The degree of AMS, represented by the P parameter, is also relatively homogeneous and relatively strong, mostly ranging from 1.15 to 1.25 (Fig. 4c). 5.3. Diapir magnetic fabric and its origin In the lateral margins of the source layer, the magnetic foliations are virtually horizontal or show only very gentle dips (Fig. 5a). The magnetic lineations are also relatively flat, oriented towards the central hole
Fig. 5. Magnetic fabric in the diapir. (a) Orientation of magnetic foliations in individual specimens. Contoured diagrams of magnetic foliation poles in characteristic domain. (Equal-area projection on lower hemisphere). (b) Orientation of magnetic lineations (arrows denote directions of lineation plunge). Contoured diagrams of magnetic foliation poles in characteristic domain (Equal-area projection on lower hemisphere). (c) Contoured diagram of shape parameter T. (d) Contoured diagram of parameter of the degree of AMS, P. (The parameters P and T were interpolated using the “spline” method in ArcGIS9 environment).
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verging towards the diapir (Fig. 5b). The AMS ellipsoid is neutral to slightly oblate here (Fig. 5c) and the degree of AMS is low to moderate (Fig. 5d). These parts of the model were evidently thinned in vertical direction due to the vertical load (final thickness of the layered model is less than one half of the original thickness on the sides) and the material moved towards the central hole through which it ascended to create a diapir. The subhorizontal orientation of the magnetic foliation was retained, but the magnetic lineation was reoriented from the original parallelism to the X axis (direction of casting of the model material into the apparatus) into the direction pointing towards the central hole. The AMS ellipsoid got a shape of neutral ellipsoid. The degree of AMS is comparable to that of the pre-diapiric model, even though one would expect strengthening of the prediapiric magnetic fabric. Possible explanation of this phenomenon is the assumption of primarily weaker AMS degree than that measured in the model of prediapiric magnetic fabric. Even though the conditions for creating the pre-diapiric and diapiric models were kept as similar as possible, longer time during solidification of the pre-diapiric model in sub-horizontal layers may have resulted in stronger AMS than in the pre-diapiric model. Below the base of the diapiric column in the source layer, the magnetic foliation and lineations are moderately inclined, and becoming progressively vertical in the lower part of the diapir (Fig. 5a,b). The magnetic fabric is clearly linear in this part and the degree of AMS is moderate (Fig. 5c,d). This magnetic fabric evidently originated through vertical channel flow of the model material. In the central part of the diapiric body and in about a half of the height of the experimental diapiric column a transitional zone occurs that is characterized by sudden development of horizontal magnetic foliations and lineations coupled with progressive increase of the degree of oblateness and the decrease of degree of anisotropy. Higher in the column, the foliations and lineations tend to remain subhorizontal, the fabric becomes oblate and the degree of anisotropy increases. In addition, the magnetic foliations and lineations are very steep to upright in the marginal parts of the whole diapir except the apical part (Fig. 5a,b). The magnetic fabric is predominantly oblate with moderate to strong degree of AMS. As the diapir diameter is mostly larger than the diameter of the central orifice, it is obvious that marginal parts of the diapir were affected by the forces pressing them against the outer walls.
6. Discussion 6.1. Material transfer processes inferred from coloured plaster layers and AMS fabrics The material transfer during the whole process inferred from the coloured plaster layers and magnetic fabric can be summarized as follows. In the base, the convergent flow induced by vertical squeezing results in radial horizontal motions of the material towards the central hole. This region displays increase of thickness namely of the lowermost white plaster layer coupled with a modification of oblate fabrics in the lateral sides to highly constrictional fabrics extending to the vertical channel. Convergent flow towards the narrow tube in hydrodynamically flowing material is typically related with increasing strain rate resulting in high finite strains and constrictional fabrics (Paterson et al., 1998). The degree of elongation is symmetrical with respect to the vertical flow axis, with the most prolate fabric typical for convergent flows in narrow tubes in the centre. Subsequently, this prolate fabric is being reworked during the upward flow into a subhorizontal oblate fabric. This transition zone is marked by prominently low degree of AMS. The generating flow profile exhibits a symmetrical imbrication pattern of oblate subhorizontal fabrics along the flow axis and the imbrication angle decreases continuously towards the lateral channel boundaries. The transition zone results from superposition of vertical axial flattening superimposed onto constrictional fabric with vertical elongation axis. Progressive axial shortening of constrictional fabric leads to a gradual decrease of prolateness and decrease of the degree of anisotropy. Finally, strong axial flattening leads to entire reworking of the vertical fabric and development of horizontal oblate ellipsoids in the central part of the diapiric column. The whole process of fabric transition is developed in inner white and dark plaster layers in which we observe progressive widening of vertical channel coupled with development of horizontal AMS fabrics. This widening of extrusion channel is certainly associated with divergent type of flow; therefore decrease of strain rate with a natural tendency to development of oblate fabrics (Paterson et al., 1998). At the same time the external parts of dark layer and external white plaster layer show vertical fabrics with oblate ellipsoids. The material in the central part of the column is pushed upwards and it becomes weakly laterally extruded towards the uppermost domain. During this process, limited downward material flow along the margins of the diapir cannot be excluded.
