TECTONICS, VOL. 17, NO. 3, PAGES, 441-457 JUNE 1998

Birth and decay of an intracontinental magmatic swell: Early Cretaceous tectonics of southern Israel

Zohar Gvirtzman and Zvi Gaffunkel Institute of Earth Sciences, Hebrew University, Jerusalem, Israel

Gedaliahu Gvirtzman

Department of Geography, Bar Ilan University, Ramat Gan, Israel

Abstract. The Early Cretaceous history of southern Israel is an example of the formation, growth, and decay of an in- tracontinental swell associated with magmatism. In this paper we document and quantify this process and analyze its geody- namic mechanism. The magmatism and the uplifting contin- ued for about 10 Myr and produced a 150 to 200-km-wide dome, from whose crest nearly 1000 m of sediments were re- moved. Shortly after the magmatism ended, a period of cooling and subsidence began, and sediments started to cover the swell's margins. However, this subsidence was much smaller than the initial uplift and did not bury the swell's crest, which remained elevated for an additional 10 Myr. The fact that most of the uplift remained indicates that the major cause for uplifting was the permanent buoyancy effect of in- trusions. Transient effects such as heating at the base of the lithosphere and dynamic support of the asthenosphere may have also occurred, but their contribution to the local uplifting was minor. The distinction between temporal and permanent effects is possible because of the long-term history provided by the stratigraphic record (a full life cycle of a fossil swell). In currently active swells this distinction is much more com- plicated, and from this point of view this case provides unique information. The tectonostratigraphic analysis we present il- lustrates how geological observations can be used to calculate tectonic uplift and to estimate accordingly the volume of magmatism that produced it. Taking into account the sea level rise during uplift and considering the topographic relief that remained after the erosion, the calculated tectonic uplift amounts to about 500 m or 40% higher than the uplift inferred only from the amount of erosion. Thermal-mechanical mod- eling indicates that this uplift can be explained by intrusions with a volume equivalent to a 4 to 5-km-thick sill, consistent with other geological and geophysical observations.

1. Introduction

Most of what has been deduced about swells comes from

oceanographic studies. It seems that seafloor processes are sometimes simpler to analyze and understand than similar

•Now at Department of Geophysics, Stanford University, Stan- ford, California.

Copyright 1998 by the American Geophysical Union.

Paper number 98TC00235. 0278-7407/98/98TC-00235 $12.00

processes on the continents, partly because oceanic crust is relatively young and less has happened to complicate its structure and partly because the seafloor is less affected by erosion, so the relief of swells can be determined. In contrast, uplifting of continental regions is usually difficult to estimate, since in many cases the thickness of the eroded section is un- known. In this paper we analyze a fossil continental swell that was active in southern Israel during the Early Cretaceous (Figure 1). The amount of uplifting and the subsequent decay of this swell can be documented from the stratigraphic record, and thus the factors controlling the swell can be analyzed.

One of the fundamental questions about swells is how they are isostatically supported. Since most swells are associated with hotspot activity, many researchers have suggested mechanisms such as heating of the lithosphere [Detrich and Crough, 1978; Crough, 1978, 1983; Morgan et al., 1995], heating beneath the lithosphere [Crough, 1983; Davies, 1988; Olson, 1990, Sleep, 1990, 1992, 1994; Morgan et al., 1995], dynamic support by upwelling mantle convection [Morgan, 1971; Mentad, 1973; Anderson et al., 1973], and crustal thickening or underplating [Burke and Whiteman, 1973; Fur- long and Fountain, 1986; McKenzie, 1984; White and McKenzie, 1989]. In reality, the swells relief may be due to several mechanisms, and usually it is hard to evaluate the relative contribution of each component. In our case this can be achieved since we analyze a fossil swell whose long-term evolution enables us to distinguish between temporal and permanent effects. The stratigraphic evidence we present strongly suggests that the main cause for uplifting in the southern Israel swell was shallow magmatic intrusions that penetrated the crust and produced a permanent change in the buoyancy of the lithosphere. Temporal effects such as dy- namic support or heating may have caused additional uplift- ing. However, their effect was much wider than the local swell studied here. At this time the regional trend of Early Cretaceous uplifting in the entire Levant region cannot be determined.

This study has two aims: first, to document a full life cycle of a continental swell from the time it was uplifted until it was gradually covered by younger sediments, and second, to trans- form the stratigraphic information to geodynamic terms that will permit us to estimate the volume and depth of the mag- matism that intruded the lithosphere and produced the swell. In what follows, we begin with a stratigraphic analysis of the Early Cretaceous section in southern Israel. We use this in- formation to constrain the tectonic component of the uplift

441

442 GVIRTZMAN ET AL.: BIRTH AND DECAY OF A CONTINENTAL SWELL

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Figure 1. Location map showing the extent of Early Cretaceous swell in southern Israel. Open circles repre- sent boreholes. Dashed contours indicate the estimated thickness of the eroded section, modified after Gar- funkel and Derin [ 1988].

Figure 2. North-South cross section along the Negev region, southern Israel. For location see the XX' line marked in Figure 1. (a) The reconstructed sedimentary cover prior to the Early Cretaceous truncation [modi- fied after Gaffunkel and Derin, 1988]. Dotted line indicates the level of future truncation. (b) Early Creta- ceous uplifting and erosion. The truncated section is the part of the section above the dotted line in Figure 2a. Note that the lithostratigraphic nomenclature in Figure 2a is replaced by its equivalent chronostratigraphic nomenclature in Figure 2b. (c) Posttruncation sediments as described in previous studies [after Gaffunkel and Derin, 1988]. In this description the stratigraphic units thicken gradually northward. However, this is not ex- pected theoretically as (d) and (e) illustrate schematically. Because if Cretaceous sediments covered a rem- nant topographic relief, we would expect to find local thinning in the central Negev as illustrated in Figure 2d. Conversely, if the remnant topographic relief was insignificant, we would expect to find local thickening in the central Negev that was cooling and thus should have subsided more than its surroundings, as illustrated in Figure 2e.

GVIRTZMAN ET AL.: BIRTH AND DECAY OF A CONTINENTAL SWELL 443

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444 GVIRTZMAN ET AL.: BIRTH AND DECAY OF A CONTINENTAL SWELL

and then estimate the volume of the magmatism by using a quantitative model developed by Gvirtzman and Garfunkel [ 1997]. Finally, in light of this specific example and in view of some theoretical considerations we speculate on the fate of continental swells in general.

