Coseismic elastic models of folds above blind thrusts in the Betic Cordilleras (Spain) and evaluation of seismic hazard

223

Tecfonophysics, 220 (1993) 223-241 Elsevier Science Publishers B.V., Amsterdam

Coseismic elastic models of folds above blind thrusts in the Betic Cordilleras (Spain) and evaluation of seismic hazard A. Taboada, J.C. Bousquet and H. Philip Laboratoire

de Tectonique et Giochronologie, U.R.A 1371, Universite’ de Montpellier II, Sciences et Techniques du Languedoc, Place E. Bataillon, 34095 Montpellier Cedex 5, France

(Received October 21, 1991; revised version accepted September 3, 1992)

ABSTRACT Taboada, A., Bousquet, J.C. and Philip, H., 1993. Coseismic elastic models of folds above blind thrusts in the Betic Cordilleras (Spain) and evaluation of seismic hazard. Tectonophysics, 220: 223-241. Although it is generally considered that near-surface earthquakes result from movements along faults that cut through the surface, several recent large earthquakes have been partly attributed to blind thrusts. Movements along blind thrusts lead to the formation of surface folds, which are highly dependent upon fault geometry at depth, and often not considered in seismic hazard evaluation. Several authors have studied the relationship between surface folding and thrusting for geological situations in which fault geometries are quite simple. However, active fault geometries can be quite complex, e.g., segmented thrust faults associated with strike-slip faults. The aim of this contribution is to reconstruct the fault kinematics at depth for a relatively complex geological structure located in the Eastern Betic Cordilleras (Orihuela-Guardamar-Torrevieja region) using the patterns of kilometre-scale folds observed in the field. In order to model surface deformation, the assumption is made that surface km-scale folds have been created by coseismic deformation associated with movement along blind thrusts. By means of a coseismic deformation model, movements at depth have been calculated for three possible hypotheses. Hypothesis 1 assumes that each superficial fold is created by an independent fault. Hypotheses 2 and 3 assume that a sequence of two superficial folds can be created by movement along a single fault displaying a flat and ramp geometry. In Hypothesis 2, the flat is a superficial decollement level between the sedimentary cover and the Betic basement; in Hypothesis 3, it is a deeper dtcollement level within the Betic basement. Knowing the approximate age of surface deformation, rough estimates of fault slip-rates and recurrence periods for two possible earthquake magnitudes (7 MS and 6.7 MS) have been made, from calculated dislocations at depth. Slip-rates and recurrence periods for flat and ramp fault geometries are in the range of 0.75-l mm/yr and 1000-2000 yr, respectively. These values are close to those calculated by direct methods in similar seismotectonic contexts.

surface folding (Yeats, 1986; Ring et al,, 1988;

Introduction Until recently it has been assumed that surface folds result from continuous deformation in the upper crust and have no relation with seismicity. Despite this apparent lack of connection, recent papers have emphasized the close relationship that exists between active thrusting at depth and

to: Dr. A. Taboada, Laboratoire de Tectonique et Geochronologie, U.R.A 1371, Universite de Montpellier II, Sciences et Techniques du Languedoc, Place E. Bataillon, 34095 Montpellier Cedex 5, France.

Correspondence

0040-1951/93/$06.00

Stein et al., 1988; Stein and Yeats, 1989; Mitra, 1990; Suppe and Medwedeff, 1990). In the same way, several recent earthquakes have shown how surface folds and movement along seismic faults are intimately related. The El Asnam fault in Algeria is a clear example where surface folding is related to an active fault plane that cuts through to the surface (Cisternas et al., 1982; Ruegg et al., 1982; Philip and Meghraoui, 1983). The Coalinga fault in California, USA, clearly illustrates the relationship between blind thrusts and surface folding. Here, the only field evidence of fault activity is a fold located on top of the blind thrust

0 1993 - Elsevier Science Publishers B.V. All rights reserved

A. TABOADA

Fig. 1. General (B) within geological

the

located

of the modelled

Iberian

case situated

1 = Quaternary gene,

location

Peninsula.

strike-slip

from geophysical

of

of the

to the East of the Betic Cordilleras.

and Neogene,

3 = Major

area. (A) Location

(B) Localisation

2 = formations

faults, studies.

4 = thrust

older than Neofaults,

5 = faults

A.M. F. = Alhama

de Mur-

cia fault, S.C. = Sierra de Carrascoy.

(Stein and Ring, 1984). A significant example that combines the two mentioned above is the Spitak fault in Armenia, for which fault traces are not always visible: in some parts, the only evidence of fault activity at depth is a surface fold, whose axis is parallel to the major fault (Cisternas et al., 1989; Philip et al., 1992). Nevertheless, superficial folding is sometimes left aside from the definition of seismic hazard and only faults that reach the surface are taken into account. In fact, movement at depth along a seismic fault which does not reach the surface, can create surface folds whose setting is highly dependent upon the dislocation distribution along the fault and upon its superficial geometry. The aims of this contribution are, first, to look into the relationship between km-scale surface folding and blind thrusts, and, second, to estimate fault slip-rates, by reconstructing the surface deformation pattern of dated sedimentary levels. To do so, a geological example from the Eastern Betic Cordilleras has been chosen (Fig. 11. In this area (Orihuela-Guardamar-Torrevieja region), located east of the northern termination of the Alhama de Murcia Quaternary strike-slip fault (Bousquet and Montenat, 19741, there is a sequence of Quaternary surface folds of short wavelength, situated in the vicinity of thrusts and strike-slip faults (Fig. 2).

ET Al..

In this study we assume that in areas with active seismic faults, geological structures result from the added effects of individual earthquake cycles Wing et al., 1988; Stein et al., 19881. In addition, our working hypothesis is that for surface folds whose wavelength does not exceed a few kilometres (such as most of the folds in the Orihuela-Guardamar-Torrevieja region), the deformation in a seismic cycle is that which occurs during the earthquake (coseismic deformation) (King and Brewer, 1983; Vita-Finzi and Ring, 1984). In fact, the wavelength of geological structures resulting from the whole earthquake cycle, including interseismic deformation by stress relaxation at depth, is much greater than the mean wavelength of superficial folds that are considered in this study (Thatcher and Rundle, 1979; Rundle, 1982; Savage and Gu, 1985; King et al., 1988; Stein et al., 1988). The geometry of surface km-scale folds is determined, above all, by shallow fault kinematics (i.e., superficial fault geometry and slip distribution along the fault). The relationship between surface folds and blind thrusts can also be studied by means of cross-section balancing techniques (Bayer and Elliott, 1982; Butler, 1982; Cooper and Trayner, 1986; Mitra, 1990; Suppe and Medwedeff, 19901.