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It is important to consider the stress distribution controlling the transition from vertical to horizontal fabrics in diapirically ascending material. The vertical stress applied on the horizontal plaster layer is pushing the material vertically through a circular hole in a similar manner to natural diapiric systems. In analogue and theoretical models of fabric development during buoyant diapiric rise (e.g. Dixon, 1974; Cruden, 1990), the level of transition of vertical prolate fabrics to subhorizontal oblate fabrics is constrained to the uppermost level of the diapiric head or bulb (Jackson and Talbot, 1989). The bulb at the same time originates after the ascending material reaches the level of neutral buoyancy, which is generally coinciding with the earth surface and results in extrusion like for Zagros salt domes in Iran (Talbot, 1993). However, in our case study, the transition from vertical to horizontal fabric occurs in relatively deeper levels, in the middle of the vertical column. Despite the collapse of our vertical fabric is controlled by experimental conditions, our results imply that in nature the gravity driven collapse of low viscosity materials may occur in greater depths than it might be expected (Rey et al., 2001). 6.2. Correlation of AMS model fabric pattern with natural examples of granitic plugs Among the bodies of granitic rocks, the AMS of those having shapes of steep up to upright granitic stocks has been investigated relatively frequently. It could be interesting to compare the results of this investigation of the natural bodies with the results obtained from our model. In this way, an impression can be obtained how realistic our modelling is. The AMS of granitic stocks was for instance investigated by King (1966), Chlupáčová et al. (1975), Cogné and Perroud (1988) and Hrouda and Lanza (1989). In all the stocks investigated, the magnetic foliations are very steep to upright regardless of the position within the pluton, often conforming in their strikes the shape of the stock outcrop. The magnetic lineations show variable plunges ranging from almost vertical to subhorizontal. The steep magnetic foliations correspond well to the assumed approximately vertical paths of the ascending magma in the stock. However, magnetic lineations indicate that the magma flow is complex giving rise to roughly horizontal magnetic lineations in some parts in contrast to the relatively simple laminar vertical flow in volcanic necks with homogenous vertical magnetic lineations. In our model diapir, the magnetic foliations are steep to upright in the very marginal parts along the entire
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length of the body, while in the central part of the body they show transitions from steep plunges in the lowermost domain to horizontal plunges in the uppermost part. The steep orientations of the magnetic foliations in the marginal portions of the model agree well with those in natural stocks. There is a small difference in the orientation of magnetic foliation in the central portions of the stock. While in natural stocks the magnetic foliations were found steep throughout the stock, including central parts, they are steep only in the lower part of the body in our model. The explanation of this difference is not simple. The possible suggestion is that the erosion levels of the natural stocks investigated are relatively deep and the AMS was measured on specimens coming from the lower part of the body. Alternatively, the overlying rocks of the natural stocks may have been more permeable for magma than was the sand in the model used and the vertical compaction of the magma was effective only in the very apical parts of the stocks. The difference in the orientation of magnetic lineations in our model and in natural stocks is larger. In the model, the flat magnetic lineations correspond to the flat magnetic foliations just as the steep magnetic foliations with the magnetic lineations. In natural stocks, there are numerous and probably even dominating specimens in which the magnetic foliations are steep, but the magnetic lineations are gently inclined, even subhorizontal. This may indicate that the magma flow in natural stock may be more complex than the relatively simple flow of the model material. We speculate that the natural flow comprises also the horizontal flow components that have no equivalents in our model. As the natural stocks often show “tails”, sometimes considered feeder paths for the stocks, horizontal flow from the tail along the circumference of the body may explain generation of relatively numerous flat magnetic lineations and simultaneously steep magnetic foliations. 6.3. Implications for magma movement in dykes Even though our model was primarily constructed to simulate flow in diapiric plutons, its results can be used in solving some problems of generating the AMS in dykes. As magma flow in dykes is often considered to be an important mass transfer within the Earth's crust, the AMS in dykes has been investigated relatively frequently. The AMS in dykes has been classed into four types (for summary see Raposo and Ernesto, 1995). The first and most common type is characterized by approximately parallel orientation of magnetic foliation