2. Geological Background The information about the swell is based on the amount of

erosion. A regional erosional unconformity at the base of the Cretaceous is a widespread and important stratigraphic feature in Israel and adjacent areas [Picard, 1959; Bentor and Vro- man, 1960; Gaffunkel, 1988; Druckman, 1974]. The strati- graphic gap represented by this unconformity increases pro- gressively southward; however, reconstruction of the missing

section shows that maximal truncation occurred at the central part of the studied area [Garfunkel and Derin, 1988]. Figures 2a and 2b show that in the southern edge of the studied area, near the city of Eilat, the entire Jurassic, Triassic, and most of the Paleozoic section is missing, but not much more than 100- 200 m were removed by the Early Cretaceous erosion. Far- ther north in the central Negev (Hameishar site in Figure 2a), only the Jurassic and a part of the Triassic section were eroded, but the thickness removed was nearly 1000 m. The lateral distribution of Early Cretaceous denudation indicates a domal uplifting of a 150 to 200-km-wide swell that broadly coincides in time and space with intrusive magmatic activity [Garfunkel and Derin, 1988; Gaffunkel, 1989]. This obser- vation is reinforced by an aeromagnetic study [Gvirtzman et a/., 1994] which showed that the largest magmatic bodies are,

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1 O0 350 200 100 350 Figure 3. (a) Bouguer gravity map of southern Israel. The positive anomaly bounded by two dashed lines coincides with the Early Cretaceous swell described in Figure 1. (b) Aeromagnetic map of southern Israel. The shortwave anomalies within the bounded region (marked with rectangles) indicate the presence of several near surface basic magmatic bodies [Gvirtzrnan et al., 1994; Segev et al., 1996]. These bodies which are a few kilometers wide are better seen in the aeromagnetic map which was prepared from a denser grid. In ad- dition, acidic bodies that do not produce a significant magnetic signal because of their low magnetic suscepti- bility might also exist in this region. Note that the crowded anomalies on the southern edge of the map are related to the exposed crystalline basement and not to the Early Cretaceous magmatism. These maps were prepared from a grid provided by the Geophysical Institute of Israel. Regional maps of the entire Levant re- gion were recently published by Rybakov et al. [ 1997].

200

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GVIRTZMAN ET AL.: BIRTH AND DECAY OF A CONTINENTAL SWELL 445

indeed, located at the site of maximal truncation (Figure 3). In addition, evidence for crustal heating was also found [Fein- stein, 1985; Feinstein et al., 1989; Kohn et al., 1990], so the overall picture strongly suggests a causal relation between magmatism, heating, and uplifting. Field relations which will be described in section 3.3 (point 2 in Figure 7 caption) and section 4.2 suggest that magmatic intrusions were the first to initiate this chain of events. Igneous material emplaced in the lithosphere disturbed the thermal and isostatic equilibria and caused heating, uplifting, and erosion [Gvirtzrnan and Gaf- funkel, 1997].

When magmatic activity stopped, the region began to sub- side, and Cretaceous sediments gradually covered the ero- sional surface. In previous studies the geometry of the Lower Cretaceous section was described as gradual thickening A northward (Figure 2c). This trend seemed to indicate that shortly after the Early Cretaceous uplifting, southern Israel returned to normal continental margin conditions. However, theoretically this is not expected; because if Early Cretaceous sediments buried a remnant relief, we would expect to find local thinning of the section toward the region which was ele- vated, including onlap relations and wedge outs (Figure 2d). On the other hand, if no significant relief was left by erosion, we would expect to find the opposite, that is, local thickening at least of some Lower Cretaceous units in a region that was previously heated and then should have cooled and subsided more than its surroundings (Figure 2e).

In this study we reexamine the Early Cretaceous section in southern Israel and present thickness and facies variations that were not previously known. We begin with a brief review of the local stratigraphy. Our new findings are then presented in cross sections, isopach maps, and paleogeographic recon- structions. Finally, we use the stratigraphic evidence in order to describe quantitatively the gradual decay of the Early Cre- taceous swell. The high-resolution stratigraphy we present B provides the basis for the quantitative tectonic analysis in the second part of this paper.

3. Early Cretaceous Stratigraphy in Southern Israel

3.1. Stratigraphic Nomenclature and Regional Correlation

The Early Cretaceous sequence in southern Israel (Negev region) is mainly composed of continental sandstones, silt- stones, and clays with several marine intercalations. These rocks are exposed along the cliffs of the Arava Valley (the Dead Sea Transform) and in several deep erosional cirques, named Hatira, Hazera, Ramon, and Har Arif (for location see Figure 1). They are also known from many boreholes, mainly in the northern part of the studied area. The lithostratigraphic units that were defined in various parts of southern Israel are shown in Figure 4 (see reference in captions). The regional correlation is mainly based on interfingering of marine tongues within the typical clastic continental section. In the central and southern parts of the studied area where marine tongues are less clear and partly missing, correlation is sup- ported by the presence of volcanics in the sedimentary se- quence [Beyth and Segev, 1983; Weissbrod et al., 1989, 1990c].

The volcanic divides the Lower Cretaceous section into

two units (Figure 4b) which will be used throughout this pa- per. This volcanic event represents a second pulse of mag- matism that occurred 5-10 Myr after the first pulse mentioned above. Geodynamically, these two magmatic pulses were very different from one another. The first caused uplifting and erosion whereas the second did not. The tectonic signifi-

Judean Northern Central Southern

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Figure 4. (a) Stratigraphic nomenclature of the Lower Creta- ceous section in southern Israel. Lithostratigraphic units at the Zohar 1 borehole (Zuweira, Deragot, Malhata, and Uza) after Aharoni [ 1964]. The Hatira Formation in the Hatira cir- que is after Shaw [1947] and Greenberg [1968], and in the Ramon cirque is after Gvirtzman et al. [1996]. The Amir, Av- rona, and Samar Formations in the southem Negev are after Weissbrod [1969, 1970, 1993]. The regional correlation is modified after Weissbrod et al. [1994]. (b) Three generalized subunits used in the present paper. The lower unit (prevol- canic) includes the Zuweira Formation in the north and the Amir and Avrona Formations in the south. The upper unit (postvolcanic) includes the Deragot, Malhata, and Uza For- mations in the north and the Samar Formation in the south. The middle unit, which is limited mainly to the central Negev, includes volcanic flows and fossil laterite soils (the Red member mentioned by Wieder et al. [ 1994] and by Gvirtzrnan et al. [ 1996]).