01

QJ2

m3

[z94

m5

-6

Fig. 2. Geological

map of the studied

Montenat,

1 = Recent

nary,

3 = Pliocene,

Neogene layer

1972). volcanic

dips. E.S.F.

Quaternary,

4 = Miocene, rocks, 7 = faults,

A- A’=

location

= Bas Segura

07

area

of

5 = Betic

p@9

rt9

(simplified 2 = Old

after

Quater-

basement,

6=

8 = hypothetic

faults,

cross-sections

in

Fig.

fault. 5. M.F. = San Miguel fault.

9= 4,

However, these methods are not well adapted for three-dimensional problems and for this reason are left aside in this study. To calculate the surface displacements caused by movement along a fault plane (coseismic defo~ation) we make use of a computer program ~rn~i~ed from Cisternas et al., 1982). The program uses the analytical solution proposed by Mansinha and Smylie (1971) to calculate the displacement field created by a uniform dislocation defined on a rectangular plane in a uniform elastic half-space (Savage, 1980). The model is relatively simple and it supposes that displacements in the elastic medium decrease ass~ptotically to zero away from the fault. This boundary condition is in agreement with observations on coseismic displa~ments (see Ruegg et al., 1982). The application of the seismic model to the Grihuela-Guardamar-Torrevieja region shows that the disposition and size of surface folds can be positively correlated with fault geometry and with movement along fault planes at depth, and therefore allows us to estimate the seismic hazard in the area. principles of the three-dimensional model of fadtiFtg Fault planes are defined as inclined rectangular dislocation loops. Two sides of the dislocation loop are parallel to the fault strike and the other two are parallel to the fault dip. The model supposes that movement along the fault is parallel to the fault surface. Thus, using ~nematic te~inolo~, displacement along the fault only involves sliding and tearing; opening is not taken into account. Sliding and tearing modes (Petit, 1988) correspond to edge and screw dislocations. The dislocation vector (Burger vector) along the fault is defined as a constant arbitrary vector that can be decomposed into a strike-slip component and a dip-slip ~mponent (respectively parallel and perpendicular to the strike of the fault plane). The model is valid only for small defo~ation; it assumes that the half-space behaves as a perfectly elastic, linear solid, for which the Lame parameters A and J.L,are taken to be equal (Pois-

son solid). For this type of solid, the Poisson’s ratio v = 0.25. This value is quite representative of the Poisson’s ratio for typical rocks in the upper crust. For example, for sandstone v E (0.2, 0.3) and for limestone v E (0.25, 0.3) (Turcotte and Schubert, 1982). Thus, the model assumptions roughly agree with the elastic behaviour of the upper crust during an earthquake. The equations given by Mansinha and Smylie (1971) define the displacement field resulting from slip on a fault in an infinite elastic medium; they are derived from the Betti reciprocal theorem. To obtain the solution for the half-space (which is geophysically more interesting) the shear stresses along the free surface can be eliminated by introducing an image dislocation loop above the free surface. The normal stresses at the free surface produced by the two dislocation loops are cancelled by a distribution of normal stresses at the surface of the half-space. The supe~sition of the displacement fields for the two dislocation loops and the distribution of normal stresses at the surface yields the solution for the dislocation loop in the half-space (Savage, 1980). For a linear elastic solid, the relationship between displacements and dislocation magnitudes is linear. This implies that the displacement field resulting from movement along several fault planes can be calculated by superposing the displacement fields from each individual fault plane, Additionally, the model assumes that the transition between the undeformed state and the final state is immediate. This means that movements along different fault planes occur simultaneously, and that other factors that influence defo~ation, such as stress relaxation at depth, sedimentation and erosion, are not taken into consideration (King et al., 1988; Stein et al., 1988). In the geological examples, fault geometries are quite complex and the dislocation distribution along faults is not necessarily homogeneous. Therefore, to apply the seismic model, faults are approximated by means of ruled surfaces of known equation, which are then decomposed into small rectangular dislocation loops (Appends 1). Seismic deformation created by inhomogeneous displacement along these complex fault geometries is obtained by adding the incremental defor-

226

A. TABOADA

mations associated with small rectangular loops, each of which has a constant dislocation. This appro~mation can be made as fine as desired, by reducing the size of rectangular loops. The slip direction along small rectangular loops is not known because major blind thrusts do not reach the surface, Thus, a simpIe assumption is made to set the slip direction aIong each rectangular loop: movement has the same direction and sense as the applied shear stress (Bott, 1959). The shear direction can be calculated from the knowledge of the regional tectonic stress principal directions and the stress ellipsoid shape ratio, R = ffl2 -@3)&l - (r3) @Ott, 1959). These stress parameters are known from the analysis of microtectonic data such as striated microfaults, striated pebbles and tension gashes, and they are quite homogeneous in this area (Bousquet and Philip, 1976; Ott d’Estevou and Montenat, 1985; Garcin, 1987; Montenat et al., 1987). Geological setting

qf the

modeled area

The Betic Cordilleras are located within the Ibero-Maghrebian region, which consists of a large mobile zone set between the African and the North European plates (Fig. 1). These two pIates have been converging along a N-S to NNW-SSE direction for the past 70 Ma (see Dewey et al., 1989). The Quaternary tectonic activity of the Ibero-Maghrebian region is characterised by strike-slip and reverse faulting (Bousquet and Phihp, 1981; Philip, 1987). In several areas of the North Maghrebian region and to the east of the Betic Cordiileras, km-scale Quaternary folds are often observed. The Quaternary and Neogene geological history of the Eastern Betic Cordilleras is characterized by movement along major strike-slip fauIts (Bousquet, 1979). Amongst these, the Alhama de Murcia fault (Bousquet and Montenat, 1974), oriented NE-SW (Fig. IS), is an active left-lateral fault whose surface trace is visible for more than 100 km between Huercal-Qvera and Alcantarilla. The fauit has been traced to Alicante by geophysical methods (Gauyau et al., 1977). The southwestern termination of the Alhama de Murcia fault joins an E-W thrust system,

