Description:

_Journal of Structural Geology 32 (2010) 278–287_ _Contents lists available at ScienceDirect_ _Journal of Structural Geology_ _journal homepage: www.elsevier.com locate jsg _Scaling relationships between stratabound pressure solution cleavage spacing and layer thickness in a folded carbonate multilayer of the Northern Apennines (Italy)_ _S. Tavani a,*, F. Storti b, J.A. Munóza_ _Geomodels, Departament de Geodinamica i Geo?sica, Facultat de Geologia, Universitat de Barcelona, Spain_ _b Dipartimento di Scienze Geologiche, Univerista` degli studi ‘‘Roma Tre’’, Italy_ _article info_ _Article history: Received 24 November 2008 Received in revised form 19 November 2009 Accepted 6 December 2009 Available online 4 January 2010_ _abstract_ _Pressure solution cleavage is one of the most important deformation structures at shallow crustal levels. Its relationships with environmental, dynamical, textural, and chemical parameters have been broadly studied, particularly at the microscale. However, it is still under debate whether, at the outcrop scale, cleavage surfaces tend to form at rather constant spacing or not, and whether, in the case of stratabound elements, cleavage spacing scales with the host layers thickness._ _This work reports on relationships between tectonic pressure solution cleavage spacing (S) and bed thickness (H) from a folded carbonate multilayer of the Northern Apennines. Data were collected mainly in three well-layered carbonatic units, where beds are separated by thin clayish films which acted as barrier for the cleavage vertical propagation, determining its stratabound appearance. Statistical analysis of cleavage spacing and spacing to bed thickness ratio allows recognising a dependence of the cleavage spacing on the host layer thickness. Our analyses also suggest that this dependence relates to an infilling dominated evolution of pressure solution cleavage, where new dissolution surfaces preferentially develop between old cleavages characterised by high spacing to bed thickness ratios._ _? 2009 Elsevier Ltd. All rights reserved._ _1. Introduction_ _Pressure solution cleavage is one of the most important deformation structures occurring in rocks deformed at shallow crustal levels, particularly in carbonate successions exposed both in fold-and-thrust belts (e.g., Alvarez et al., 1978; Mitra and Yonkee, 1985; Marshak and Engelder, 1985; Holl and Anastasio, 1995; Ohlmacher and Aydin, 1995; Sans et al., 2003; Tavani et al., 2006) and in their slightly deformed adjacent foreland sectors (e.g., Arthaud and Mattauer, 1969; Illies, 1975; Railsback and Andrews, 1995). It consists of irregular surfaces coated with residues of insoluble materials (Stockdale, 1922; Dunnington, 1954; Park and Schot, 1968) and usually oriented perpendicular to the maximum acting stress (e.g., Fletcher and Pollard, 1981; Koehn et al., 2007). The relationships between the pressure solution process, the environmental conditions of deformation (e.g., Dieterich, 1969; Carannante and Guzzetta, 1972; Siddans, 1972; Weyl, 1959; Rutter, 1976, 1983; Groshong, 1988; Andrews and Railsback, 1997), and the textural chemical rock properties (e.g., Marshak and Engelder, 1985; Peacock and Azzam, 2006) have been widely studied, particularly at the microscale._ _On the other hand, it is still unclear whether, at the outcrop scale, pressure solution development is an organized process, where distinct surfaces tend to develop at rather constant spacing (e.g., Alvarez et al., 1978; Fletcher and Pollard, 1981; Merino et al., 1983; Fueten et al., 2002), or not (e.g., Railsback, 1998), and whether, in the case of stratabound elements, solution cleavage spacing scales with the host layer thickness (e.g., Durney and Kisch, 1994; Tavani et al., 2006, 2008) or not (e.g., Alvarez et al., 1978; Holl and Anastasio, 1995)._ _With progressing deformation, two processes concur to reduce pressure solution cleavage spacing and, accordingly, to modify the statistical attributes of a given cleavage population: (1) dissolution of material along cleavage surfaces, which implies the reduction of their spacing (e.g., Stockdale, 1922; Dunnington, 1954; Park and Schot, 1968); (2) infilling, which is the process whereby new surfaces form between two pre-existing surfaces (e.g., Merino et al., 1983; Narr and Suppe, 1991; Becker and Gross, 1996; Bai and Pollard, 2000) (Fig. 1a). These processes produce different evolutionary pathways concerning the reduction of the cleavage spacing as deformation progresses with time. If the dominant process is the dissolution of the microlithons, cleavage spacing will reduce progressively with time. On the other hand, if infilling occurs cleavage spacing will follow a stepwise reduction (Fig. 1a). These two end-member processes will result in different cleavage spacing statistical attributes of a cleavage population._ _S. Tavani et al. Journal of Structural Geology 32 (2010) 278–287_ _279_ _Fig. 1. (a) Cross-sectional spacing variation associated with cleavage infilling. See text for details. (b) Example of cleavage infilling, where at least two distinct cleavage generations are visible. Scaglia Rossa Formation. Northern Apennines (Italy)._ _In some circumstances it may be possible to infer infilling has occurred from field observations as we may expect that the newly formed cleavage domains will be thinner and smoother or less stylolitic (Fig. 1b). However, a question arises if, not having field evidences, the statistical analysis of cleavage populations may distinguish which of these end-member processes (acting together during deformation progression) plays the major role during cleavage evolution._ _In order to conduct such analysis, it is important to collect data in outcrops characterised by different deformation intensities and to ensure constancy, in different sampled populations, of the mechanical environmental parameters conditioning the cleavage spacing (like rock composition, temperature, fluid circulation; e.g., Marshak and Engelder, 1985)._ _In practice, it is rather difficult to reduce the ‘‘lithological