446 GVIRTZMAN ET AL.: BIRTH AND DECAY OF A CONTINENTAL SWELL

cance of this important observation will be discussed section 4 following the stratigraphic analysis.

3.2. Thickness and Facies Variations

Gradual thickening of the Early Cretaceous sequence from 200-250 m in the southern Negev to 600-700 m in the north- ern Negev has been known for many years (Figure 2c, see reference in captions). Two exceptionally thin (only -80 m) columnar sections were measured about 40 years ago at Har Arif cirque (M. Zemel (Eyal) et al., Geological mapping of Arif cirque, unpublished, Israel Geological Survey, 1956; see also Zilberman [1983]) and at Areif E-Naqa cirque (Y. Zak, personal communication, 1996). However, they were never explained and usually ignored. In contrast, we think that these sites are the key to the understanding of the tectonic history of this region. Therefore we reexamine all the avail- able stratigraphic data from southern Israel, from the Sinai peninsula (Egypt), and from Jordan, looking for more evi- dence to support the local thinning of the section in the central Negev region. Our study is based on more than 100 columnar sections derived from outcrops and boreholes.

First, we prepared isopach maps of the different parts of the section, showing the spatial and the temporal thickness variations (Figure 5). These maps show that the local thin- ning in the central Negev is a prominent phenomena and that the thinning is mainly due to the lower unit (i.e., the prevol- canic sediments).

Second, we prepared paleogeographic maps (Figure 6) showing the paleoshorelines during the four Early Cretaceous marine invasions (locally called Zuweira, Deragot, Malhata, and Uza marine tongues). For each invasion we mapped all sites where marine traces were found (solid circles) and all sites where marine traces are absent (open circles). The re- constructed paleoshorelines indicate that the Zuweira, Der- agot, and Uza transgressions surrounded the central Negev but did not cover it. These results follow several recent re-

ports about marine beds found in places that were not previ- ously known [Lewy and Weissbrod, 1993; Lewy et al., 1994; Weissbrod, 1993; Weissbrod et al., 1990a,b, 1994; Weissbrod and Gvirtzman, 1996; Gvirtzman et al., 1990, 1996). Our study extends these findings and explains their tectonic origin.

The overall picture indicates that during the first stage of sedimentation the swell's crest remained above the base level

of sedimentation and was not covered by sediments nor by the water during sea level rises. At later stages it was buried by the uppermost part of the Lower Cretaceous sequence.

3.3. Chronostratigraphy

The chronostratigraphic information compiled from vari- ous sources is summarized in Figure 7 (see references in cap- tion). The important conclusions for the following tectonic analysis are as follows:

1. Field relations indicate that most of the Early Creta- ceous erosion took place after the first magmatic pulse had al- ready begun (see point 2 in Figure 7 caption). The age of sediments that cover the erosional un•onformity indicates that sedimentation resumed shortly after magmatism ended (points 3 and 4 in Figure 7 caption). In other words, the period of erosion broadly coincides with the first magmatic pulse. This

conclusion supports the basic observation made by Gaffunkel and Derin [1988] that suggested that magmatism was the cause for the uplifting. Now we can better constrain the tim- ing and the duration of this process to approximately 10 Myr.

2. It is likely that there is a time gap between the two Early Cretaceous depositional cycles. The first cycle ended in the mid-Aptian stage or earlier (it is constrained by the age of the overlying Ramon basalt, points 6, 7, and 8), and the second depositional cycle had begun only toward the end of the Ap- tian (point 5), leaving a few million years gap between the two cycles. The tectonic significance of this observation is that the subsidence period following the first magmatic pulse was relatively short, and at least most of it decayed before the second magmatic pulse began. Using the Gradstein's time- scale [Gradstein et al., 1994, 1995] that sets the ISEA event (a short reversed magnetization found in the basalt) at 115.5 Ma, the duration of the first depositional cycle is constrained to a maximum of 6 Myr (Figure 7).

The presence of fossil laterite soils between the two Lower Cretaceous units supports this conclusion. Since soils cannot develop with a continuous supply of clastic material, they are likely to indicate landscape stability and nondeposition con- ditions (Figure 7, point 9). The fact that these soils developed to laterites further supports this interpretation, since intensive leaching requires not only humid tropical weather but also a long period of time [McFarlane, 1976; Wieder et al., 1994]. Using Gradstein's timescale, we conclude that the break con- tinued at least 3 Myr. Since in several places the laterites un- derlie the volcanics, the break may have begun earlier, and thus its duration may have been longer.

The depositional break seems to extend beyond the boundaries of the central Negev. In the southern Negev, Weissbrod et al. [1994] identified an erosional unconformity between the Avrona and Samar Formations. In addition, a stratigraphic gap of about the same age was also observed in Saudi Arabia and in the Persian Gulf [Harris et al., 1984], where it is expressed by a major unconformity that distin- guishes the Lower Cretaceous sequence (Thammama Group) from the Middle Cretaceous sequence (Wasia Group). This widespread event may be related to a global sea level drop (as seen in the eustatic curve in Figure 7) superimposed on the local tectonic activity.

3. The second Early Cretaceous period of deposition (up- per unit) began toward the end of the Aptian and continued into the Albian [Weissbrod et al., 1990a; Lewy and Weiss- brod, 1993; Lewy, 1990]. The subsidence curve presented below shows that this was the beginning of a prolonged sub- sidence that continued a few tens of millions of years and in- cluded the Judea, Mount Scopus, and Avedat Groups (see Figure 10). In section 4.1we will relate this long period of subsidence to lithospheric cooling that followed the second Early Cretaceous pulse of magmatism.

To summarize the stratigraphic observations (Figure 8), we have shown that the paleogeography and the tectonics of southern Israel during the Early Cretaceous are directly re- lated to the uplifting that occurred in the beginning of that pe- riod. The elevated region that was not covered by sediments nor by the sea during the Aptian-Albian transgressions (this work) is the same region that was mostly uplifted and eroded previously [Gaffunkel and Derin, 1988] and the same region

GVIRTZMAN ET AL.' BIRTH AND DECAY OF A CONTINENTAL SWELL 447

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Figure 5. Isopach maps of the Lower Cretaceous section. (a) total thickness, (b) lower unit, and (c) middle and upper units. In Jordan the Lower Cretaceous sequence is named Kumub Group [Powell, 1989], which is identical to the Hatira Formation used in Israel (the two names are synonyms). The Jordanian outcrops are currently laterally shifted by the Dead Sea Transform -105 km north of their Negev equivalents. This rela- tively young movement was restored when isopach maps were prepared.