ET AL.

which cuts Quaternary sediments near HuercalQvera (Briend, 1981). At its northeastern termination (Orihuela-Guardamar-Torrevieja region, Fig. 11, Quaternary tectonic activity has led to the formation of km-scaIe folds in sedimentary deposits of late Miocene, Pliocene and early Quaternary age (Fig. ‘2). Younger Quaternary formations are also involved. Examples are a marine terrace from the lower Quaternary (Montenat, 1970) or the middle Quaternary (Dumas, 1977) close to the Guardamar anticline (Fig. 3) and stream terraces along the San MigueI fault trace (Fig. 3) (Echallier, 1977). Other younger Quaternary formations (from the upper Pleistocene and Holocene) are also deformed by faulting in the Bas Segura plain, as described by geophysical data (Echallier et al., 1978; Echallier and Lachaud, 1980). Besides recent folding, the frequency of shailow earthquakes in this area is another clear sign of present tectonic activity (Rey-Pastor, 1951; Rey-Pastor and Romero, 1954; Mezcua, 1982). The intensity of earthquakes can be quite high, as shown by the Iatest great earthquake of the Betic Cordilleras (March 21, 1829; intensity X M.S.K.) whose epicenter was estimated to lie between Torrevieja and Guardamar (Mezcua, 1982). The geology of the Orihuela-GuardamarTorrevieja region has been studied by Montenat (1972,1977), who mapped the area at a l:l~,~O scale and interpreted geophysical profiles and borehole data collected by COPAREX. Garcin (1987) also studied and mapped part of the area at a 1:25,000 scale. Major folds strike roughly E-W and display a northward vergence: northern anticlina1 limbs are steep and reach a vertical position in several places (e.g., upper Pliocene of Bigastro), whereas southern anticlinal limb dips are shallow (between 10 and 20”). Major folds are bounded to the north by the Bas Segura plain, with an average altitude between 10 and 20 m. In contrast, altitudes in the area of Quaternary folding reach 260 m in the west and 127 m in the east. Using geophysical data, Montenat (1977) suggested that a south-dipping E-W blind thrust (Bas Segura fault) is located underneath these major folds; its continuation wouid intersect the surface at the foot of the northern anticlinal

COSEISMIC ELASTIC MODELS OF FOLDS ABOVE BLIND THRUSTS (BETIC CORDILLERAS, SPAIN)

227

Fig. 3. (A) Structural contour map on the base of the Pliocene. Contour lines are drawn every 50 m. Dotted lines indicate the intersection between contoured surface and topography. 1 = Hurchillo-Bigastro anticline, 2 = Pulpit0 syncline, 3 = Torremendo anticline, 4 = Lomas de la Juliana anticline, 5 = synclinal structural saddle between anticlines 4 and 6, 6 = Benejuzar anticline, 7 = Cueva Blanca anticline, 8 = Rojales-Guardamar de1 Segura anticline, 9 = Salinas de la Mata syncline, 10 = Cabo Cervera anticline, 11 = Sahnas de Torrevieja syncline, L.J.T.F. = La Juliana thrust front, R.G.T.F. = Rojales-Guardamar thrust front. A-A’ represents the location of cross-sections in Fig. 4. (B) Block-diagram of Pliocene surface. Vertical scale is 5 times exaggerated. Notice that the block-diagram has been rotated in comparison with structural contour map.

limbs (Fig. 2). A minor fold exists to the north of the Bas Segura fault, close to La Marina (Fig. 2). This fold was not taken into consideration in the model due to its small extent. Nevertheless, it may be associated with a small blind thrust north of the Bas Segura fault, or with a small subhorizontal fault related to the Bas Segura fault. The surface deformation pattern in the area is well ill~trated by the structure contours in Figure 3. This map was constructed from topographic and geological maps of the area (Montenat, 1972; Garcin, 1987) and represents the deformation pattern of the base of the upper Pliocene (boundary between Pl and P2 on the

geological map by Montenat, 1972). This boundary was chosen because of its good exposure, in comparison with other markers. Its intersection with topography (control points) is illustrated by the dotted lines in Figure 3A. Prodded this boundary was roughly horizontal in its initial state, the current shape results from Quaternary folding, as the upper Pliocene and lower Quatemary are ~nfo~able in this area ~Montenat, 1977). However, absolute displacements associated with Quatemary deformation cannot be inferred from this map. The initial elevation of the chosen marker with respect to current sea level is not known. Prior to folding, the upper Pliocene was

228

possibly affected by subsidence. For construction of contour lines, in areas where Pliocene has been eroded (core of anticlines) and in those where it is covered by younger deposits (synclines), elevations were extrapolated. For anticlines, elevation was calculated by adding to topography the average thickness of missing Pliocene layers; for synclines, by subtracting the average thickness of Quaternary and upper Pliocene from topography. These approximations are valid within a range of 20 to 25 m, which is quite acceptable, compared with fold amplitudes (which reach 500 m). We now attempt to solve an inverse problem: what are the dislocation distributions along fault planes, for which coseismic surface deformation is as close as possible to the field deformation pattern (Fig. 3). Three possible fault geometries consistent with available data will be tested. Application to the Orihuela-Guardamar-Torrevieja region

The studied area is bounded to the east by the Mediterranean coast as no geological nor geophysical information is available to constrain the continuation of fault planes or surface folds offshore. Available geophysical and geological data were used to constrain the disposition of fault planes in space. However, due to a lack of precise information, the following hypotheses were tested: Hypotheses on fault kinematics

(1) The San Miguel Quaternary right-lateral fault (Fig. 3) has been continued towards the southeast with a slight change in direction at San Miguel. Southeast of San Miguel, the fault is assumed to dip steeply southwest (Echallier, 1977). (2) Although the Bas Segura thrust is not visible at the surface (Montenat, 19771, it is assumed to be a blind thrust dipping southwards (Fig. 3). Furthermore, it is supposed that all thrusts responsible for surface folding in the area dip southwards. In this way, south-dipping thrusts underlie the Hurchillo-Bigastro fold (11, the

A. TABOADA

ET AL.

