ROLE OF MANTLE DERIVED MAGMAS I?! THE PRODUCTION OF CRUSTAL MELTS Dissertation for the Degree of Ph. D. MECHEGAN STATE UNWERSITY LEIAND WILBUR YOUNKER 1974 ‘A. 1Mr'7u3 4'54 3 . A‘a'“ 118‘!“ D ' 1‘- ' . L : avers: a 111 mu; m an m mm in mam: {I}; 1:1 mm 293 This is to certify that the thesis entitled Role of Mantle Derived Magmas in The Production of Crustal Melts presented by Leland W. Younker has been accepted towards fulfillment of the requirements for Ph . D . degree in Geo Iggy Major professor Date November 14, 1974 0-7839 P ‘Vu_N-n'_:‘ ‘ ' . alumna av n D ecux mom "I". ; ABSTRACT ROLE OF MANTLE DERIVED MAGMAS IN THE PRODUCTION OF CRUSTAL MELTS BY LELAND WILBUR YOUNKER The purpose of this study is to model the melting process in lower crustal rocks, evaluate the role of mantle-derived magmas in providing the heat necessary for fusion, and to thereby test the via- bility of a lower crustal origin for granitic magmas. It is concluded that crustal fusion occurs under water-deficient conditions at about 35 kilometers in a source region of intermediate composition. Tem- peratures required for partial melting cannot be produced by a normal geothermal gradient. In order to assess the role of 'penetrative convection' of mantle derived magmas in the production of crustal melts, two models are evaluated: The static mode1(Model I) and the dynamic model(Mode1 II). The static model has as its essential feature the intrusion of a basaltic or andesitic magma derived from the upper mantle into crustal material, and LELAND WI LBUR YOUNKER the subsequent cooling and crystallization at a given depth. The potential for producing crustal melts in the surrounding rock by this mechanism is evaluated using the finite difference numerical approximation to the heat transport equations modified for partial melting. In the dynamic model, the effect of rapidly rising magma diapirs on the thermal structure of the crust is evaluated. Such activity serves to preheat the lower crust making partial melting via Model I more likely. Results of the study support a lower crustal origin for batholiths such as those of the western United States. Temperatures required for partial melting under water deficient conditions can easily be reached by repeated penetration of the lower crust by mantle derived magmas. Providing the crust has been preheated by a period of magmatic activity, emplacement of a magma body is shown to be capable of generating crustal melt. The potential for pro- duction of hybridized liquids of intermediate com- position is verified by demonstrating the coexistence of significant amounts of crustal melt with differen- tiated basaltic magma throughout a substantial portion Leland Wilbur Younker of the crystallization interval. A relationship between plate dynamics and crustal melts, leading to batholith formation is established. There are two critical rates of plate descent; the first rate is that rate necessary to bring the upper portions of the subduction zone to the basalt solidus; the second rate is defined as that rate which produces an intensity of magmatic activity sufficient to trigger melting in the over- lying crust and the subsequent development of batholiths. ROLE OF MANTLE DERIVED MAGMAS IN THE PRODUCTION OF CRUSTAL MELTS BY Leland Wilbur Younker A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Geology 1974 ACKNOWLEDGMENTS I extend my appreciation and thanks to the following people: Dr. T. A. Vogel, Dr. J. V. Beck, Dr. B. H. Weinberg, Dr. H. F. Bennett, and Dr. W. Cambray. Special thanks to the following graduate students in the Department of Geology for creating an atmosphere conducive to this type of study: Jean, Gary, Bruce, Kevin, Steve, Dane, Ruth, Graham, and Jeanne. ii TABLE OF CONTENTS ACKNOWLEDGMENTS ..............................ii LIST OF FIGURES ..............................iv INTRODUCTION.................................. 1 MELTING IN THE CRUST.......................... 6 General Discussion ........................ 6 Temperatures of Melting ................... 9 Composition of First Formed Liquid ........10 Summary of Melting in the Crust ...........13 THEM MODELS OF MELTING...’.0...............14 SOURCE OF HEAT FORMELTING 0.0.00.00000000000021 PENETRATIVE CONVECTION AS THE SOURCE OF HEAT 0.0...OOO...OOOOOOCOOCOCCCOOOOO0.0026 STATIC MODEL...OOOOOOOOOOOOOOOOOOOOOOOO0.0.0.028 Mathematical Statement of the Mbdel........31 General Results: Static Model .............37 DiscuSSion: Static MOdeI-OO0.0.0.0000000000043 DYNAMIC MODEL.0.0..00...00...0.0.00.000000000046 RELATIONSHIP BETWEEN PLATE DYNAMICS AND BATHOLITH ACTIVITY.OOOOOOOOOOOOOOOOOO00.00.57 CONCLUSIONS....0...O0....00.000.000.000000000063 ”FERENCES CITEDOOOOOOOOOOOOOOOOO0.00.00.00.0067 iii LIST OF FIGURES Figure 1. Plot of percent crystals versus temperature: curve I is for hydrous granodiorite(Piwinskii, 1968): Curve II is for basalt(Shaw, 1969); Curve III is linear relationship typical of solid solution melting ........................l9 Plot of geothermal gradient and conditions of melting for three types of melting. Geothermal gradient taken from Roy and others(1968). Conditions of melting taken from Brown and Fyfe(1970).....................................22 Plots of temperature versus position for magma(ha1fwidth-$ km.) with initial tem- perature of 1400 C. intruding countay rock with initial temperature of 400 C........38 Plot of temperature versus position for a magma of halfwidth l km. with an initial temperature of 1400 C.