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448 GVIR1ZMAN ET AL.: BIRTH AND DECAY OF A CONTINENTAL SWELL

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Figure 6. Paleogeographic maps showing reconstructed shorelines during the four Early Cretaceous trans­gressions: (a) Zuweira, (b) Deragot, (c) Malhata, and (d) Uza marine tongues. Open circles represent sites with a well-documented section which does not include any marine traces. solid circles represent sites where marine tongues were identified. Shaded areas represent paleocontinental regions. These maps follow several recent reports about marine traces in previously unknown places [Lewy and Weissbrod, 1993; Lewy et al. 1994; Weissbrod, 1993; Weissbrod et al., 1990a, b, 1994; Weissbrod and Gvirtzman, 1996; Gvirtzman et aI., 1990, 1996]. For example, the Zuweira and the Uza marine intercalations that wedge out within the bounda­ries of the Ramon cirque were found to appear again farther south. Following these findings, we examined several recently drilled water wells in the Arava Valley (e.g., Zofar 20, Paran 20, and Shizafon 1) and identi­fied there three marine intercalations (Zuweira, Deragot, and Uza). We also found descriptions of marine beds in studies conducted in Jordan (e.g., studies of Wetzel and Morton [1959], Powell [1988], and W. Lillich (Stratigraphic investigations on the Paleozoic and Mesozoic sandstones on the east side of the Dead Sea, German geological mission in Jordan, 1964). The overall picture as summarized here indicates the survival of the Early Cretaceous swell more than 15 Myr after deposition renewed at its margins. (The movement along the Dead Sea Transform was restored as in Figure 6.)

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GVIRTZMAN ET AL.: BIRTH AND DECAY OF A CONTINENTAL SWELL 449

TIME STAGE MAG- EUSTASY MAGMATIC LITHO- & BIO-

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that was mostly affected by magmatism [Gvirtzman et aL, 1994]. Together, these are three independent pieces of evi- dence for the Early Cretaceous tectonic activity in southern Israel that all focus on the same place, about 20 km south of the Ramon erosive cirque (central Negev).

4. Tectonic Interpretation

4.1. Relationship of Magmatism, Heating, and Uplifting

We have shown that the two Early Cretaceous magmatic pulses were associated with very different tectonic move- ments. The first pulse (130-120 Ma) was associated with up- lifting and intensive erosion; the second (-115 Ma) was not. Following a model we have presented in a previous work [Gvirtzman and GaFfunkel, 1997], we suggest that these two pulses produced opposite isostatic perturbations. The first pulse injected magma into the upper part of the lithosphere within the gabbro stability field and thus added relatively light material to the lithosphere, causing uplifting (Figure 9). The second pulse injected magma mainly into deeper parts of the lithosphere within the eclogite field and thus added a rela- tively heavy material to the lithosphere. The second pulse did not cause a noticeable uplift at the beginning; however, during its cooling it produced significant subsidence (Figure 9).

Our model distinguishes between the initial movement, which is the rapid isostatic response of the lithosphere to the addition of the new material (of the order of 104 years), and the subsequent thermal subsidence which is much longer (10 •- 10 • years) and continues until a new thermal equilibrium is approached. These two movements are calculated using a one-dimensional approximation for the intrusion, that is, an infinite sill-like intrusion.

Figure 7. Compilation of chronostratigraphic evidence con- cerning the Early Cretaceous section of southern Israel. Ab- solute timescale, stage boundaries, and magnetostratigraphy after Gradstein et al. [1994, 1995]. Eustacy is based on Haq et al. [1987] with some modifications concerning the Aptian (our data as well as data from the Arabian peninsula [Harris et al., 1984] and data from southern England [Ruffell and Watch, 1991 ] indicate main regression in the Mid-Aptian and not in the Early Aptian). The following points correspond to circled numbers on Figure 7. (1) The age of the first mag- matic pulse is shown. K-Ar ages indicate two events 135-129 Ma and 130-120 Ma [Lang et al., 1988; Lang and Steinitz, 1989]. More recently published Ar-Ar ages reduce the possi- ble range to 130-129 Ma for the first event and around 122.5 Ma for the second [Lang and Steinitz, 1994]. (2) Early Ox- fordian rocks found in a volcanic vent within the Ramon cir-

que indicate that during the magmatic activity these rocks were still present [Garfunkel and Katz, 1967; GaFfunkel and Derin, 1988]. Even if this vent is the oldest representative of this magmatic phase, the beginning of major erosion is con- strained to about 130 Ma and not earlier. (3) Samples taken from the basal Cretaceous section in Zohar 1 borehole (Ju- dean desert) indicate a Late Barremian palynologic assem- blage [Brener and Binckoff, 1992; Gvirtzman et al., 1996]. According to several global timescales [e.g., Gradstein et al., 1994, 1995; Obradovich, 1993; Kent and Gradstein, 1985] Late Barremian is approximately the end of the first magmatic pulse (-122 Ma). In other words, the period of erosion more or less coincides with a pulse of magmatism that began -130 Ma (Early Hauterivian) and continued for about 10 Myr. (4) Early Aptian fauna in Zuweira marine tongue were found at Hatira cirque [Greenberg, 1968], at the Hazera cirque [Lewy et al., 1994], and at the Ramon cirque [Weissbrod et al., 1994, Gvirtzman et al., 1996]. (5) The Aptian-Albian boundary in the Hatira erosive cirque was defined by Lewy and Weissbrod [1993] at the lowermost part of the Deragot Formation (9 m above the base), indicating that the second depositional cycle began toward the end of the Aptian. (6) A transition from re- verse to normal magnetization, found by Ron and Baer [ 1988] at the base of Ramon Basalt flows, correlates to the end of the ISEA reversal [Gvirtzman et al., 1996]. (7) The ISEA rever- sal was very short, maybe less than 100 kyr [Tarduno, 1990]. It is biostratigraphically constrained to the Late Aptian [Tar- duno, 1990]. Pringle et al. [ 1992] constrained it as older than 115 Ma and Pringle and Duncan [1995] constrained it as younger than 118 Ma. Gradstein et al. [1994, 1995] set it at 115.5 Ma. (8) Ar-Ar age of the Ramon basalt is indicated. Steinitz and Lang [ 1991] suggested 118-115 Ma, consistent with magnetostratigraphy and biostratigraphy [see Gvirtzman et al., 1996]. Conversely, Lang and Steinitz [ 1996] suggested 111-108 Ma, which extends too deep into the Albian. (9) A period of nondeposition and laterites accumulation is shown (see text for a full explanation). (10) The stratigraphic loca- tion of Middle-Late Albian fauna, found in the Uza marine tongue, is shown [Lewy and Weissbrod, 1993; Weissbrod et al., 1994]. (11) The stratigraphic location of Late Albian fauna at the base of the Hevyon member (Hazera Formation, Judea Group) is shown [Lewy and Weissbrod, 1993]. Note that the exact ages of the Deragot, Malhata, and Uza Forma- tions were defined in a way that best fits the subsidence curves in Figure 10.