BenejGzar fold (61, the Lomas de la Juliana fold (41, and the Rojales-Guardamar fold (8). The isolated character of surface folds suggests that thrust fronts are discontinuous and offset by minor strike-slip faults (Figs. 2, 3). (3) It is supposed that the magnitude of the offset along the Bas Segura thrust and other thrusts decreases as fault planes approach the surface. (4) Variations of displacement along faults are also considered. This hypothesis is based on the whale-back geometry of surface folds whose maximum relief varies along the anticlinal ridge: the variable structural relief can be partly interpreted as the consequence of variations of fault displacement at depth parallel to strike. In fact, as explained later in this paper, the size of surface folds depends directly upon the dislocation magnitude on the fault. (5) It is supposed that the direction of movement along fault planes is directly determined by the regional tectonic stress tensor. Thus, the stress tensor parameters have been chosen to be in accordance with recent neotectonic studies carried out in the area (Bousquet and Philip, 1976; Ott d’Estevou and Montenat, 1985; Garcin, 1987; Montenat et al., 1987): according to these studies the Quaternary deformations result from a stress field whose principal compressive and extensional axes, al and (~3, are both horizontal and trend northwards and eastwards, respectively. For the stress ellipsoid shape ratio, R = (a2 - a3)/(al - a3), a value of 0.2 seems to be quite representative of the regional tectonic context, because it allows for both strike-slip faulting and thrusting. (6) It is conceivable that other minor faults played a minor role in fold genesis. Thus, geophysical data allow us to identify a fault between Benejfizar and Cabo Cervera (Fig. 2). Although Quaternary activity on this fault is uncertain, right-lateral movement may have occurred because its strike is parallel to that of the San Miguel fault. Anyway, the fault geometry hypotheses that are proposed include two fault segments which line up quite well with the Benejtizar-Cabo Cervera fault and whose movement displays a right-lateral component. Our interpretation is different from that given by Mon-

COSEISMIC

ELASTIC:

MODELS

OF FOLDS

ABOVE

BLIND

THRUSTS

tenat (19771, who interprets this as a left-lateral strike-slip fault according to the arrangement of surface folds. From a study of two km-scale fault segments oriented NE-SW, Montenat (1972) inferred a left-lateral fault east of Benijofar and west of Montesinos (Fig. 2). Nevertheless, the geophysical evidence for it is not conclusive. In our model this fault is considered as a minor fault that accommodates the relative movement between the hangingwall of the La Juliana thrust front and the Rojales-Guardamar thrust front (Fig. 3). (7) To constrain fault geometry at depth, data from several boreholes are used to locate approximately the limit between the sedimentary Neogene cover and the Betic basement (Figs. 2 and 4). Among these boreholes, only the one located west of Guardamar, above the Bas Segura fault, cuts through an intensely crushed zone overlying the Betic substratum. This crushed zone was attributed to the Bas Segura fault by Montenat (1977). As we have had no access to seismic profiles to constrain the fault geometry within the upper crust down to 15 km, we consider three possible N-S cross-sections which illustrate the relationship between fault geometry at depth and surface folding (Fig. 4). These three hypotheses are consistent with the surface fold patterns and take into account available borehole data. The location of these cross-sections is given in Figures 2 and 3. In Hypothesis 1, each fold is created by an independent blind thrust (Fig. 4a). In Hypotheses 2 and 3, pairs of folds are created by movement along a single fault with a flat and ramp geometry. Two mechanisms of ramp formation are envisaged (Fig. 4b, c>: In the first mechanism (Fig. 4b), the flat is a shallow decoliement level between sedimentary cover and Betic basement. Initiation of the ramp could be due to tectonic inversion, as shown in Figure 4b. Indeed, previous to the compressional tectonic phase which began in the late Pliocene, the region was subjected to an extensional tectonic phase (Bousquet and Philip, 1976; Garcin, 1987). In the second mechanism, the flat is located at a deeper level within the Betic basement

(BETIC

CORDILLERAS,

229

SPAIN)

S

N 6 S F.

B.S F.

S.S.F

s Mf

S.M.F

SMF

Fig. 4. Schematic cross-sections -illustrating 3 possible fault geometries at depth. The location of cross-sections is shown in Figures 2 and 3A. Numbers correspond to folds in Figure 3A. B.S.F. = Bas Segura fault, S.M.F. = San Miguel fault, 1= borehole, 2 = Neogene and Quaternary, 3 = Betic basement, 4 = bottom of Upper Pliocene layer. Horizontal and vertical scales are equal (with the exception of topography and reference level, which are 5 times exaggerated).

(Fig. 4~) due to reactivation of older thrust faults. In fact, the Alpine structure of the internal zones of the Betic Cordilleras displays low-angIe overthrusts (Egeler and Simon, 1969). Prior to seismic modelling of the studied region, several theoretical examples will be treated, in order to elucidate the relationship between

230

superficial fault geometry and km-scale fold sequences. Relationship between fault geometry and folding

We briefly study the effects of fault dip and dislocation distribution upon seismic deformation at surface level. Seismic deformation has been calculated along a surface profile perpendicular to the fault trace, for isolated fault plane segments dipping at several angles (Fig. 5). These plane segments do not represent real situations because displacement is terminated abruptly at the lower fault termination (2-5 km depth). However, these examples will be useful to visualize the effect on surface deformation of movement along specific segments of a fault displaying a flat and ramp geometry. Thus, each profile represents the contribution of movement along part of a fault that cuts through the upper crust. Fault segments are limited to the upper 5 km of the crust because we are interested in the effect of superficial fault geometry on surface deformation (the length of fault plane segments measured along the dip of the plane is constant and equal to 4.5 km). As this paper is focused on blind thrusts, fault segments do not cut the surface but are stopped at a depth of 0.5 km. Two different dislocation distributions are considered. (1) The dislocation is constant and equal to 200 m along each fault segment (Fig. 5a>. (2) The dislocation decreases linearly from a 200 m value at maximum depth, to a zero value at minimum depth (Fig. 5b).

A. TABOADA

ET AL.