°intruding country rock of temperature 500 C.....................39 Plot of temperature versus position. Speci- fications are same as Figure 4 except for temperature variable conductivity in the country rock...................................4O Flow chart for dynamic model calculation ......48 Plot of geothermal gradients and melting conditions: 1 is the normal geothermal gradient; 2, 3, and 4 represent geothermal gradients produced by 10, 20, and 50 times the observed volcanic activity in JapanOOOOOOO...OOOOOOOIOOOOOOOOOOOOOOO0.0.0.0.055 iv INTRODUCTION The origin of granitic batholiths in the circum- Pacific region is still one of the fundamental problems in igneous petrogenesis. The concept of generating these granitic magmas by partial fusion of crustal material is based primarily on geochemistry, petrology, and field relationships, with experimental petrology setting limits on the potential models of petrogenesis. Recent developments in the plate tectonic theory have provided a convenient tectonic framework for the development of granitic batholiths and stimulated new interest in their origin. The occurence and distribution of Mesozoic batholiths around the Pacific Ocean leaves little doubt that the generation of batholiths is re- lated to subduction zones. Indeed, the origin of granitic plutonism in marginal continental crust must be coupled with the mechanisms of destructive plate margins and consumption of oceanic crust at depth. The potential of the lower crust as a source region for granitic magmas has been considered by several authors. Tuttle and Bowen(l958) presented an anatectic model based on melting experiments in the water saturated albite-potassium feldspar-water system, and this work was extended by wyllie and Tuttle(1959) to include sedimentary rocks. Winkler(l967) extensively developed the anatectic model relating it to the formation of migmatites and origin of granitic magmas. Piwinskii and wyllie(1968) and Piwinskii(l968; 1973) gave further support to the crustal anatectic model by experimentally determining the phase equilibrium relationships of a series of igneous rocks from the calc—alkaline batholiths under water-saturated conditions. Brown and Fyfe(1970), Fyfe(197l; 1973) and Brown(1973) presented a model for crustal magma generation for water deficient systems which con- tained water only in the hydrous minerals. In their model, granitic magmas were produced as a response to ultrametamorphism, with metamorphic rocks yielding a liquid fraction produced by the breakdown of muscovite, followed by a biotite fraction and finally an amphibole fraction. Presnall and Bateman(l973) compared fusion relations in the system NaA131308 — CaA1281208 - KA131308 - H20 with the granitic rock types in the Sierra Nevada Batholith and concluded that a major portion of the present batholith must have been derived from partial melting of the lower crust. The anatectic model is not without its critics however. Dickinson(1970) and Matsumoto(1967), noting the relationship between batholiths and destructive plate margins suggest granitic batholiths are fed by partial melts directly from the mantle or the under- lying subduction zone. Stern and wyllie(1973), however, on experimental evidence, concluded that primary granites or rhyolites are not likely to be produced by partial fusion of oceanic crust in subduction zones. In addition, a notable feature of circumpacific batho- liths is their restriction to areas, underlain by rather extensive continental crust(Presnall and Bateman, 1973). If the source region was in the sub- ducted plates or in the mantle overlying the plates, one would expect to find batholiths in areas where continental crust is absent(Presnall, et. al., 1973). Experimental petrology and spatial distribution of batholiths therefore strongly support a lower crustal origin for granitic magmas, rather than an upper mantle origin. One of the basic prerequisites for the lower crustal origin of granitic rocks is that temperature must be high enough to partially melt these materials. Thermal structure of the normal continental crust is mainly a function of the distribution of radio— active heat sources in the crust and upper mantle. Lachenbruch(1968) calculated maximum geotherms in the Sierra Nevada region under assumptions of constant mantle heat flow and uniform distribution of heat sources. He concluded that the temperature at the base of the crust prior to the onset of magmatic activity was 2500 C., far below that required to partially melt crustal material. In a similar fashion, typical continental geotherms given by Roy(1968) and Smithson and Decker(1974) suggest temperatures at the base of the crust are substantially lower than those required for partial fusion. In areas of extensive 'penetrative convection', this thermal structure will be entirely altered by repeated episodes of magmatic activity originating in the subduction zone and penetrating the continental crust. This magmatic activity may provide the thermal accident necessary to produce crustal melts. The overall goal of this study is to model the melting process of lower crustal rocks, evaluate the role of mantle derived magmas in providing the heat necessary for fusion, and to thereby test the viability of a lower crustal origin for granitic magmas. MELTING