bias’’, particularly when the area of investigation is bigger than few km2. This bias can be at least partially reduced by: (1) increasing the number of observations; (2) analysing and comparing data collected in outcrops characterised by rather similar mechanical environmental conditions. When satisfied, these conditions allow the assumption that the mechanical environmental parameter variability is low and similar in the different sampled populations, which in turn allows evaluation of whether, in a first approximation, a given evolutionary pathway is consistent with data._ _The aim of this work is to find a procedure to unravel the predominant processes acting during pressure solution cleavage development and spacing reduction as deformation progresses. To check the proposed method, a cleavage data set has been collected from a folded carbonate multilayer in the Sibillini anticline of the Northern Apennines._ _2. Cleavage spacing theoretical models_ _2.1. Spacing reduction by infilling_ _When a cleavage population Pi is ‘‘infilled’’ it transforms to Pj (see Table 1 for full definition of parameters). Each infilled cleavage is characterised by a min value (being min either Sin or Sin Hin) in the Pi population that is replaced, in the Pj population, by m0 ? ainmin and m00 ? (1 ? ain)min (0 < ain < 1) (Fig. 1). In a cross-sectional view, this process includes both apparent infilling, if the infilling is due to the lateral propagation of ‘‘old’’ cleavages, and infilling sensu strictu if the infilling relates with the development or lateral propagation of newly developed cleavages._ _The average values of m (i.e., m) in Pj relate to that of Pi through the following equation (see Appendix for derivation):_ _n_ .mj ? min ? f_ _(1)_ _where n is the data number in the Pi population and f is the number of ‘‘infilled’’ cleavages (so that the number of cleavages in the Pj population is n ? f)._ _In a continuum space, the variance of m (s2) in a given population relates to its average value (m) through the following relationship:_ _!_ _vs2_ _s2_ _? 2Pf_ _in_ _1_ _ain?1_ _?_ _ain?m2in_ _f ? ?m?2_ _vm ? m ?_ _m_ _(2)_ _This equation can be simplified if we assume a constant Table 1 Definition of variables used in Sections 3, 4 and in Appendix._ _S H Pim min m0 and m00 mi n f Q 3ij Distance between adjacent sub-parallel cleavages measured perpendicular to the cleavage surfaces Layer thickness The cleavage population in the ith step of deformation The equations describing the evolution of cleavage spacing during the infilling process are identical to those describing the evolution of cleavage S H. In order to avoid duplicating each equation (one for S and one for S H) we introduce the parameter m that, accordingly, in the following equations can be read as either cleavage spacing or cleavage S H The m value of the cleavage that, in the next step of deformation, will be infilled. The m value of the two cleavages that replace min after infilling (see Fig. 1). By definition the sum of m0 and m00 is equal to min, so that m0 and m00 can also be expressed as: m0 ? ainmin; m00 ? (1 ? ain)min, being 0 < ain < 1 Average value of m in the Pi population Number of individuals in a given P population Number of cleavage that will be infilled in the next step of deformation, so that, being n the number of cleavage in the Pi population, the number of cleavages in the Pj population (which results from the deformation by infilling of Pi) is n ? f Proportionality factor between the original population and the infilled part of the dataset. This parameter is introduced by assuming that such a relationship exists, so that the mathematical handling of equation (2) can be extremely simplified Amount of cleavage perpendicular strain necessary to transform a population Pi into Pj in the hypothesis that sp_ Ключевые слова: tectonophysics, spacing reduction, spacing bed, in?lling, mm, cleavage, layer thickness, joint spacing, correlation, data, inlled, bed, pf ?, solution cleavage, tavani journal, tavani, pi, relates, carbonate, parameter, bi-logarithmic space, synthetic population, siddans, deformation progress, relationship, strain, science, reduction shadow, surface, evolution, cleavage inlling, apparent inlling, anastasio, tectonics, weyl, high spacing, higher, deformation pattern, shadow, gross bai, fracture, dieterich, pollard, evidence, inlled population, pn, randomly selected, acting, eld observation, in?lled, random, stylolites, text, pf, rock, lithology, york, propagation, structural, thrust, rutter, developed, fracture mechanics, frequency distribution, solution, characterised, n?f, spacing average, ratio, cleavage development, representative parameter, geology, scaling relationship, corbett, inlled cleavage, process, inlling step, groshong, inlling process, study area, bed thickness, scaglia, mechanical, dissolution, population, structural geology, mechanical stratigraphy, merino, min, anticline, scaglia rossa, outcrop, deformation, cleavage spacing, stress, sampled population, maiolica, appendix, reduce, joint, pj, dependence, engelder, includes, scaglia bianca, petrology, pn l?, constant, development, fold, constant spacing, northern, term, thickness, result, equation, stockdale, bulletin, formation, lachenbruch, lithological bias, crestal sector, rst approximation, limestone, mitra, spacing, pressure, high angle, layer, illies, reduction, scale, step, lateral propagation, evans, high, evolutionary pathway, journal structural, material, nature, outcrop characterised, spacing distribution, dunnington, stratabound, random inlling, number, original population, frequency, shortening, analysis, cox, inlling, cleavage evolution, statistical, koehn, dn, average, dissolution surface, chester, multilayer, cleavage characterised, railsback, ? mi, rossa, gross, dataset, pressure solution, ? pf, bianca, cleavage surface, variance, observation, cleavage population, pressure solution cleavage, schot, time, statistical attribute, journal structural geology, journal, mi, collected, azzam, deformation intensity, scaling, fueten, ?eld, distribution