Constraints on Rift Thermal Processes from Heat Flow and Uplift

Tectonophysics, 94 (1983) 277-298 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

277

CONSTRAINTS ON RIFT THERMAL PROCESSES FROM HEAT FLOW AND UPLIFT

PAUL MORGAN Lunar and Planetary Institute, 3303 NASA Road One, Houston, TX 77058 (U.S.A.) (Revised version received August 19, 1982)

ABSTRACT Morgan, P., 1983. Constraints on rift thermal processes from heat flow and uplift. In: P. Morgan and B.H. Baker (Editors), Processes of Continental Rifting. Tectonophysics, 94: 277-298. Heat is of fundamental importance in the genesis of continental rift zones. Heat flow data are available from the Baikal, Basin and Range (North America), East African, Rhine and Rio Grande rift systems, and most of the data indicate high heat flow, with means of 70-125 mW m~ 2 , from the grabens in the rift systems. Data from the essentially non-volcanic sections of the East African rift system indicate normal to low heat flow, however. With the exception of the Basin and Range system, and parts of the Rio Grande system, the high heat flow appears to be restricted to the grabens, and is not measured on the broad domal or plateau uplifts associated with the rift systems. The uplifts associated with rifts typically are on the order of 1 to 2 km, with diameters of a few hundred kilometers or more, and the duration of the main phase of uplift is on the order of a few tens of million years, or less. These broad uplifts probably result from thermal changes in the lithosphère-asthenosphere system. Two thermal models of the lithosphère are developed for comparison with the heat flow and uplift data. The first model assumes very slow lithospheric thinning so that the lithosphère remains in a state of quasi-equilibrium during the thinning. The second model assumes that thinning occurs at a rate significantly faster than heat can be conducted into the base of the lithosphère, with thermal relaxation of the lithosphère occurring after the cessation of thinning. Comparison of uplift rates with the model results indicates that for uplift purposes in rift genesis, the lithosphère is in a state between the two models, i.e. partial heating of the lithosphère, or close to the rapid thinning state. Some uplift is predicted to continue after thinning has ceased due to thermal relaxation in the lithosphère. With respect to surface heat flow, however, the rapid thinning model is always predicted to apply, and a surface heat flow anomaly is not predicted to develop until after thinning has stopped. Local (graben) heat flow anomalies are thought to be primarily due to convection of heat into the rift zones by ascending magmas. A regional conducted thermal anomaly is not predicted to develop until after uplift is essentially complete. These predictions are compatible with the available heat flow and uplift data.

INTRODUCTION

Heat is of fundamental importance in the genesis of continental rift zones. Active thermal processes in rifts are dramatically manifested by volcanism, and temperature 0040-1951/83/$03.00

© 1983 Elsevier Science Publishers B.V.

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is perhaps the most important parameter controlling the localization of lithospheric deformation, if not at the initial stages of rifting, definitely after significant lithospheric thinning has occurred. Surface heat flow measurements provide information from which deductions can be made on the nature, magnitude, and history of thermal processes and subsurface temperatures in rift zones. Epeirogenic movements in rift zones, dominantly uplift, is primarily an isostatic response to density changes and thinning of the lithosphère, which result from structural, chemical, and thermal modification of the lithosphère during rifting. If the structurally and chemically induced components of uplift can be identified, the thermal component of uplift can be used to provide information on the thermal modification of the lithosphère during rifting. As lithospheric thermal perturbations are a transient phenomenon, significant surface heat flow anomalies related to the rifting processes are measured only in Cenozoic rifts. The transient heat flow signature of older rifts has decayed to insignificant levels by the present. Older rifts may have modern heat flow anomalies, but these anomalies are generally attributed to thermal refraction effects due to lateral inhomogeneities in the crust (e.g. the Oslo Graben: Haenel et al., 1974, 1979; Swanberg et al., 1974), or deep groundwater circulation, possibly along reactivated rift faults (e.g., the Upper Mississippi Embayment: Swanberg et al., 1979). Epeirogenic movements may leave a more permanent record of transient thermal processes through erosion or sedimentation, but this record is difficult to decipher with the precision required to constrain usefully the thermal processes. As with the surface heat flow measurements, therefore, useful uplift data are restricted to Cenozoic rift systems. Heat flow data are available from five major Cenozoic continental rift systems, the Baikal rift, the Basin and Range province (North America), the East African rift system, the Rhinegraben, and the Rio Grande rift. The purpose of this paper is to discuss the implications of these heat flow data to the processes of continental rifting, and to use simple thermal models of lithospheric thinning which predict uplift to further constrain the thermal processes in the lithosphère during rifting. HEAT FLOW DATA FROM CONTINENTAL RIFT ZONES

Heat flow data from the Baikal, East Africa, Rhine and Rio Grande rift systems have recently been compiled by Morgan (1982), and compilations of data from the North American Basin and Range province are given by Lachenbruch and Sass (1977, 1978), Blackwell (1978), and Sass et al. (1981). These compilations are summarized in Table I, and the salient results of these compilations are discussed very briefly below.