For a constant dislocation (Fig. 5a), the wavelength of structures created by seismic deformation is more or less equal to the size of the fault segment (King et al., 1988). For shallow fault dips (flat decollement level), a well marked frontal fold appears and a negative relief (basin) of greater wavelength appears in the hangingwall, behind the frontal fold. For fault dips of 45”, the frontal fold reaches its maximum amplitude. Furthermore, the frontal fold is asymmetric for all fault dips and displays quite steep dips in the hangingwall, near the fault plane. In the footwall, fault movement creates a frontal basin whose size and depth increases as the dip of the fault plane increases. Where dislocation magnitudes atenuate towards the surface (Fig. 5b), the size of folds is less than previously and the anticlinal ridge has moved backwards, reducing the asymmetric character of the frontal fold. Despite the overall decrease in seismic deformation, the wavelength of geological structures remains almost the same as previously. Surface depressions are less marked but still appear in the footwall for steep fault planes and behind the frontal fold for gently dipping fault planes. We have also calculated the seismic deformation created by movement along simplified fault patterns representing the three hypotheses stated above. These theoretical calculations will be discussed in the light of previous results (Fig. 5) and will prove to be useful for the analysis of the geological example treated later. For all calculations, fault planes have been continued down to

Fig. 5. Influence of the dip of a reverse fault segment on coseismic surface deformation (surface displacements are 10 times exaggerated). (a) Dislocation along fault segments is constant and equal to 200 m. (b) Dislocation along fault segments decreases linearly from a maximum value at depth (200 m), to a zero value below the surface.

COSEISMIC ELASl7C MODELS OF FOLDS ABOVE BLlND THRUSTS (BETIC CORDCLLERAS, SPAIN)

10 km depth, yet block-diagrams are focussed upon the upper 5 km.

H~oth~~s I, with two independent blind thrusts (Fig. 6, top), has been tested for a disIocation distribution which is the same in both fault planes. For depths greater than 2.5 km, disiocation magnitude is Constant and equal to 100 m; for depths less than 2.5 km, the dislocation de-

HYPOTHESIS 1

231

creases linearly to a zero value below the surface. We have calculated the deformation for fault planes that are closely spaced {Fig. 6, top, A) or widely spaced (Fig, 6, top, B). Whatever the spacing, seismic defo~ation produces 2 a~etr~~ anticlines, whose steeper limbs are located in the hanging walls above fault planes. The wave length of the frontal fold is about equal to the distance between the fault planes. The size and relief of the frontal fold is fess than that of the fold

._

WYPOTHESIS 2

HYPOTHESIS 3

Fig, 6. Block-diagrams illustrating theoretical coseismic deformation for three fault geometries (deformation is 10 times exaggerated). In Hypothesis 1, folding is associated with two independent blind thrusts, whose dislocation magnitudes are equal, and decrease linearly towards the surface. In Hypotheses 2 and 3, folding is associated with a single blind thrust displaying a flat and ramp geometry, either superficial or at depth. (A) The dislocation is absorbed mainly within the final ramp. (B) The dislocation is absorbed equally within the flat and final ramp. Shaded columns illustrate offsets along faults.

232

located behind the second fault plane. This is because movement along the frontal fault, besides creating the frontal fold, will tend to uplift the second fold. The uplift is more visible where fault planes are closerly spaced. Shallow dkollement

Hypothesis 2, where a single fault displays a shallow flat and ramp geometry, has been tested for two different dislocation distributions (Fig. 6, middle). (1) In the first distribution (Fig. 6, middle, A), only 20% of the displacement is absorbed in the flat and the rest is linearly absorbed in the ramp, where the fault approaches the surface. Thus, the flat level is a true decollement. (2) In the second distribution (Fig. 6, middle, B), the dislocation decreases linearly in both the flat and ramp, to a zero value below the surface. For both distributions, the flat is located at a depth of 1 km and the dislocation magnitude at depth is 200 m. For the first distribution (Fig. 6, middle, A), the surface shows a well marked frontal fold of small wavelength, a basin above the flat, and a large fold behind the basin. The size and width of the frontal fold is mostly determined by the length of the ramp (relatively small in this example). The location and size of the basin can be analysed in terms of the elastic deformation associated with movement along different parts of the fault: movement along the decollement creates a superficial basin to the rear of the flat (Fig. 5a); movement along the deep ramp creates a fold located above the ramp and a superficial frontal basin (Fig. 5a). The superposition of the displacement fields associated with these fault segments defines the geometry of the basin. Figure 6, middle, A, mimics quite well the surface deformation along cross-section A-A’ of the geological example (Fig. 4): the frontal fold is quite similar to fold 8, which itself is fairly narrow and asymmetric; the basin is like syncline 9; and finally the rear fold, which is larger, is comparable to anticline 10. For the second distribution (Fig. 6, middle, B), the frontal fold and the basin are much smaller than the rear fold.

A. TABOADA

ET AI..

Deep dkollement

In Hypothesis 3, a single fault displays a flat and ramp geometry at a deeper level (2.5 km) (Fig. 6, bottom). This was tested for dislocation distributions similar to those of Hypothesis 2. Thus, whereas in Figure 6, bottom, A, displacement along the flat is nearly constant and is linearly absorbed in the ramp, in Figure 6, bottom, B, displacement is absorbed linearly throughout both flat and ramp. As expected, the size of the frontal fold and basin is greater where the dislocation is only absorbed in the ramp (Fig. 6, bottom, A). The wavelength of the frontal fold for this hypothesis is greater than for Hypothesis 2, since the depth of the ramp is greater. In the same way, the basin between the two folds is less pronounced than in Hypothesis 2. To summarize, movement along fault planes displaying flat and ramp geometries, where flats are decollement levels, results in asymmetric folds. Seismic modelling of the area

The dislocation distribution along the three possible fault geometries previously put forward, is calculated so that surface coseismic deformation is as close as possible to the deformed reference level in Figure 3. The structure contour map is used in the modelling under the following assumptions: (1) The limit between Pl and P2 was horizontal in its initial state (though not necessarily at present sea level). (2) Considering that the wavelength of folds in Figure 3 is quite small, excepting the Torremendo anticline (3), it is supposed that the present deformation of the reference level results from the superposed effects of coseismic deformation, associated with a large number of earthquake cycles. Interseismic deformation due to viscous relaxation at depth may have reduced the relative amplitude of the Torremendo anticline (3) in comparison with other folds in the area. Therefore, the calculated displacement along the fault that created the Torremendo fold corresponds to a minimum value.