IN THE CRUST GENERAL DISCUSSION The main variables influencing the produc- tion of melts in the crust are composition of the source rocks, depth of magma genesis, and the amount and composition of pore fluids. The crust is composed primarily of rocks ranging in composition from granite to gabbro with an average composition near that of andesite(Ronov and Yaroshevsky, 1969). Although traditionally the composition of the lower crust was assumed to be gabbroic, Ringwood and Green(1966) con- cluded that an intermediate composition is more pro- bable. They point out that at the base of a dry continental crust, eclogite would be the stable phase and seismic velocities do not support the presence of eclogite. Crustal mineralogy is predominantly feldspar and quartz and models for the source terrane must there- 3O8 - CaA1281208 - KAlSi3O8 - SiO2 - H20 as suggested by Presnall and fore be dominated by the system NaAlSi Bateman(l973) or expanded to the rock-water system (granodiorite - water) as suggested by WYllie(l97l). Both of these systems will be used to illustrate the pertinent aspects of crustal melting. The amount of water available is vitally important in determining the conditions of crustal fusion. Robertson and wyllie(l97l) have defined four basic types of melting based on this variable. Type I melting is anhydrous; Type IV melting has excess water available; Types II and III melting are water deficient. Type II melting has all of the water tied up in hydrous minerals. Type III melting has an aqueous vapor phase present but in insufficient quantities to saturate the liquid when melting is complete. Rock water systems with excess water present(Type IV) have traditionally provided the basis for partial fusion in the crust. Most deep- seated magmatic processes occur in the water deficient region(Brown and Fyfe, 1970; Fyfe, 1971: wy111e, 1971: Brown, 1973). The depth at which melting begins is important in determining the composition of the first formed melt. Tuttle and Bowen(l958) concluded that melting begins at depths between 20 and 25 kilometers. Based on metamorphic assemblages, the depth of melting is between 25 kilometers and SO kilometers(Fyfe, 1971). In summary, it is reasonable to assume that crustal fusion occurs under water-deficient conditions at approximately 35 kilometers in a source region of intermediate composition. TEMPERATURES OF MELTING The temperatures of incipient melting are highly dependent on the amount of water available. If any free water is available, initial melting will take place at the water-saturated minimum defined by Bowen(1954), and the amount of melt produced is deter- mined by the amount of water available(Wyllie, 1971). If no free water is present, the temperatures required for initial fusion are higher. If water is present in hydrous phases, fusion will occur with the breakdown of the hydrous minerals. In deep-seated metamorphic rocks where pore fluids are unlikely(Fyfe, 1971), the curve for the beginning of melting may correspond to the dry muscovite + quartz reaction: Muscovite + quartz -+Orthoclase + Kyanite + Liquid The difference in temperature in these two types of melting at 10 kilobars pressure is about 100°C.(Huang and Wyllie, 1973). If the muscovite in the system is exhausted by this reaction, no further melting will be possible until the temperature of biotite dehydra- tion is reached. Using natural rock systems, Brown and Fyfe(l970) suggested that melting in the crust 10 can be described by the reaction: Biotite-hornblende-schistm—r-water under- saturated melt + less hydrated, more refractory residue For water saturated systems the temperature of incipient melting is 650°C. at 35 kilometers(Tuttle and Bowen, 1958). For anhydrous melting, the temperature of incipient melting would be near lOSOOC. at 35 kilo- meters(Green and Ringwood, 1966). In Type II melting the exact temperature of melting would depend on the type of hydrous minerals present. If biotite was the dominant hydrous mineral, melting would commence at about 800°C. at a depth of 35 kilometers(Brown and Fyfe, 1970). COMPOSITION OF THE FIRST FORMED LIQUID Since most experimental studies of the fusion of crustal materials have involved water saturated conditions, this system will be described first and then qualitatively corrected for water deficient melting. The system Ab-An-Or-Q-HZO has been extensively discussed by Winkler(1967) and Presnall and Bateman(l973). In general, fractional fusion of compositions within 11 the solidus volume of plagioclase + K-feldspar + Quartz yields initial liquids on a cotectic line. The exact composition of the first melt is a function of source composition and pressure. Melting begins at about 6500 C. with fusion of quartz plus two feldspars plus solution of vapor producing a water-saturated liquid of granitic com- position. A small increase in temperature produces much additional water saturated liquid indicating that melting probably occurs at an invariant point(Piwinskii, 1968). If there is not enough water to saturate the liquid, the pore fluid rapidly disappears within a few degrees of the solidus. The rock is not completely molten until a temperature of nearly 11000 C. Robertson and wyllie(l97l) contrasted the water saturated melting behavior with the melting behavior in the water deficient region. If there is pore water present, melting begins at the vapor