279 TABLE I Summary of rift heat flow data * Rift system

Region

Heat flow (mWrn-2)

Reference

Baikal

Rift Zone Including Lake Baikal

typical area mean heat flow values "Eureka Low" "Battle Mountain High" Cordilleran Thermal Anomaly Zone adjacent northern Mexico Sierra Nevada central Colorado Plateau

92 + 22(52) 83+ 34(39) 88 ± 28(17) 71 + 34(166) 75+ 35(166) 45 ± 6(13) 46 ± 10(4) 45+ 7(34) 54+ 12(14) 56+ 10(12) 70-125 65 105 65- 85 50-160 65 65

1 2 3 4 4 1 2 3 2 3 5, 5, 5, 5, 9 5, 5,

East Africa

Lake Malawi, North Lake Malawi, Centre Lake Malawi, South Lake Tanganyika, excluding high value Lake Tanganyika, high value Lake Kivu Kenya Rift floor Kenya western Rift shoulder Kenya eastern Rift shoulder

22+ 13(12) 96+ 25(5) 31+ 3(3) 38+ 13(11) 150(1) 17-185(5) 105+ 51 (15) 57+ 17(4) 39+ 21 (10)

11 11 11 12 12 13 14, 15 14, 15 14, 15

Rhinegraben

Upper Rhinegraben

107+ 112+ 73+ 70+

16 17 16 17

Lake Baikal, uncorrected Lake Baikal, corrected adjacent Siberian Platform

adjacent Caledonian Fold Belt Basin and Range

adjacent Hercynian foldbelt Rio Grande

Rift Zone, excluding values greater than 167 mW m~ 2 adjacent Great Plains adjacent Basin and Range and Colorado Plateau central Colorado Plateau

35(26) 34(8) 20(147) 10(22)

107+ 27(25) 60 80- >100 65

6, 6, 6, 6,

7, 7, 7, 7,

8 8 8 8

6, 7, 8 6, 7, 8, 10

18 5, 8 5, 18 5, 6, 7, 8, 10

* Data are either given as mean values with standard deviations, or ranges of values. The number of data used in calculating the means are given where appropriate in parentheses. References: 1 — Lubimova et al. (1972); 2—Lysak (1976); 3—Moiseenko et al. (1973); 4—Golubyev and Osokina (1980); 5—Lachenbruch and Sass (1977); 6—Lachenbruch and Sass (1978); 7—Blackwell (1978); 8—Swanberg and Morgan (1978/79); 9—Smith et al. (1979); 10—Keller et al. (1979); 11—Von Herzen and Vacquier (1967); 12—Degens et al. (1971); 13—Degens et al. (1973); 14—Morgan and Wheildon (1983); 15—Williamson (1975); 16—Hurtig and Oelsner (1977); 17—Bram (1979); 18—Reiter et al. (1979).

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Baikal Rift Zone There are inconsistencies in the published data sets for the Baikal Rift, as reported by Morgan (1982), but all the data sets indicate the same basic pattern of heat flow. The rift zone is characterized by high heat flow, 75-100 mW m~ 2 , with a narrow transition to normal to low heat flow, 45-50 and 54-56 mW m~ 2 in the adjacent Siberian Platform and Caledonian fold belt to the northwest and southeast of the rift zone, respectively. There is a larger scatter in the data in the rift zone than in the provinces adjacent to the rift by a factor of two or three. North American Basin and Range Province The Basin and Range province is much wider and more complex than the other Cenozoic rifts, and the broad zone of Cenozoic faults extending from southwestern Canada to northern Mexico (see Stewart, 1978) is characterized by generally high heat flow, with means in the range 70-125 mW m" 2 . This zone of high heat flow includes the well developed block faulting in the central and southern western United States to which the term Basin and Range province is usually applied, and also extends north into what has been termed the CordiUeran Thermal Anomaly Zone (Blackwell, 1978), and south into northern Mexico. One area of lower heat flow, less than 65 mW m - 2 , has been defined in the province, the "Eureka Low", but this is probably due to a regional groundwater system which convects heat away from the area (Lachenbruch and Sass, 1977). Another area of very high heat flow has been defined, the "Battle Mountain High" (Lachenbruch and Sass, 1977), which Blackwell (1978) extends into the young volcanic provinces of the northwestern United States. On some sides the high heat flow zone is flanked by normal to low heat flow, such as the Sierra Nevada and central Colorado Plateau, but the high heat flow appears to encroach into the margins of the neighbouring structural provinces (Keller et al., 1979). East African Rift System Heat flow data from the lakes in the western segment of the East African rift system indicate predominantly low to normal heat flow, 22-38 mW m~ 2 . These low to normal data come from Lakes Malawi and Tanganyika, in essentially non-volcanic areas of the rift. High heat flow values in these lakes were measured at locations where offsets in the main structural trends of the rift occur. A wide range of heat flow values was measured in Lake Kivu in a volcanic section of the rift. A high mean heat flow, 105 mW m~ 2 , with a large scatter in the data, has been determined in the Kenya section of the eastern arm of the rift, a section dominated by volcanics. However, low to normal mean heat flow values, 57 and 39 mW m" 2 , were determined for the volcanic flow covered shoulders of the rift to the west and east, respectively.

281

Rhinegraben The upper Rhinegraben is characterized by high mean heat flow, 107-112 mW m~ 2 , with moderately high mean heat flow, 70-73 mW m" 2 , in the adjacent Hercynian fold belt. The transition between the two thermal regimes is as abrupt as the spacing of the data can define, however, and there is no evidence of a broad transition zone of increased heat flow bordering the rift. Rio Grande Rift The Rio Grande rift is characterized by high heat flow, and excluding values greater than 167 mW m~ 2 , the mean heat flow is 107 mW m~ 2 . As with the Basin and Range province, the boundaries of the high heat flow in the rift are not constrained by the structural boundaries of the rift. To the east, away from areas of young volcanic activity, the heat flow decreases fairly rapidly to values less than 60 mW m" 2 , typical of the Great Plains. To the west, the high heat flow of the rift continues into the adjacent Colorado Plateau and Basin and Range Province, only decreasing to values less than 65 mW m~ 2 in the central Colorado Plateau. Rift heat flow data summary It can be concluded that continental rift zones are generally associated with elevated heat flow. The only rift zone for which the data do not define high heat flow is the non-volcanic areas of the western arm of the East African rift system. Some corrections to these data for the effects of the local lake environment may be appropriate, but in the absence of any reliable correction criteria, these data must be accepted as they stand until more reliable data can be obtained. Tentatively a correlation between high heat flow and volcanism in rifts is made, non-volcanic sections of rifts not necessarily being associated with high heat flow. Data from the marginal zones of the Baikal, Kenya section of the East African, and Rhine rift systems indicate that no broad zones of anomalous heat flow are associated with Cenozoic rifts. High heat flow extends outside the structural margins of the Basin and Range and Rio Grande rift systems, but young volcanism also extends into these marginal zones of high heat flow, and again a correlation between high heat flow and volcanism is suggested. Where marginal young volcanism is absent, the heat flow decreases rapidly at the margins of the rift zones. UPLIFT IN CONTINENTAL RIFT ZONES