COSEISMIC

ELASTIC

MODELS

OF FOLDS

ABOVE

BLIND

THRUSTSTBETIC

CORDILLERAS,

SPAIN)

233

the horizontal projection of each fault is given by a dashed quadrilateral. Notice that faults are numbered independently in each fault geometry. To characterize fault geometry at depth, the following definitions will prove to be useful (Fig. 8): (1) Each fault trace defines a vector P’ in the horizontal plane. (2) Vector 6 is parallel to the dip of the fault and points downwards. The orientation of P’ is such that the cross product 3 A 8, points downwards. Thus, each fault is defined by two vertical cross-sections xi,* and K~ 2, that are perpendicular to the trace of the fault (i represents the fault number; Fig. 7). Cross-sections K~,~ and IQ_ intersect the origin and the tip of 9, respectively (Figs. 7, 8, 9). Each fault is then defined by a ruled surface, generated by joining the points of the cross-sections IC~,~ and K~,*, that are located at the same depth (Fig. 8). The horizontal projection of ruled surfaces is given by the quadrilaterals in Figure 7. Concerning the magnitude of the disl~ation along fault surfaces, the following suppositions are made: (1) For each fault i, let &r(x) and &Jx) be two continuous functions, defining the dislocation F

Of..,,I,.. 0

._

--

5 Km

‘.__ -LLLLu_d_.~_-,_.-~~...~

z

3

L_L

Fig. 7. Horizontal projection of fault geometry hypotheses. Light lines represent fault traces kt surface, and heavy lines represent strike-slip fault traces. Dashed quadrilaterals represent the horizontai projection of fault surfaces. Flat dicoliement levels are indicated by shaded regions in Hypothesis 2 and 3. Faults are numbered in each hypothesis. xi,t and IQ = examples of location of cross-sections perpendicular to the fault trace (see Fig. 9 and text). ABDC represents the projection of fault plane in Figure 8.

Geometry and movement along faults are presented in the following way: the description of each fault geometry in the horizontal plane is given by a simplified structural map (Fig. 7) where fault traces are represented by straight lines and

Fig. 8. Example of ruled surface (fault 4, Hypothesis 3). ABDC is a horizontal quadrilateral whose opposite sides are not parallel in between them (see Fig. 7). Rectangle _EFBA is limited by two vertical sides and two horizontal sides. Vector P” is parallel to line segment EF and vector 6 is parailel to the dip of the fault. Notice that the fault surface has been decomposed into small rectangular loops. Slip direction in each rectangular loop is indicated by a line segment.

234

magnitude 4 in terms of the depth x for any two cross-sections perpendicular to the fault trace P’. Then, a constant p exists such that

(2) The variation of the dislocation magnitude along any horizontal line belonging to the fault, is linear. The first supposition implies that the dislocation magnitude profiles are proportional for any cross-section. The second condition implies that the dislocation magnitude in any point of the fault can be calculated from the value of $(x> for two different cross-sections. To facilitate the analysis of results, for each fault surface the functions c#J&) and c#&) are calculated, for cross-sections K~,~and K~,* (Fig. 9, right). To calculate the dislocation distribution along fault planes, the general form of function 4(x) is fixed and, by successive approximations, the values of &i(x) and c$Jx) are calculated for each fault plane. In general it is supposed that 4(x) varies progressively from a zero value below the surface to a maximum value at a given depth; from there on b(x) remains constant. The best solution is found by minimizing the difference between calculated displacements and field elevations along anticlinal ridges and synclinal troughs. Analysis of results Two independent faults

Hypothesis 1 (Figs. 7a, 9a) supposes that each surface fold is created by an independent blind thrust (as previously examined in the theoretical examples). Thus, a fault is associated with each fold; the trace of the fault is parallel to the fold axis (Fig. 7a). Fault planes are defined down to a depth of 10 km; their lateral extension is chosen to be proportional to the size of folds. Thus, fault dips vary from 45 to 70”. It is interesting to note that, since surface fold axes are not parallel, fault traces are not either. Figures 10a and lla show the best solution obtained for surface deformation associated with movement along this fault geometry. Dislocation

A. TABOADA

ET AL.

magnitude solutions are given in Figure 9a. Note that dislocation magnitudes are constant for depths over 2 km, The general pattern and size of folds is quite similar to those observed in the field (folds are identified by the numbers previously given in Figure 3). In this way, structures such as syncline 2, whose axis dips to the west, are well described by the model. However, anticline 4, the synclinal structural saddle 5, and the important relief associated with anticline 1, are not satisfactorily calculated by the model. This can be explained by the small distance between the two fault planes that pass under these two folds: as previously seen in the theoretical examples, the size of the frontal fold decreases in comparison with the second fold, as fault planes become closer. Notice that for this solution no negative reliefs are created within the folded area. Anticline 8 is well described, although its wavelength seems to exceed the one observed in the field. As expected, important horizontal variations of the dislocation magnitude, parallel to fault traces, are predicted by the model (Fig. 9). Thus, displacement along blind thrusts decreases close to the San Miguel and Benijofar strike-slip faults (faults 5 and 6, Fig. 7). This results from fold crests, which (except for anticline 8) are located away from the intersection between thrust faults and strike-slip faults. The amount of shortening along a N-S direction is quite homogeneous from west to east: the total displacement magnitude at depth along faults for any N-S cross-section varies from 1 to 1.5 km. Shallow dtkollement

The second fault geometry (Figs. 7b, 9b) assumes that sequences of two superficial folds are created by movement along a single fault plane, displaying a flat and ramp geometry. The flat corresponds to a decollement level between the 1 km thick sedimentary cover and the Betic basement. According to the theoretical examples treated previously, decollement levels (shaded quadrilateral areas in Figure 7) have been located below

COSEISMIC ELASTIC MODELS OF FOLDS ABOVE BLIND THRUSTS TBETIC CORDILLERAS, SPAIN)

5 Km

HYPOTHESIS

3

Fig. 9. Cross-sections perpendicular to blind thrusts, and dislocation distributions as functions of depth, for the three different fault geometries. K~,~and ~~~~represent cross-sections across fault i, according to fault numbers in Figure 7. Horizontal and vertical lines are in km. &fr) and &&x) represent dislocation functions for cross-sections ICY,* and IC~,~ (horizontal scale is bectometric).