450 GVIRTZMAN ET AL.: BIRTH AND DECAY OF A CONTINENTAL SWELL

- NORTH - - SOUTH -

_

-100 -

-200 - -

-300 - -

-400-

-500 -

-600 -

-700 '

i:i•:::•i'•'i'i=• •::• ?:•::•:•?•:•:•%5h.. :• •:•)•'•:?•:• •-;•: • .:•?•?: •'•'•: .......... •::' ............... •:::u::.•-•"•-•::-•-•-%:::•.•-::-•:: "' ............. . .................... ??•:•:• 5:.

•:•:•'::' GO0t ............................................ 5:•6 '"• .......... Marine

....... •:.:':::•.•:::•.•:•.•:•:•:•:•:•::•:•::•::"• ......

?•::?f•':': .... • Red laterite

0 25 50 75 100 125 150 175

--0

- -100

- -200

- -300

- -400

- -500

- -600

-700

200 km

COASTAL NORTHERN CENTRAL SOUTHERN PLAIN NEGEV NEGEV NEGEV

Figure 8. A summary of the stratigraphic information concerning the Lower Cretaceous section in southern Israel in the form of a geological cross section and a chronostratigraphic chart (Wheeler Diagram, time axis instead of depth). This cross section broadly coincides with the XX' mark in Figure 1. Location of specific sites can be traced in previous maps (Figures 5 and 6).

Assuming local isostasy, it follows that the initial move- ment (immediately after solidification of the intrusion) is given by

H o =W(I- Pi(1-o•T/) p,n0-aT.) ) 0)

where cr is the coefficient of thermal expansion, Pi and Pm are the densities of the solidified intrusion and mantle rocks at

0øC, respectively, W is the thickness of the intrusion, Ta is the temperature of the asthenosphere, and T• is the initial tem- perature of the intrusion. (T•. is actually about 360øC higher than the real temperature of the upwelling magma. This is done in order to consider the latent heat of crystallization. For details see Gvirtzman and Gaff unkel [ 1997].)

The subsequent thermal subsidence S(t) is calculated rela- tive to the surface after the initial movement. It is calculated

from the temperature changes that occur from time zero, taken as the moment immediately after the intrusion solidifies, to a any later time t:

S(t) -o• [p, i/xr(z,t) & + p, = • ' z,t)dz 1- t2• a p• o p•

C+W L+W

+ Pc I AT(z,t)dz + IAT(z,t)dz] (2) Pm D+W C+W

where AT(z,t) is the temperature change T(z,t)-T(z,0), z is the depth axis, D is the depth to the top of the intrusion, and C and L are the original depths to the base of crust and to the base of the lithosphere which after emplacement becomes C plus W and L plus W, respectively. The integration in (2) is separated into four intervals, so the different densities of the crust Po intrusion Pi, and mantle p,,, are considered.

Using these equations, Gvirtzman and Garfunkel [1997] showed that gabbroic intrusions initially produce uplift that is about 12% of the intrusion thickness (Ho=0.12W) and then subsequent thermal subsidence that decreases this uplift to a residual value of 9-10% of the intrusion thickness (Ho- S/=0.095 W, where S/stands for the final subsidence). Eclogite intrusions, however, are slightly denser than mantle rocks.

GVIRTZMAN ET AL.: BIRTH AND DECAY OF A CONTINENTAL SWELL 451

Uplifted swell •,..End of solidification (B)

Prernagmatic surface level ....

Time '-

Intracratonic basin (C) (D)

,; Premagmatic surface level

End of solidification

Time •

Figure 9. Uplift and subsidence of the lithosphere caused by magmatic activity as described by Gvirtzman and Gaffunkel [1997]. (a) A cartoon shows a swell produced by a gabbroic intrusion which is significantly lighter than mantle rocks and therefore causes isostatic uplift. (b) In such a case the initial rapid uplift is followed by a slower thermal subsidence that decreases the initial uplift by about 20%. (c) A cartoon illus- trates an intracratonic basin produced by an eclogite intrusion which is somewhat heavier than mantle rocks and thus causes

subsidence. (d) In this case the initial subsidence is very small; however, the thermal subsidence increases it to a sig- nificant residual value. Note that the thermal subsidence in

the second case is significantly slower and longer than in the first case. Dashed lines represent a short-lived stage while magma is still liquid (for details see Gvirtzman and Gaffunkel [1997]).

magma was not emplaced in the crust during the second magmatic pulse but mainly in deeper levels of the lithosphere.

In other words, we suggest that the Ramon basalt is the surface representative of midlithospheric magmatism. This conclusion is also supported by xenolith data and by the geo- chemical and mineralogical features of the basalt that indicate the presence of magma reservoirs at depths of 50-70 km [Stein et al., 1993]. It is also consistent with vitrinite reflec- tance data [Feinstein, 1985] which indicates that the sedi- mentary column was heated only by the first pulse and not by the second (for more details see Gvirtzman and Gaffunkel [1997]).

4.2. Calculating the Volume of Magmatism From the Tectonic Uplift

Given the vertical movements, the model enables us to cal- culate the thickness of the intrusion and to evaluate its relative

depth within the lithosphere. However, the tectonic move- ment should first be inferred from the stratigraphic record. We shall now perform this exercise to model the first mag- matic pulse and the uplift it produced. A similar modeling of the second pulse requires a quantitative analysis of the subsi- dence (backstripping) during the entire Cretaceous-Eocene interval which is beyond the scope of this paper. (The back- stripping procedure is outlined by Sleep [1971], Watts and Ryen [ 1976], Steckler and Watts [ 1978], Sclater and Christie [ 1980], Royden and Keen [ 1980], and others. The subsidence curves in Figure 10 do not include corrections for compaction, paleobathymetry, and eustacy).