It has long been recognized that continental rifts are associated with plateau or domal uplift, the structural graben being formed both by subsidence of the rift floor and uplift of the adjoining plateaus (e.g. Holmes, 1965, p. 1046, et seq.). Unfor-

282

tunately, determinations of absolute uplift during rifting are poorly constrained (e.g. see Withjack, 1979, table 2), and determinations of uplift rates are even less easy to obtain. Some modern uplift rates are available for rift zones deduced from geodetic observations (e.g. Tryggvason, 1982), but it is often difficult to extrapolate the relevance of short term observations to long term deformation rates. Typically, however, rifts are associated with plateau or domal uplifts on the order of 1-2 km, with widths of a few hundred kilometers or more. The duration of the main phase or phases of uplift is on the order of a few tens of millions of years or less. Regional epeirogenic movements in rift zones result from regional changes in the density structure of the asthenosphere-lithosphere system during rifting. McKenzie (1978) has modelled subsidence associated with rifting and the formation of sedimentary basins with an instantaneous lithospheric stretching model of "rifting". McKenzie's model predicts instantaneous high heat flow over the stretched lithosphère. This model may be suitable as a gross approximation of the subsidence and heat flow of the floors of rift valleys (although it is obvious that the actual rifting processes are much more complex than simple stretching), but it does not explain the uplifted shoulders, the plateau uplifts or domes associated with rifts. Jarvis (1981) has extended McKenzie's model to include the effects of lateral diffusion of heat from a stretched rift floor, and shows that under certain lithospheric conditions, some uplift (less than 1 km) can be produced for a limited distance (up to a few tens of km) away from the rift margin. This still fails to explain the magnitude and width of the uplift typically associated with rifts. On a broader scale, perhaps the most important cause of uplift is thinning of the lithosphère, or decoupling of part of the lithosphère by the emplacement of a sub-crustal low density mantle (asthenosphere?) pillow. Models of heat transfer into the base of the lithosphère and lithospheric thinning by conduction have been presented by Birch (1975), Crough and Thompson (1976), Gass et al. (1978), Wendlandt and Morgan (1982), and others. A model including convective heat transfer through the base of the lithosphère was presented by Withjack (1979). In the main rift zone, the changes can be complex with structural, thermal and chemical modification of the lithosphère during rifting. Outside the main rift zone, however, in the broad zone of uplift, there is often little evidence of major faulting or volcanism, during the main phase(s) of uplift, hence thermal modification of the lithosphere-asthenosphere system is expected to dominate. Two simple models of the thermal modification of the lithosphère during rifting are examined below as extreme cases of the rates of thermal lithospheric modification during rifting. In the first model it is assumed that the lithosphère is thinned either thermally or by diapiric intrusion of the asthenosphere at such a slow rate that the heat flows into the overlying unthinned lithosphère at a significantly faster rate than the thinning proceeds, and the lithospheric geotherm remains in a state of quasi-equilibrium. With these assumptions, uplift will occur while thinning is taking place, but will stop when thinning ceases. This model and the temperature and density profiles in the

283

DENSITY

/?S I

m y°u

c

ft

/

flfCl

F°Ç2J il

ni

LU

ol

\lfPa

2

1

Pujl

r

PA [_D_EPT_H_0_F__ COMPENSATION

Fig. 1. a. Hypothetical lithosphère-asthenosphere columns before (l) and after (2) lithospheric thinning, b, c. Temperature and density profiles in the columns as defined by the slow thinning model. Symbols are explained in the text.

lithosphère during thinning are shown in Fig. 1. For the second model it is assumed that thinning occurs very rapidly so that the thermal effects of the thinning do not significantly penetrate into the lithosphère during the thinning event. Rapid thinning could be caused by rapid thermal thinning, rapid diapiric intrusion of the asthenosphere, lithospheric delamination (e.g., see Bird, 1979), or the rapid emplacement of a low density mantle pillow into the lithosphère. In this case a two phase uplift is predicted: rapid uplift during the main lithospheric thinning event, followed by slow uplift as the unthinned lithosphère heats up after thinning. This model and the temperature and density profiles in the lithosphère prior to the lithosphère heating up after thinning are shown in Fig. 2. Both models assume very simple properties for the lithosphère-asthenosphere system. The asthenosphere is assumed to be isothermal, at or close to the solidus, and the lithosphère in its undisturbed state is assumed to have a linear geotherm

DENSITY

i°S

-fiL

£c A:

_DEPTH_0_F_ COMPENSATION

Fig. 2. a. Hypothetical lithosphère-asthenosphere columns before (1) and after (2) lithospheric thinning, b, c. Temperature and density profiles in the columns as defined by the rapid thinning model. Symbols are explained in the text.