236

A. TABOADA

the Salinas de la Mata basin (91, the synclinal structural saddle back of the Lomas de la Juliana

ET AL

(a)

fold (51, and the Pulpit0 plunging syncline (2). D&collement levels are limited laterally by strikeslip faults. Figures

10b and llb

for surface

illustrate

deformation;

the associated

and

dislocation

mum dislocation

the best solution Figure

distribution.

is reached

at a depth

9b, shows The maxiof about

1.5 km, below the d&ollement

levels. Dislocation

along

decreases

and

flat

d&collement

is mostly

absorbed

levels

in the

ramp.

slightly For

this

(b)

hypothesis, surface deformation is also quite close to field deformation, although there are some important differences in comparison with Hypothesis 1. The wavelength of folds on the whole is smaller (anticlines 1 and 8). Thus, small structures, such as anticline 4 and the synclinal structural saddle back of this fold (51, are now well described by the model. Another difference is the negative relief created at syncIine 9. The size and relief of anticline 6 seems to fit the field values better. Although the model seems to fit the structure contour map quite well, several features are not properly calculated. For example, the elevations of the frontal anticline 1 and the second fold (3) are quite similar in the model, whereas fold (1) is much higher than fold (3) in the field. This may be due to the smal1 size of the ramp, which is not large enough to create a greater frontal fold. Horizontal variations of the dislocation magnitude and the total amount of shortening are similar to those in Hypothesis 1 (the sum of fault displacements along a N-S cross-section is about 1 and 1.5 km). Deep dtkollemen t

0 5 Fig. 10. Coseismic

10 15 20 deformation for the three

25 Km different

geometries.

traces

are

according

to Figure

(0.05 km). Shaded structural structural

This final fault geometry (Figs. 7c, SC) is equivalent to Hypothesis 2, with the difference that flat dCcollement levels are located at a depth of 2.5 km within the Betic basement. The location of dCcollements (shaded quadrilateral areas in Fig. 7) is similar to the one in Hypothesis 2. As in Hypotheses 1 and 2, the optimum solution for surface deformation (Figs. 1Oc and 11~) fits the fold pattern observed in the field quite

Fault

contour contour

and

7. Contour

fault

numbers

lines are drawn

areas correspond maps

can

to negative

be directly

map of Pliocene

fault

included,

every 50 m reliefs. These

compared

and Quaternary

to the deforma-

tion (Fig. 3).

weI1. Nevertheless, several deformation features distinguish this hypothesis from the others: (1) Fold wavelength is larger than in Hypothesis 2. (2) Frontal anticline 1 is higher than in the previous two hypotheses and fits field observations better.

COSEISMIC

ELASTIC

HYPOTHESIS

c.-_

(a)

MODELS

OF FOLDS

ABOVE

BLIND

THRUSTS

f

y--L

HYPOTHESIS

HYPOTHESIS

2

3

Fig. 11. Block diagram representations of structural contour maps of coseismic deformation for the three different hypotheses. The relief is 5 times exaggerated. Notice that the block diagrams are rotated in compa~son with the structural contour map (Fig. 10).

(3) No negative reliefs are created within the folded area. Differences 1 and 2 are a consequence of the length of ramps, which are larger in this hypothesis than in Hypothesis 2, the third difference results from the increase of depth of the decohement levels. Horizontal variations of the dislocation magnitude (Fig. 9) are similar to those of Hypotheses 1 and 2. The amount of displacement at depth along faults for a N-S cross-section, is slightly greater than in Hypotheses 1 and 2 (1.5 km). Evaluation of seismic hazard

The knowledge of displacements along fault planes, resulting from surface folding modelling,

(BETIC

CORDILLERAS,

SPAIN)

237

allows us to evaluate the recurrence of major earthquakes within this area of the Betic Cordilleras. However, because of the large number of suppositions that have been made on active fault geometry at depth, these results are to be taken as rough estimates of seismic hazard. It should also be recalled that modelling was carried out presuming that only coseismic deformation along faults of the Orihuela-GuardamarTorrevieja region is responsible for surface folding. Thus, neither the effect of interseismic deformation nor the effect of the Alhama de Murcia strike-slip fault were taken into consideration in the model. In particular movement along the Alhama de Murcia strike-slip fault may have created part of the Torremendo anticline relief (fold 3, Fig. 3). This fold is the northeastern continuation of the Sierra de Carrascoy, an important relief parallel to the Alhama de Murcia fault (Fig. 1). It has been considered that the maximum magnitude of an earthquake in this area should be around MS = 7. The intensity of the largest known earthquake in this region (X M.S.K., 21/03/1829; Mezcua, 1982) seems to be in good accordance with this supposition. The values of seismic recurrence have been calculated for two possible magnitudes, A4= 7 and M = 6.7. For these magnitudes, m~imum displacement along faults at depth are supposed to be equal to 1.5 m and 1 m, respectively. These displacements have been estimated from statistical relations between earthquake magnitudes and surface ruptures (Bonilla et al., 1984). Therefore, recurrence periods may be underestimated, since displacement at depth may be greater than surface ruptures. The evaluation of seismic hazard has been made for the three hypotheses (Figs. 7, 9, 10). Whereas for Hypothesis 1, the total maximum displacement along a N-S cross-section (1.5 km) is distributed among two independent fault planes, for Hypotheses 2 and 3 the total displacement is attributed to a single fault. Since deposits of lower Quaternary (1.5 Ma) are conformable to deposits of upper Pliocene (2 Ma) (Montenat, 1972, 19771, folding was supposed to begin at the end of Pliocene (2 Ma) or at the beginning of the early Quaternary (1.5 Ma).

238

A. TABOADA

Thus, earthquake recurrences are calculated supposing that fault movement also began about 2 Ma or 1.5 Ma ago. Results on the evaluation of recurrences and slip-rates at depth are presented in Table 1. These results may be compared with those obtained by a different method used for the El Asnam fault (Algeria), which is situated in a similar seismotectonic context. Thus, the thrust fault activated during the 10/10/1980 El Asnam earthquake, is also associated with a surface fold. Nevertheless, this fold seems to be older than the Orihuela-Guardamar-Torrevieja folds, as evidenced by progressive unconformities between Pliocene and Quaternary (Meghraoui, 19881. Moreover, unlike thrusts in the studied area, the El Asnam fault cuts through the surface. According to paleoseismic studies carried out in the El Asnam fault, the recurrence period for a 7.3 magnitude earthquake is 2000 yr (Meghraoui et al., 1988). Slip-rates, calculated from field observations and trenches, are estimated to be between 1.5 and 0.5 mm/yr (Meghraoui, 1988). These slip-rates are slightly higher than those calculated for the Orihuela-Guardamar-Torrevieja region, particularly for the two last hypotheses. Calculated recurrence periods in this area, may be shorter than for the El Asnam fault, since

TABLE 1 Estimated recurrence periods and fault velocities for the three different fault geometry hy~theses Magnitude (MS)

Time (Ma)

Hypothesis No. 1 (td = 0.75 km)

Nos. 2 and 3 (td=1.5km)

(’ (mm/yr

R.P. tyr)

(’ tmm/yr)

(yr)

R.P.