When a continental region is uplifted and eroded, the tec- tonic uplift H is strongly amplified because of unloading of rock mass (isostatic rebound). The thickness of the eroded section E is much greater than the topographic relief that would have been developed without erosion. Assuming local isostasy, the tectonic uplift is:

H = E( pm-ps ) + R + Asl (3) ,o m

They produce a quite small initial subsidence which is in- creased during thermal relaxation to a final value of-4% of the intrusion thickness. In both cases the rate of the thermal

subsidence strongly depends on the depth of the intrusion. It is relatively fast when the intrusion is shallow but considera- bly slower when the intrusion is deep. Numerical simulations show that after intrusion into crustal levels most of the ther-

mal subsidence ends within less than 20 Myr, whereas after midlithospheric magmatism it takes more than 100-150 Myr to reach a new equilibrium [Gvirtzman and Garfunkel, 1997].

Within the frame of this model we suggest that the first Early Cretaceous depositional cycle (lower unit) represents the thermal relaxation after the first magmatic pulse, and the second cycle (upper unit) represents the subsidence following the second pulse (Figure 10). The first cycle was rather short. The quiet period in the mid-Aptian stage (i.e., the depositional break) constrains its duration to less than 6 Myr and thus indi- cates relatively shallow intrusions. In contrast, the second cy- cle was much longer and continued 60-70 Myr. The pro- longed subsidence and the fact that it was not associated with significant erosion indicate that a significant quantity of

where Ps is the density of eroded sedimentary rocks, Pm is the density of mantle rocks, R is the remnant topographic relief after erosion, and asl is the sea level change during the erosion period.

The value of E is usually hard to estimate, since stratigra- phers do not always know whether a discontinuous rock rec- ord is due to nondeposition or to uplifting and erosion. Fortu- nately, in our case there is a field evidence to constrain this uncertainty. Early Oxfordian limestone blocks were pre- served within a volcanic vent in the Ramon cirque (central Negev). These blocks prove that Upper Jurassic rocks, now missing there, were originally deposited in the central Negev and that they were eroded during the Early Cretaceous uplift- ing [Gaffunkel and Katz, 1967; Gaffunkel and Derin, 1988]. According to the thickness of these units in the northern Negev, Gaffunkel and Derin [1988] estimated that in the Ramon cirque 500-700 m were eroded, and 20 km farther south at the swell's crest, 750-1000 m were eroded (Figure 2). Porosity-depth relations [e.g., Sclater and Christie, 1980; Royden and Keen, 1980] indicate that the average density ps of such a section should be about 2000-2100 kg/m 3.

452 GVIRTZMAN ET AL.' BIRTH AND DECAY OF A CONTINENTAL SWELL

200

400

600

800

100(

120(

120 110 100 90 80 70

SarJ Aptian I Albian I Cen 'i Tur Iconlsal Campanian i i • 1- Hatira Cirque

i' 'Z { '.i :i ! --•--2-SouthRamon 'i • i i • 3-Areif-E-Naqa

i break i/ v'%"4o?x,, •,,•,• • • 4 - Sinall borehole _ : V•lcan•m a't •he •., ;• ,••at _ [ cen•al Ne•ev

,owor ' II ß • Z•w•'r• D•r•got•,,q Formatioq • • • Menuha _ - u• R Formation kash • - - • Hatira (Kumub) Group Judea Group Mount Scopus Group -

_

a,e I a,e - •[ Aptian Albian Cen I Tur Co S Campanian _. I,,,,I • ,

120 110 100 90 80 70

50 100 150

SOUTHERN

050 ISRAEL

oo0

95o EGYPT

( JORDAN 900

50 100 150

(3)

(4)

200 1100

1050

'1000

950

'900

200 ]•rn

Time, Ma Figure 10. Burial curves showing the two Early Cretaceous cycles of deposition. The break in subsidence indicates that the thermal relaxation following the first magmatic pulse was quite short. The second cycle that began a few million years after the second magmatic pulse was much longer and continued during the Late Cretaceous. Note that in site 3 (Areif E-Naqa), which is located at the swell's crest, deposition began in the Middle Albian, because earlier it was above the base level of deposition. Timescale is after Gradstein et al. [ 1994, 1995].

The change in sea level bsl during the erosion period (Hauterivian-Barremian) is taken from global eustatic curves [Vail et al., 1977; Haq et al., 1987] that show a 80-m rise during that time. Later on, during the Aptian and Albian, these curves show sea level rises which were 30-40 m each.

This information constrains the topographic relief that re- mained after the erosion, since the Aptian and Albian trans- gressions did not cover the swell's crest. In particular, the last transgression (Uza marine tongue, Middle-Late Albian) indi- cates that even 10 Myr after the end of the first Early Creta-

ceous depositional cycle the swell's crest remained elevated at least 30-40 m above its surroundings. Taking into account that during the first depositional cycle sediments about 100 m thick were deposited at the swell's margins, we may conclude that immediately after the erosion the swell's crest was higher than its surroundings by as much as 100-150 m (Figure 11).

Substituting into (3) E=750-1000 m, ps=2000-2100 kg/m 3, pm=3300 kg/m 3, As/=80 m, and R=100-150 m, the initial tec- tonic uplift at the swell's crest becomes 450-590 m. This cal- culation does not take into account the flexural effect of the

R, . Surfac e

i2 Risingsealevel Figure 11. Schematic illustration of the way we constrain the paleorelief. R1 is the initial topographic relief at the end of the uplifting and erosion period (Late Barremian). R2 is the residual relief that remained after the thermal subsidence (indicated by the black arrows) and before the last marine invasion (Middle-Late Albian). During the subsidence period, sediments were deposited at the swell's margins and produced more than a 100-m-thick section. The amount of subsidence at the swell's crest is not clear but should be 100 m or more.

This subsidence was not enough to terminate the topographic relief, and the last sea level rise (30-40 m) still did not cover the swell's crest. Therefore it seems that R2 is at least 30-40 m, and taking into account the thermal subsidence, R1 should be 100-150 m.