284

from the asthenosphere temperature at its base to the surface temperature at its top. This latter assumption implies that the lithosphère has a uniform thermal conductivity, and no upward concentration of radiogenic heat producing elements. In view of the great uncertainties in the thermal conductivities at depth and at high temperatures (e.g., cf. Roy et al., 1972; Sclater er al., 1980; and Basaltic Volcanism Study Project, 1981, pp. 1151-1155), constant conductivity is a reasonable assumption for the present purposes, and more complex conductivity structure is difficult to justify. The lack of upward concentration of heat producing elements is obviously incorrect for a model of the continental lithosphère (e.g., see Roy et al., 1972). However, for the thinning models, if lithospheric thinning does not proceed to a stage where the upper crust, where the heat producing elements are concentrated, is thinned, the assumption of linear undisturbed geotherm for the lower portion of the lithosphère is a reasonable approximation. The effect of radiogenic heat production in the upper crust is discussed in more detail below with the results from the models. A further assumption is that the lithosphère has a uniform volume coefficient of thermal expansion of 3 - 1 0 " 5 ° C _ 1 (typical value for olivine and other mafic minerals up to 1000°C; Roy et al., 1981), and that density differences between the mantle lithosphère and the asthenosphere are solely the result of thermal expansion or contraction. The crustal density is also assumed to vary with temperature as a function of the same expansion coefficient, and a uniform density contrast between the crust and mantle at the Moho of 0.43 g c m - 3 is assumed (Drake et al., 1959). A constant density of 3.2 g cm" 3 (based on peridotite composition at 1200°C) is assumed for the asthenosphere. Both models predict uplift with lithospheric thinning as a result of replacement of colder and more dense lithosphère by hotter and less dense asthenosphere. Additional uplift is produced during thinning by the slow thinning model due to heating and thermal expansion of the unthinned lithosphère. In the rapid thinning model, this second component of uplift is delayed until after thinning ceases. Slow thinning model For the slow thinning model, the assumption that heat is conducted into the lithosphère much more rapidly than thinning occurs results in the lithosphère being essentially in a conductive steady-state at all times. This state is illustrated in Fig. 1 by the linear geotherms which meet the asthenosphere isotherm at the base of the lithosphère in both the thinned and unthinned lithosphère. This model is analagous to the variable thickness crust model used to relate elevation to surface heat flow and lithospheric thickness for Venus by Morgan and Phillips (1982), except that for the lithospheric thinning model, the crustal thickness is assumed to remain constant. From Fig. 1 and Morgan and Phillips (1983), the condition of isostasy for the lithosphère before and after thinning gives: Pc\c +

PLI(LI

- c) = Pcic +

PLI(L2

- C) + pAA2

(1)

285

where pCn and pLn are the mean crustal and mantle lithosphere densities in the nth columns respectively, pA is the asthenosphere density, C is the crustal thickness, Ln is the lithosphere thickness in the nth column, and A2 is the thickness of asthenosphere replacing lithosphere in the thinned lithosphere column. As shown in Fig. 1, pCn and pLn are different for different columns as the Moho temperature TMn, and hence the temperature drop across the crustal and mantle portions of the lithosphere are dependent on the crust to lithosphere thickness ratio. From the geometry illustrated in the temperature and density profiles shown in Fig. 1, it is easily shown that: PL„ = P A [ 1 + « ( 7 ; - 7 ; ) ( 1 - C / L „ ) / 2 ]

(2)

and: Pc = (PA [1 + «(T'A - Ts)(\ - C/L„)] - Δρ}[ΐ + a(TA - Ts)(C/L„)/l]

(3)

where a is the volume coefficient of expansion, 7^ — T s is the temperature drop across the lithosphere, and Δρ is the Moho density contrast. Thus for a given crustal thickness, C, and initial and final lithosphere thicknesses, L, and L 2 , eq. 1 can be used to calculate the thickness of asthenosphere, A2, that replaces lithosphere in the thinned lithosphere column, and the surface uplift, £/, is then given by: U=L2 + A2-LX

(4)

Rapid thinning model In the rapid thinning model, the thinning is assumed to occur at a rate significantly faster than heat can be conducted into the base of the lithosphere; the lithosphere geotherm does not change during the thinning, but the base of the lithosphere is marked by a step increase in temperature from the temperature of the initial undisturbed geotherm at that depth to the asthenosphere temperature. The rapid thinning model and the resulting temperature and density profiles are shown in Fig. 2. The condition of isostasy for the two columns in Fig. 2 is identical to that in Fig. 1, and defined by eq. 1, but as shown in Fig. 2, the crustal temperature profile, and hence its mean density, remains constant during thinning, i.e. pCn remains constant for all n. The initial lithosphere conditions for the rapid thinning model are identical to those in the slow thinning model, therefore the initial mean mantle lithosphere density, p L 1 , is calculated from eq. 2. The constant mean crustal density, p c , is calculated from eq. 3 using the initial lithosphere thickness for Ln. As can be seen from the temperature and density profiles in Fig. 2, however, the mean mantle lithosphere density changes more slowly as the lithosphere thins in the rapid thinning model than in the slow thinning model. From the geometry in Fig. 2, it can be easily shown that the mean mantle lithosphere density for the rapid thinning model is given by: p L 2 = pA[\ + a(TA - Ts)(l - L 2 /L,)]{1 + a{TA - TS)[(L2 - C)/Lx]/2)

(5)