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to the dyke plane with the magnetic lineation subparallel to the direction of flow of magma in a dyke. During magma flow, the larger surfaces of magnetic minerals orient approximately parallel to the dyke, while the longer dimensions orient parallel to the magma flow direction. The second type is characterized by approximately perpendicular orientation of magnetic foliation to the dyke plane and magnetic lineation parallel to the dyke. It is presumed that this orientation originates through a compaction of a static magma column along the dyke when the magnetic minerals are re-oriented with their larger surfaces perpendicular to the flow direction (Park et al., 1988; Raposo and Ernesto, 1995). The third type is rare, being characterized by horizontal magnetic foliation and also horizontal magnetic lineation perpendicular to the dyke; this magnetic fabric may be attributed to secondary processes such as hydrothermalism (Rochette et al., 1991). The fourth type shows almost random orientation of magnetic foliations and lineations, which may result from very complex flow pattern or from severe post-magmatic changes of the magnetic minerals (Hrouda, 1985). In addition, another secondary aligning processes following initial emplacement (or very late stage processes) can affect the magnetic fabric in dykes, but these are out of scope of this paper. The results of our modelling support the hypothesis by Park et al. (1988) and Raposo and Ernesto (1995) concerning the mechanism of the generation of the preferred orientation of magnetic minerals in the type two. In the upper domain of our diapir the magnetic foliations and magnetic lineations are flat, perpendicular to the material motion. This orientation is evidently due to the pressure of already ascended material by the portions of coming material in one continuous process. If similar mechanical conditions are at work in the Earth's crust, the type two magnetic fabrics in dykes can quite well originate as suggested by Park et al. (1988) and Raposo and Ernesto (1995). 7. Conclusions The experimental results highlight a strong correlation between the AMS fabric and bulk flow pattern inferred from the geometry of the colour banding. The analogue models of AMS give the constraints to the flow regimes operating in different parts of the diapiric bodies that reflect the changing boundary conditions (Jackson and Talbot, 1989). In the base of the model, the flow is described by the radial stretching field verging to the narrow constrictional channel. The lower part of the vertical channel is
dominated by relict (or inherited) prolate vertical fabrics due to convergent flow. The upper part displays symmetrical imbrication profile of subhorizontal oblate fabrics marked by low degree of AMS, which corresponds to a zone of superposition of axial flattening on vertical constrictional fabrics in the centre of the plug associated with widening of the plug and divergent flow. High shear strain on the lateral margins of the active channel associated with viscous drag of vertically ascending plaster led to the development of zones of intense deformation. The transition from vertical to horizontal fabric in the centre of the plug is interpreted in terms of gravity collapse of plaster column thanks to the weight of the overlying plaster and pressure of overburden. The AMS fabric of the model is correlated with fabrics in natural granite plugs and dykes and it is proposed that the vertical pressure driven by weight of overburden is a leading factor controlling the fabric transition observed in the modelled example. Our non-scaled analogue modelling of AMS provides interesting insights and helps to unravel the internal strain pattern during ascent of non-linear viscous materials. Plaster served as a convenient analogue medium, which has a potential to model structures in natural magmatic systems or salt diapirs, while it reproduces both shear zones and folding in a ductile regime. 8. Uncited reference Borradaile and Jackson, 2004 Acknowledgement Dr. Chris Talbot is thanked for fruitful discussions concerning the topic and for friendly reviewing the draft of the manuscript. We are grateful to Ing. Bomberová of P/D Refractories CZ a.s. for providing us with magnetite powder and to Ing. Josef Záruba for his help with designing the analogue apparatus. We appreciate the help of Mgr. Veronika Kopačková of Czech Geological Survey in the ArcView GIS presentation of our results. This research was supported financially by the Ministry of Education of the Czech Republic (FRVS 2850/2003) and by the Grant Agency of the Czech Republic (GACR 205/03/0204). References Borradaile, G.J., Alford, C., 1987. Relationship between magmatic susceptibility and strain in laboratory experiments. Tectonophysics 133, 121–135.
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