7 (id = 1.5 mf

f.5

0.38 0.5

4000 3000

0.75 1

2000 1500

6.7 (id = 1 m)

2 1.5

0.38 0.5

2650 2000

0.75 1

1330 1000

Values calculated for two possible earthquake magnitudes and for two possible deformation time intervals. u = velocity, R.P. = recurrrence period, td = total displacement at depth along the fault system, id = incremental displacement at depth with an earthquake cycle.

they correspond tudes (Table 1).

to smaller earthquake

ET AL.

magni-

Conclusions Previous studies (Philip and Meghraoui, 1983; Yeats, 1986; Cisternas et al., 1989; Stein and Yeats, 1989) have shown that surface Quaternary folding is closely related to active thrusting and seismic&y. Using physical deformation models, many authors have analyzed simple situations where superficial folds are created by movement along seismic faults. Some examples are the Coalinga blind thrust (Stein and Yeats, 1989) and the El Asnam fault (Cisternas et al., 1982; Ruegg et al., 1982). This study shows that the coseismic deformation model that was used is well adapted to estimate movement along a complex system of blind thrusts and strike-slip faults, from the deformation pattern of small wavelength superficial folds observed in the field. In this particular example from the eastern Betic Cordilleras, small features such as asymmetric folds displaying curved axes are well simulated thanks to coseismic deformation modelling. However, interseismic deformation must be taken into account to analyse folds of larger wavelength such as the Torremendo fold (fold 3, Fig. 3). The results of the three fault geometries tested in this paper, are quite satisfactory. Nevertheless, Hypotheses 2 and 3, which consider fault planes with flat and ramp geometries, seem to be more plausible than Hypothesis 1, which assumes that each fold is created by an independent thrust fault. Indeed, the relative size and shape of folds created by coseismic surface deformation is closer to the field deformation pattern in Hypotheses 2 and 3 than in Hypothesis 1. The considered fault geometries and kinematics may appear to be unrealistic; however, recent examples of earthquakes (Spitak, El Asnam) have shown that thrust planes can display complex geometries. This situation is well illustrated by the Spitak earthquake, where the distribution of surface ruptures and aftershocks, indicates that

COSEISMIC

ELASMC

MODELS

OF FOLDS

ABOVE

BLIND

THRUSTS

the fault surface is segmented and associated with several strike-slip faults. The evaluation of seismic hazard for Hypotheses 2 and 3 gives recurrence periods in the range of 1000-2000 yr (for earthquake magnitudes between 6.7 and 7.01, and slip-rates at depth between 0.75 and 1 mm/yr (recurrence periods would be longer if earthquake magnitudes were over 7.0). These recurrence periods and &p-rates, turn out to be within the same range of values, as those established by direct methods for the El Asnam fault (Meghraoui et al., 1988). This similarity confirms the reliability of our modelling, which would have seemed doubtful if calculated values had been abnormally high or small. Nevertheless, as mentioned above, these results represent only rough estimates of the seismic hazard and additional data, such as seismic profiles, are necessary to constrain fault geometry at depth. This kind of approach should be refined and improved, but it is in any case a promising tool in seismotectonics since it allows to take into consideration surface folding when evaluating the seismic hazard. Acknowledgements We thank A. Cisternas and R. Gaulon, who introduced the authors to coseismic elastic models, R. Gaulon, B. CXltrier, M. Seranne and C. Montenat for helpfu1 comments on the paper, P. Cobbold and J.P. Platt for very helpful and thorough reviews, P. Cobbold, M. Alleman and K. Rawnsley for correcting the English, and J. Garcia for his technical help. The ~nancial support of GEO-TER is gratefully acknowledged. Appendix 1 In this appendix the equations defining ruIed surfaces are given, used to approximate complex fault geometries. Figure Ala illustrates a smooth fault surface with a flat and a ramp. To approximate a part of this surface by means of an analytical equation we proceed in the following way: (1) A quadrilateral AECD is defined such that its vertices belong to the fault surface, and its

(BETIC

CORDILLERAS,

239

SPAIN)

(a)

ON

Fig. Al. Approximation of fault surface by means of a ruled surface. (a) Fault with a flat and ramp geometry. The part of the fault to be approximated is represented by quadrilateral ABCD. (r, 0) = polar coordinates. (b) Ruled surface in space defined within quadrilateral ABCD (see eq. Al).

edges AB and DC are horizontal. Notice that edges AB and DC are not necessarily parallel. (2) If edges AB and DC are parallel then the surface is approximated by a plane, otherwise, a reference frame S = (Sx, Sy, Sz> is defined such that Sy is parallel to the fault strike at surface, sz is vertical and 3.x = Sy A & (Fig. Ala). The origin of reference frame S is located at the intersection between edges AB and DC on the horizontal plane. (3) A ruled surface is generated by moving a horizontal line around vertical axis & as indicated in Figure Alb. The parametric definition of this surface using cylindrical coordinates (r,8,z) is given by: x =f sin(e) y = r cos(0)

(Al)

z = A tan( 0) + B

where A and B are constants and (x, y, z> are the rectangular coordinates of a point in the surface. Notice that the intersection between the ruled surface and a vertical plane perpendicular

240

A. TABOADA

to gy is a straight line whose dip decreases away from the origin.

tonique

recente

(Unpubl.

data).

Echallier,

la province

J.C. and Lachaud,

Rio Segura

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du domaine Notes Mtm.,

geodynamique

betique 21: 11-49.

oriental

F.D. des

(Espagne).

and

bassins Total

COSEISMIC ELASTIC MODELS OF FOLDS ABOVE BLIND THRUSTS (BETIC CORDILLERAS, SPAIN)

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