286

with notation as before. With the modification that the mean crustal density remains constant, the calculation of uplift is identical to the slow thinning model for the rapid thinning model, using eq. 1 to calculate the thickness of asthenosphere that replaces the thinned lithosphère, then using eq. 4 to compute the uplift. Model results The uplift predictions of the slow and rapid thinning models assuming a crustal thickness of 40 km, and a lithosphère temperature drop of 1200°C, are shown in Figs. 3 and 4, starting with initial lithosphère thicknesses of 100 and 200 km, respectively. For the slow thinning model, the uplift is almost a linear function of lithospheric thickness; for the rapid thinning model, uplift is always less than for the slow thinning model, and uplift is relatively minor for the initial thinning, increasing as thinning progresses. For both models, the crustal thickness has little effect on uplift, unless thinning progresses into the crust, when subsidence occurs. For slow thinning, which represents the final equilibrium condition for both models, the ratio of uplift to thinning is only slightly dependent on the initial lithospheric thickness, decreasing from 0.0191 for thinning from 100 to 40 km, to 0.0185 for thinning from 200 to 40 km. Minor modifications of uplift magnitude result from both models if the asthenosphere density is varied, but as the asthenosphere density is thought unlikely to vary outside the range 3.1-3.5 g cm" 3 , these variations are insignificant. The major changes in uplift magnitude for both models result from changes in the product of the expansion coefficient and the temperature drop across the lithosphère, a(TA - Ts). Uplift magnitude in the range of reasonable values for this product is essentially linearly dependent on the product; i.e., halving the temperature drop, TA - Ts, halves the uplift, doubling the expansion coefficient, a, doubles the uplift. Unfortunately this product is not well constrained.

100

90 80 70 60 50 40 LITHOSPHERIC THICKNESS, km

Fig. 3. Predicted uplift as a function of lithospheric thickness for the slow (upper curve) and rapid (lower curve) models with an initial lithospheric thickness of 100 km.

287

There is some constraint on the temperature drop across the lithosphère from known surface temperature (typically 0°-20°C), and experimental studies which constrain the mantle solidus to be around 1200°C (e.g., see Wendlandt and Eggler,

LITHOSPHERIC THICKNESS,

km

Fig. 4. Predicted uplift as a function of lithospheric thickness for the slow (upper curve) and rapid (lower curve) models with an initial lithospheric thickness of 200 km.

1980). However, as discussed earlier, the upward concentration of radiogenic heat producing elements in the continental lithosphère will increase the geotherm in the upper crust, and decrease the geotherm in the remainder of the lithosphère (e.g., see Blackwell, 1971; Roy et al., 1972). The models described above are only sensitive to the geotherm in the portion of the lithosphère that is thinned, and upper crustal heat production can be compensated by decreasing the temperature drop across the lithosphère to yield the correct initial geotherm in the lower portion of the lithosphère. For example, Pollack and Chapman (1977) suggest that on a regional scale, the ratio of "mantle" heat flow (heat flow below the upper zone enriched in radiogenic elements) to surface heat flow is 0.6. Thus, for the thinning models, we can approximate this condition by scaling the lithosphère temperture drop by a factor of 0.6, reducing 1200°C to 720°C. This would reduce the maximum uplift for the 200 km initial lithosphère model (Fig. 2) from 3.0 to 1.8 km, which is still sufficient to explain the uplift associated with the Cenozoic continental rifts (e.g., East Africa; see Baker et al., 1972). If a thinner initial lithosphère is assumed, less uplift results. The volume thermal expansion coefficient for the mantle is poorly constrained, and the assumed value o f 3 - 1 0 " 5 o C _ 1 could easily be in error by ±25%, perhaps more (see data in Roy et al., 1981). This results in an uncertainty of at least ± 25% in the calculated uplift values, although if the assumption that this coefficient is essentially uniform throughout the lithosphère is valid, the relative results of the models are valid.

288

In calculations of gravity anomalies and uplift as a function of lithospheric thickness, it is common to assume a constant density contrast between the lithosphère and asthenosphere (e.g., Brown and Girdler, 1980; Bodell and Chapman, 1982). In a dynamic thermal lithosphère-asthenosphere system, as illustrated by the models above, this density contrast assumption is almost certainly wrong. If there is a significant portion of melt trapped in the upwelling asthenosphere, however, the assumption of a single-phase expansion coefficient for the lithosphère-asthenosphere system in the models above could lead to an underestimation of the uplift. Due primarily to the different coefficients of compressibility for solid and melt, it is very difficult to predict the density of a solid/melt system under pressure, and the reduction in density from the generation of a melt fraction in a solid may be much smaller than intuitively expected (e.g., see Stolper et al., 1981). No reliable estimate of the reduction in density of the asthenosphere by the creation of a melt fraction is made at the present, but this reduction would decrease pA in eq. 1, increasing the predicted thickness of the asthenosphere column replacing the thinned lithosphère, and increasing the uplift. Rate of thinning—slow or rapid? To apply the two models of the extreme rates of lithospheric thinning given above, a criterion must be established to quantify slow and rapid in terms of the thermal effects of lithospheric thinning. This criterion can be derived from an analysis of the propagation of heat in advance of a moving plane source of heat, an analog to the heat transferred into the lithosphère from the asthenosphere as the lithosphère-asthenosphere boundary ascends during lithospheric thinning. A moving image source i& used to maintain the boundary condition of a stable temperature (arbitrary zero in this model) at the Earth's surface. This problem is illustrated in Fig. 5, and if a constant source velocity (thinning rate) and source strength are assumed, the solution can be derived from the solution for a medium moving across

IMAGE SOURCE, .strength - q ,

|

Iw

d

1 T

I

d

I

I

GROUND SURFACE I Temperature = 0

-HP tw

MAIN SOURCE. ' strength +q

Fig. 5. Geometry used to compute the thermal perturbation due to a moving planar heat source, analogous to the ascent of the lithosphère-asthenosphere boundary.