GVIRTZMAN ET AL.: BIRTH AND DECAY OF A CONTINENTAL SWELL 453

0.000

0.050

0.100 0 10 20 30 40 50

Time, Myr

Figure 12. Thermal subsidence following intrusion of a 4- km-thick sill into the crust. Marked depths refer to the sill's top. In the case studied here, magmatism was probably shal- lower than 5 km. However, note that even at a depth of 10 km, most of the subsidence occurs within 5-10 Myr.

lithosphere and thus underestimates the tectonic uplift. How- ever, since the swell was quite wide (150-200 km), the flex- ural effect is probably not too large and falls within the un- certainty of the above parameters (E, R, Asl, and Ps)'

Using the relations between magmatism and the ensuing tectonic movements (H0=0.12W), this uplift can be explained by a gabbroic intrusion 3750-4900 m thick. Furthermore, numerical simulation indicates that such a sill, emplaced at depths of 5 or 10 km, cools relatively fast and produces •-100 m of subsidence within 5-10 Myr (Figure 12), consistent with the sedimentation that occurred during the first depositional cycle (Figure 10).

5. Discussion

Though the model we have used seems to correlate with the stratigraphic data, some complications should not be overlooked.

5.1. 1-D Approximation

Field mapping, borehole data, and geophysics measure- ments indicate the presence of many near-surface magmatic bodies in the region that was uplifted (Figure 3), while the 1- D model we have used describes a single infinite sill-like in- trusion. Although this description is clearly erroneous, it gives a first-order estimate of the total volume of the magma that intruded the crust during the first Early Cretaceous pulse of magmatism. This cannot be deduced from the geophysics data, since aeromagnetic measurments cannot detect acidic magmatic bodies which have a low magnetic susceptibility, and the gravity data were not measured in a close enough grid to detect magmatic bodies with lateral dimensions of a few kilometers. Our study indicates that the total volume of the detected and undetected bodies which intruded the lithosphere during the first magmatic pulse should be equivalent to a 4 to 5-km-thick sill.

5.2. Assumption of an Instantaneous Event of Intrusion

The model we have used describes an idealized sequence of events. An instantaneous intrusion and uplift is then fol- lowed by a prolonged thermal subsidence. The separation between the initial uplift and the subsequent thermal subsi- dence is justified because dissipation of heat from the intru- sion to the surface takes more time than that required to reach isostatic compensation. The time for isostatic readjustment is of the order of 104 years, as determined from postglacial re- bound [Turcotte and Schubert, 1982]. We assume that within this time span the excess heat liberated from the intrusion is still within the lithosphere, and thus thermal subsidence still does not begin.

In reality, however, these processes can partly overlap in time, especially when the intrusion is shallow and thus the heat reaches the surface earlier. Moreover, when magmatism occurs in pulses, the heat from the first pulse may reach the surface before the last pulse begins. This overlap reduces both the upward and downward movements, as illustrated by the dashed line in Figure 13a. The initial uplift does not reach its maximal theoretical value of 12% of the intrusion thick-

ness, and accordingly, the subsequent subsidence decreases by the same amount.

Nevertheless, the error in the predicted uplift is quite small. Since the entire thermal effect is only 20% of the initial uplift and since some of the heat is always released after the end of uplifting, the associated error will never reach this value. For example, if half of the heat is released within the uplifting pe- riod, the initial uplift will be 11% of the intrusion thickness (instead of 12%), and after a complete thermal relaxation the residual uplift will be 9-10% of the thickness (which is in any case the final state). Thus, in our case, for instance, in order to explain the 450 to 590-m uplift, a 4.0 to 5.4-km-thick sill is required instead of 3.7-4.9 km that we calculated in section 4.2. Considering the fact that a sill is only an approximation for several smaller bodies, it seems that 4-5 km is a quite rea- sonable estimate for its thickness.

5.3. Sublithospheric Buoyancy

In the ongoing analysis we assumed that uplifting was mainly caused by shallow magmatism, and we neglected sub- lithospheric processes. The reason we emphasized the role of the intrusions is not only because we know for a fact that they actually exist but also because transient mechanisms such as heating or dynamic support of the asthenosphere cannot ex- plain the remnant uplift (see section 1). Nevertheless, since magma was generated somewhere at great depths, obviously, sublithospheric processes must have occurred.

These processes probably produced additional uplift. For example, if the fraction of melting was 10%, an asthenosphere layer 40-50 km thick is needed to explain the production of a 4 to 5-km-thick sill. What was the reason for the melting and what was the isostatic effect of such asthenospheric layer? Since extension of the lithosphere does not seem to have oc- curred in this region during the Lower Cretaceous, stretching could not have been the reason for upwelling and decompres- sional melting. A hot mantle plume, conversely, would pro- vide a source for this process.

What is the contribution of plumes to surface uplifting? From other examples in the world we know that plumes gen-

454 GVIRTZMAN ET AL.' BIRTH AND DECAY OF A CONTINENTAL SWELL

erate swells which are much larger (more than 1000 km in di- ameter) than the swell described in this work (150-200 km). Indeed, we do think that the local swell studied here may have been a part of a broader feature. The geographic distribution of the base Cretaceous erosional unconformity and the distri- bution of Early Cretaceous magmatism are much beyond the boundaries of southern Israel. Except for the Negev mag- matic field, Gaffunkel [1989] described a few additional Early Cretaceous magmatic fields in northern Israel, Lebanon and Syria. Gaffunkel [1991] further suggested that this large magmatic province was produced by a hotspot that later wan- dered southward to Egypt and Sudan.

Unfortunately, the amount of the regional uplift due to this plume could not be evaluated because of the lack of a refer- ence datum. Moreover, in central and northern Israel much of the magmatism was extrusive and thus the surface was buried not uplifted. For these reasons we stick to our limited region where the amount of uplifting is well constrained, and we re- turn to the basic argument that the local swell in southern Is- rael was a direct result of a shallow magmatic activityß This interpretation is consistent with the stratigraphic and geologic data as explained above. In addition, we note that this local feature was superimposed over a broader structure which can- not be evaluated according to the current available knowl- edge.

B

6. Some Speculations on the Fate of Continental Swells

One of the purposes of this study was to provide informa- tion that will allow speculations about how swells die away and how posttruncation stratigraphic sections should look (Figures 2d and e). As a result of our research, we now know that in this specific case thermal subsidence following the first magmatic pulse was not enough to bury the swell's crest, and thus it remained exposed for an additional 10-15 Myr until it was buried by a new cycle of subsidence produced by a sec- ond magmatic pulse. However, is this the only possible sce- nario? Can we envisage situations in which the late thermal subsidence will completely bury the remnant relief or maybe even produce a local basin over the erosional unconformity?