289

a plane source of heat given by Carslaw and Jaeger (1959, p. 267). Using the notation in Fig. 5, the solution is as follows: (6)

TP=(q/pcW){e*p[-W(d-z)/k]-exp[-W(d+z)/k]}

where Tp is the temperature at depth z below the surface, q is the strength of the plane source of heat, per unit time, per unit area; p, c and k are the density, specific heat and thermal diffusivity of the medium into which the heat is propagating, respectively, and W and d are the rate of ascent and depth of the heat source, respectively. Of interest for the uplift calculations is the mean temperature increase above the heat source at any point in its ascent. This mean temperature increase, r i n c , is given by the integral:

Tinc=\/df ΊTp - άζ = qk[\+

exp(-2Wd/k)

- 2 e x p ( - Wd/k)]/(pcW2d)

(7)

The asthenosphere temperature, TA, is the temperature of the moving source plane, which is given by setting the z = d in eq. 6, resulting in: TA = q[\-

(8)

cxp(~2Wd/k)]/(pcW)

therefore the mean temperature above the source, Tst, equivalent to the mean temperature of the Hthosphere in the slow thinning model is given by: Tst =TJ2

= q{\-

(9)

exp(-2Wd/k)]/(2pcW)

Thus, the ratio of the mean temperature increase in front of the moving source to the mean temperature of the lithosphère in the slow thinning model is given by ratio of eqs. 7 and 9, which reduces to: 7 , , nc /7; t = ( 2 / Ö ) [ l + e x p ( - 2 < ? ) - 2 e x p ( - Ö ) ] / [ l - e x p ( - 2 Ö ) ]

(10)

where Θ is the parameter ratio (Wd/k). This mean temperature ratio is plotted in Fig. 6 as a function of the parameter ratio Θ.

0

1

2

I

I

3 4 5 6 7 Parameter Ratio, Θ = (Wd/k)

I

L_

Fig. 6. Plot of the ratio of the mean lithosphère temperature perturbations from the rapid and slow thinning models (upper curve), and the ratio of anomalous surface heat flow from the rapid and slow thinning models (lower curve), as a function of the parameter ratio Θ = (Wd/k).

290

The ratio Tinc/Tst tends to a maximum value of 1 as the parameter ratio Θ tends to zero, i.e. as the velocity and/or depth to the source tend to zero, and/or the diffusivity tends to infinity, conditions which make the moving source model essentially steady-state, or the slow thinning model. As the parameter ratio Θ tends to infinity, i.e. the velocity and/or depth to the source tend to infinity, and/or the diffusivity tends to zero, the ratio Tinc/Tst tends to zero, there is no temperature increase above to source, the defined condition of the rapid thinning model. Thus eq. 10 can be used to quantify slow and rapid for the models. For values of Θ greater than approximately 8, the exponential terms in eq. 10 become insignificant, and the ratio Tinc/Tst is accurately approximated by Tinc/Tst — (2/0). Thus, the results shown on Fig. 6 can be easily extended to any value of the mean temperature ratio or the parameter ratio. As can be seen from eq. 10 and Fig. 6, the conditions for the slow and rapid thinning models are only absolutely met by values of the parameter ratio Θ of zero

CD

60

80

100

120

K0

160

180

LITHOSPHERE THICKNESS, km

200

Fig. 7. Lithospheric thinning velocity fields as a function of lithosphère thickness appropriate to the slow and rapid thinning models (a) with respect to uplift (mean lithosphère temperature), and (b) with respect to surface heat flow. The logarithmic scale on the velocity axis is used only to separate the velocity fields.

291

and infinity, respectively. Conditions are accepted to be essentially within the predictions of the slow and rapid thinning models if the average temperature of the lithosphère, and hence the uplift due to heating of the lithosphère, is within, for example, 10% of the extreme values defined by the models. The terms slow and rapid can thus be defined for a given set of lithosphère conditions. From Fig. 6 it can be seen that lithosphère temperature is within 10% of the slow thinning model temperature for values of Θ of approximately 1.15 or less. From eq. 10, the lithosphère temperature is within 10% of the rapid thinning model temperature for values of Θ of 20 or more. The mean temperature of the lithosphère is midway between the predictions of the slow and rapid thinning models when Θ is approximately 3.8. Figure 7 shows the fields of thinning velocity as a function of lithospheric thickness for slow, intermediate and rapid rates of thinning, assuming a diffusivity of 32 km2 (m.y.) - 1 (approximately 1 mm2 s - 1 , a value commonly used to model transient thermal phenomena in the lithosphère; Jaeger, 1965; Bodell and Chapman, 1982). From Fig. 7, for a 200 km thick lithosphère, thinning is considered to be rapid if it occurs faster than 3.2 km (m.y.) -1 , slow if it occurs at 0.18 km (m.y.) - 1 or slower, and uplift midway between the two model predictions occurs at a thinning rate of 0.61 km (m.y.)" l . For a 40 km thick lithosphère, thinning is considered to be rapid if it occurs faster than 16 km (m.y.) -1 , slow if it occurs at 0.92 km (m.y.) - 1 or slower, and uplift midway between the two model predictions occurs at a thinning rate of 3.0 km (m.y.) - 1 . Response of surface heat flow to thinning rate For comparison with the surface heat flow measurements, it is also useful to establish criteria for slow or rapid thinning with respect to the surface heat flow. In the slow thinning model, the surface heat flow responds in a quasi-equilibrium manner with the thinning and uplift. In the rapid thinning model there is no change in surface heat flow during thinning, but the surface heat flow increases during thermal relaxation after thinning. To study the effect of thinning rate on surface heat flow, again the lithosphère is approximated by an infinite medium with a moving plane source of heat, and moving image source to maintain zero surface temperature, as shown in Fig. 5. The temperature TP at depth z below the surface is given by eq. 6, as before. The geothermal gradient at depth z is given by differentiating eq. 6 with respect to depth: dr p /dz = (q/kpc)[exp(- Wd/k)][exp(Wz/k) + exp(- Wz/k)]

(11)

By letting z tend to zero, the surface geothermal gradient, Grad R , is given by: GradR = (άΤΡ/άζ)0 = (lq/kpc) exp(-Wd/k)

(12)

The slow thinning model assumes that the geotherm is in equilibrium with the asthenosphere, which is equivalent to an infinitely slow thinning rate, i.e. W = 0, so

292

for the slow thinning rate the geothermal gradient is given by: Grad s = 2q/kpc

(13)

As the surface heat flow is the product of geothermal gradient and thermal conductivity, the ratio of eqs. 12 and 13, G r a d R / G r a d s , which is simply the function exp(— Wd/k), or exp( — 0), gives the surface heat flow as a fraction of the equilibrium, or slow thinning model, heat flow, during the lithospheric thinning. This function is plotted on Fig. 6 as a function of the parameter ratio 0, and shows the different responses of the uplift and surface heat flow to different thinning rates. As for the mean lithosphère temperature and uplift, the surface heat flow only absolutely meets the conditions dictated by the slow and rapid thinning models for values of the parameter ratio, 0, of zero and infinity respectively. From Fig. 6, however, it can be seen that the surface heat flow is within 10% of the slow thinning model (equilibrium) heat flow for values of 0 of 0.11 or less. The surface heat flow is within 10% of the rapid thinning model (no disturbance) heat flow for values of 0 of approximately 2.3 or greater. The surface heat flow is midway between the predictions of the slow and rapid thinning models when 0 is approximately 0.7. The parameter ratio values are approximately an order of magnitude smaller than the corresponding parameter ratio values for mean lithosphère temperature and uplift, and shows that a much slower thinning rate is required for a surface heat flow anomaly to be observed during thinning than for effects of heating of the unthinned lithosphère to be manifested by uplift during thinning. From Fig. 6 it can be seen that before a significant (10%) thermal anomaly will be measured at the surface, approximately 70% of the thermal expansion of the unthinned lithosphère will have occurred. When 90% of the lithosphère thermal expansion has occurred, only a little over 32% of the potential equilibrium heat flow anomaly will have reached the surface. Assuming a diffusivity of 32 km2 (m.y.)~ ] , fields of thinning velocity as a function of lithospheric thickness for slow, intermediate and rapid rates of thinning with respect to surface heat flow have been calculated, and these fields are plotted in Fig. 7. For a 200 km thick lithosphère, with respect to the surface heat flow, the thinning is rapid if thinning occurs at 0.43 km (m.y.) - 1 or faster, slow if thinning occurs at 0.02 km (m.y.) - 1 or slower, and midway between the two model predications if thinning occurs at a rate of 0.11 km (m.y.) - l . For a 40 km thick lithosphère the corresponding three rates are 1.86 km (m.y.)" 1 or faster, 0.09 km (m.y.) - 1 or slower, and 0.55 km (m.y.) - \ respectively. These rates are all an order of magnitude less for the surface heat flow effects than for the mean lithospheric heating and uplift effects. Thus, if thinning is still in progress, or was recently in progress, thermally driven uplift may occur, including much of the thermal uplift from thermal expansion of the unthinned lithosphère, without a significant surface thermal anomaly.

293

Thermal relaxation of the Hthosphere after a rapid thinning event In the rapid thinning model, the geotherm in the unthinned hthosphere remains undisturbed, and therefore there will be heating of the unthinned hthosphere and further uplift as the hthosphere thermally relaxes to the conditions predicted by the slow thinning model after thinning ceases. This problem is essentially that of the relaxation of a step temperature increase on one boundary (the hthosphere-as thenosphere boundary) of a plate with parallel faces (the hthosphere), with the other boundary (the surface) maintained at a constant temperature. The general solution to this problem is given by Carslaw and Jaeger (1959, pp. 99-100), and has recently been given with specific application to uplift and surface heat flow for thermal relaxation in the hthosphere by Bodell and Chapman (1982), and will not be repeated in detail here. Of significance to the present discussion is the relaxation times for the hthosphere predicted by the solution. Bodell and Chapman (1982) quantify the transient uplift (mean hthosphere temperature) and surface heat flow response of the hthosphere to an instantaneous temperature increase at its base in terms of the slab time constant tL = (d2/4k), with notation as before. Uplift due to thermal relaxation in the hthosphere starts immediately after the base temperature increase, is 50% complete by 0.2/ L , and 90% complete by approximately 0.85*L. Assuming a thermal diffusivity of 32 km2 (m.y.) - 1 , as before, uplift would be 50% complete after 2.5 m.y. for a 40 km thick hthosphere, and 90% complete after approximately 10.5 m.y. For an 80 km thick hthosphere, 50% of the uplift occurs during the first 10 m.y., and uplift is 90% complete after 42.5 m.y. The response of the surface heat flow is much slower, and over 0.25tL is required before even 10% of the anomalous heat flow reaches the surface. Approximately 0.55/L is required for the anomalous heat flow to reach 50% of its maximum value, and approximately 1.2/L for it to reach 90% of its maximum. For a 40 km thick hthosphere, the anomalous surface heat flow is 10% of its maximum after a little over 3 m.y., 50% of its maximum after almost 6.9 m.y., and 90% of its maximum after approximately 15 m.y. For an 80 km thick hthosphere, the surface heat flow reaches 10, 50 and 90% of its maximum value after 12.5, 27.5, and 60 m.y., respectively. Again there is a significant delay in the development of the surface heat flow anomaly after the thermally induced uplift has occurred. Thus, after rapid thinning has ceased, uplift will be midway between the rapid and slow thinning model predictions after a time delay of 0.2/ L , and essentially at (within 90%) of the slow model predictions after 0.85/ L . A time delay of 0.55/ L is required for the anomalous surface heat flow to reach 50% of its final value, and 1.2/L to reach 90% of its final value. APPLICATION OF THERMAL UPLIFT MODELS TO CONTINENTAL RIFTS

There are three basic data sets that the thermal uplift models are required to explain, the surface heat flow data, the total uplift in rift zones, and the rates of