Figure 13 illustrates a few theoretical scenarios. The key question in this problem is whether or not the amount of thermal subsidence after the erosion is larger than the remnant topographic relief. It depends on several factors that charac- terize the magmatic activity as well as the swell geometry.

c

D

Figure 13. (a) Schematic illustration of the uplift and subse- quent subsidence produced by magmatism and/or heating. The solid line indicates that a single massive intrusion causes a rapid uplift which is about 12% of the intrusion thickness and then thermal subsidence that decreases the uplift to a re- sidual value which is about 10% of the intrusion thickness

[after Gvirtzman and Gaffunkel, 1997]. The dashed line shows that a series of smaller events which together emplace the same volume of magma produce several pulses of uplift that will not reach the maximal value as in the previous case but will reach the same final state. The dotted line illustrates

that heating at the base of the lithosphere that is not involved in any magma intrusions causes a considerably slower uplift, which is followed by subsidence that begins when the heat source is removed. Note that in the last case the amount of

subsidence equals the precursory uplift (no residual effect). (b) The expected final stratal geometry when thermal subsi- dence is enough to bury the swell and cover it by younger sediments. This might happen in the first case (solid line in Figure 13a). (c) The expected final state when the thermal subsidence is not enough to terminate the swell. This might happen in the second case (dashed line in Figure 13a). (d) The expected final state when uplifting is due to pure heating, and thus cooling returns the lithosphere to its initial state with no residual effect (dotted line in Figure 13a).

GVIRTZMAN ET AL.: BIRTH AND DECAY OF A CONTINENTAL SWELL 455

We might imagine a situation in which a thicker intrusion, say 10 km, is emplaced instantaneously at a great depth (but not deeper than the gabbro stability field). This should produce a strong pulse of uplift followed by rapid erosion. The thermal subsidence in this case will be delayed until the heat from the intrusion will reach the surface, and this would allow a few million years for the erosion to operate before thermal subsi- dence begins. If during that time the topographic relief is lowered by erosion below ~200 m, which is approximately the expected thermal subsidence (2% of the intrusion thick- ness), the swell might be terminated and covered by sedi- ments.

This scenario did not occur in our case because magmatism was shallow and in pulses, but it should be examined in cases of crustal underplating. Preliminary considerations suggest that it might be possible only in relatively narrow swells or when an additional mechanism is in operation. For example, a 500 to 1000-km-wide swell will probably remain a few hundreds of meters above its surroundings even after inten- sive erosion (the remnant relief depends on the topographic gradient and not only on the elevation difference). Our model requires an unreasonably thick intrusion to produce thermal subsidence that would bury such a remnant feature. There- fore, if such a swell is entirely due to magmatic intrusions, the surface will probably remain elevated (Figure 13c).

In contrast, if such a swell is entirely due to heating of the lithosphere without any magma intrusions (i.e., the opposite end-member), the subsequent subsidence should equal the precursory uplift, and thus the swell will become a basin filled with a sedimentary section as thick as the section that was previously eroded (Figure 13d). Unfortunately, there are not many documented cases that offer the opportunity to test the various possible scenarios.

7. Summary and Conclusions

1. The Early Cretaceous history of southern Israel pro- vides a unique example of the formation, growth, and decay of an intracontinental swell associated with magmatism. In the local scale we revised the stratigraphy of the Lower Creta- ceous section in southern Israel and analyzed its tectonic de- velopment. We have shown that the paleogeography and the tectonics of the region during the Early Cretaceous are di- rectly related to the uplifting that occurred in the beginning of that period. The elevated region that was not covered by sediments nor by the sea during the Aptian-Albian transgres- sions (this work) is the same region that was most uplifted and eroded previously [Garfunkel and Derin, 1988] and the same region that was most affected by magmatism [Gvirtz- man et al., 1994]. Together, these are three independent

pieces of evidence for the Early Cretaceous tectonic activity in southern Israel which all focus in the same place, about 20 km south of the Ramon erosive cirque (central Negev).

2. The tectonostratigraphic analysis presented above dem- onstrates how geological observations can be used to evaluate the amount of tectonic uplift and to estimate the volume and depth of magmatism that caused it. We have shown that the inferred tectonic uplift is significantly increased if the relief that remained after erosion and the eustatic sea level rise are

taken into account (equation (3)). In our case these correc- tions add ~40% to the value which is calculated only from the amount of erosion. They were made possible because of de- tailed stratigraphy that allowed synchronization with global eustatic curves and enabled us to reconstruct the paleorelief according to paleoshorelines during transgressions that sur- rounded the gradually decaying swell.

3. The amount of subsidence during thermal relaxation, which amounts to less than 20% of the initial uplift, suggests that in this case uplifting was mainly caused by magmatism that produced a permanent change in the buoyancy of the lithosphere. Temporal effects such as dynamic support or heating may have caused additional uplifting; however, their effect was much wider than the local swell studied here. At

this stage the regional trend of Early Cretaceous uplifting in the entire Levant region cannot be determined. The relatively quick thermal relaxation and the geological and geophysical evidence about shallow subsurface magmatism are all con- sistent with this interpretation.

4. Magmatism is an efficient mechanism to produce uplift. In our case the --500-m uplift can be explained by magmatism which is equivalent to emplacement of a 4 to 5-km-thick sill. For comparison, to produce the same uplift only by heating, the lithosphere-asthenosphere boundary should be raised by 50-60 km. The reason for this great difference is that the den- sity change caused by thermal expansion is much smaller than the density contrast between gabbro and peridotite.

5. Theoretical considerations concerning the interrelations between heating, uplifting, erosion, subsidence, and deposi- tion distinguish between swells that are predicted to remain elevated and swells which should be terminated and covered

by younger sediments.

Acknowledgments. This study is a part of the senior author's Ph.D. thesis at the Hebrew University of Jerusalem under the super- vision of Z. Gaffunkel. The project was supported by the Israel Ministry of Energy and Infrastructure. We wish to express our gratitude to T. Weissbrod for his constructive and fruitful conversa- tions in the office and in the field and to Michael Rybakov, who gave us the gravimetric and magnetometric data. We also thank Norman Sleep, Shimon Wydowinski, and Carolyn Ruppel for their construc- tive review which helped us improve this paper.

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G. Gvirtzman, Department of Geography, Bar Ilan University, Ramat Gan 52900, Israel. (email: gvirtzg@mail.biu.ac.il)

Z. Gvirtzman, Department of Geophysics, Stanford University, Stanford, CA 94305-2215. (email: zohar@ pangea. stanford.edu)

(Received April 17, 1997; revised January 16, 1998; accepted January 21, 1998.)