294

uplift. Regional uplift is typically on the order of 1-2 km, and this is easily explained by a thinning of the lithosphère on the order of 60-160 km, if an upper crust enriched in radiogenic heat producing elements is assumed (see Fig. 2 and text above). Similar uplifts can be produced with less thinning if additional reduction in density of the asthenosphere (for example by partial melting) is assumed, but this mechanism is unnecessary if the thermal lithosphère can be on the order of 200 km thick at the initiation of thinning. Mean uplift rates for rift zones appear to be on the order of 50 m (m.y.) - 1 during uplift (e.g. see Withjack, 1979), which indicates mean lithospheric thinning rates on the order of 1.5-5.0 km (m.y.)" K These thinning rates indicate that for uplift purposes, the mean temperature of the lithosphère is intermediate between the predictions of the slow and rapid thinning models (Fig. 7). However, such rates are in the rapid thinning model catagory for the purposes of surface heat flow, and little or no surface heat flow anomaly due to conduction through the lithosphère is expected during thinning. It is unlikely that uplift and/or lithospheric thinning rates are uniform during the genesis of a continental rift, and more detailed studies of uplift generally give uplift rates much more rapid than the mean rates (B.H. Baker, oral commun., 1981; and see Tryggvason, 1982). If these rapid uplifts are regionally representative, they indicate lithospheric thinning rates applicable to the rapid thinning model, and thermal relaxation of the lithosphère is to be expected after a thinning event. Unless all the uplift and lithospheric thinning occurred during the earliest stages of the development of the Cenozoic continental rifts from which data are available, however, the slow relaxation of the surface heat flow anomaly may still result in little or no surface heat flow anomaly, although uplift may be essentially complete. For the five continental rift zones for which heat flow data are available, only the Basin and Range rift system, and possibly parts of the Rio Grande rift system show a regional surface heat flow anomaly. Blackwell (1978) has shown that outside the areas of where the surface heat flow is perturbed by recent magmatic activity (areas where volcanism is 17 m.y. or less), a high reduced or "mantle" heat flow can be determined. Keller et al. (1979) and Bodell and Chapman (1982) show that the margins of the Colorado Plateau are characterized by high heat flow adjacent to the Basin and Range and Rio Grande systems. As the extensional tectonics in the Western United States did not start until late Cenozoic time (e.g., see Stewart, 1978), it may seem strange that anomalous heat flow is already measured at the surface. However, the Western U.S. was dominated in early and middle Cenozoic time by events related to a subduction system along the margin of the continent, with the widespread eruption of silicic volcanic rocks, and it is highly likely that the lithosphère was thin and heat flow high at the initiation of rifting. The heat flow pattern of the Colorado Plateau probably reflects the long history of magmatic activity at its margins. The Rhinegraben has been active since early Tertiary time, and therefore from the models presented above, it would be expected that as well as the observed uplift, a

295

regional surface heat flow anomaly would be observed. The available data do not define such an anomaly, but most of the Hercynian fold belt region to the north of the Alps is characterized by moderately high heat flow (Table 1), and it is possible that any additional regional thermal anomaly associated with the Rhinegraben is indistinguishable from the regional elevated heat flow. Both the Baikal rift system and the East African rift system have long histories of volcanism, but their main structural development has been in late Cenozoic time. The available heat flow data do not indicate a regional thermal anomaly for either of these rift systems, and it is significant that high heat flow is only well defined in the main volcanic sections of the East African rift systm. It is tentatively concluded that the high heat flow areas of both of these rifts systems are associated with magmatic convection of heat through the lithosphère. The model studies indicate that although most of the uplift may have occurred, regional surface heat flow anomalies due to the conduction of heat through the thinned lithosphère are not to be expected in these young rift systems. CONCLUSIONS

Compilations of heat flow data indicate that high heat flow is commonly associated with volcanic areas in Cenozoic rift systems. More data are required, but available data suggest that the essentially non-volcanic sections of the East African rift system, Lakes Tanganyika and Malawi, do not have high heat flow. The rift systems commonly transect broad plateau or domal uplifts, but, with the exceptions of the Basin and Range rift system and parts of the Rio Grande rift system, the available data do not define elevated heat flow over the broad uplifts. Two extreme thermal thinning and uplift models have been developed to examine the thermal effects of lithospheric thinning. Mean rift uplift rates indicate that there is significant heating of the lithosphère above the ascending lithosphère-asthenosphere boundary with respect to thermal expansion of the unthinned portion of the lithosphère and uplift, but little or no perturbation of the surface heat flow during the thinning event. More rapid short term uplift episodes indicate thinning so rapid that heating of the unthinned lithosphère may be insignificant even for uplift during the thinning event, and thinning will be followed by thermal relaxation of the lithosphère. Uplift due to expansion of the remaining lithosphère will start immediately after thinning, with a significant delay and slow response of the surface heat flow to the thinning event. Thus, in rift systems where the major development of the rift is relatively recent (less than 15 m.y.), major uplift is expected without significantly anomalous surface heat flow. However, heat flow anomalies will be measured in regions of the rift zone where heat is convected through the lithosphère by ascending magmas. This combination of rapid convective heat transfer and slow conducted heat transfer results in the sequence of heat flow and uplift events associated with rifts summarized in Table II.

296 TABLE II Sequence of uplift and heat flow events predicted and observed during continental rifting Phase

Events

Pre-rift phase

initiation or precursor of thinning—little or no uplift, local heat flow anomalies associated with magmatic activity

Main rift phase

major lithospheric thinning—major uplift, local heat flow anomalies associated with magmatic activity

Post-rift phase 1

thinning completed—further uplift due to thermal relaxation in the remaining lithosphère, local heat flow anomalies associated with magmatic activity

Post-rift phase 2

thinning completed—uplift completed, regional conducted heat flow anomaly over uplift

ACKNOWLEDGEMENTS

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