saturated solidus. For Type II melting, the temperature of incipient melting is related to the temperature of breakdown of the hydrous phase. In addition, in the water deficient region, as the amount of water decreases, the temperature range through which quartz plus two feldspars coexist with a liquid increases, and the amount of liquid produced 12 within a given temperature interval above the solidus decreases. The above differences in melting behavior are critical in determining the thermal aspects of melting and their effect on the melting process will be discussed in detail below. Brown and Fyfe(l970) discussed the dominant compositional trends for primary melts in the earth's crust produced by Type II melting. Using a system of quartz + two feldspars + hydrous minerals, they show a strong inverse correlation exists between nor- mative quartz and confining pressure, and a positive correlation between Ab/Or rations and confining pressure. They concluded that true granites are products of melting at the lowest temperatures and pressures, while intermediate magma types represent partial melting at deeper levels in the crust and correspondingly higher temperatures. It is important to note that while their results give an indication of changes in primary melt composition with depth and temperature, they were dealing only with changes in major mineral composition (quartz, feldspar) and are therefore not totally repre- sentative of true granites, diorites, granodiorites, etc., which contain a substantial proportion of mafic minerals. 13 SUMMARY OF MELTING IN THE CRUST Experimental petrology provided much valuable data on the initiation of melting in the crust and the composition of the first formed liquids. The general picture of crustal melting developed would include the following points: 1. Composition of the source terrain is more siliceous than gabbroic, probably andesitic. Melting occurs as a response to a heating episode. Much if not all original pore water is driven off leaving a Type II melting situation. Temperature of incipient melting is therefore, tied to the temperature of dehydration of the hydrous minerals present. First formed liquids fall on the cotectic trough in the system Ab-An-Or-Qtz-HZO. The extent of melting depends on the quantity of hydrous minerals in the system. Composition of melt formed is a function of the composition of the source terrain, tempera- ture, and the depth of melting. THERMAL MODELS OF MELTING Melting in the earth's crust can be ideally classified as one of three cases(Kowownakai, 1973): a. pure phase melting or melting in a eutectic system where the composition of the system is at the eutectic composition(Type A): b. solid solution melting(Type B); c. eutectic melting with composition not equal to the eutectic composition(Type C). In Type A melting, only one melting curve is defined, and temperatures are fixed until the system becomes com- pletely molten. For this type of melting, a front at temperature Imelt advances into the solid region, with a boundary having liquid on one side and solid on the other. The latent heat of fusion is totally consumed at the melt interface. In Type B melting, a solidus and liquidus curve are defined and temperature rises slowly throughout the melting interval as the amount of melt increases. In Type C melting, temperature holds at T until a phase E is exhausted and then slowly rises throughout the melting interval. In both Type B and Type C melting, there exists l4 15 an extended temperature range through which crystals and liquid coexist. Natural rock systems can be visualized as a combination of the three elementary melting processes. For example, in the system Ab-Or-Qtz, melting initially takes place in a cotectic trough. This type of melting behavior is analogous to Type B. Depending on the original composition, one of the phases is exhausted and a eutectic melting situation is encountered. Further input of heat will exhaust one of the two remaining phases, and if the melt is separated at this point a pure phase melting situation results. Thus in one relatively simple geological system, the melting be- havior is a combination of the three simple melting types. The three types of melting processes have drasti- cally different thermal behavior, and as a result, in order to accurately evaluate melting in a system, it is necessary to choose the most representative melting pro- cess. Type A would be a good representation of a system in which virtually all the melting takes place at an invariant point. Type B would be an accurate represen- tation of a system in which the percentage of liquid 16 increases linearly with temperature. Type C melting would be an accurate representation of a system which initially produces much liquid at an invariant point and thereafter, the amount of liquid linearly increases with temperature. Analytical solutions for the melting process have been mainly limited to Type A melting in which the latent heat of fusion is released at a particular tem- perature. Muehlbauer and Sunderland(l965) give an ex- cellent review of the range of analytical solutions available for such change of phase problems. In general, because of the nonlinearities inherent in the problem, these solutions are confined to one-dimensional situa- tions. Recent work by Cho and Sunderland(l969; 1974), Muehlbauer and others(l973), and Tien and Geiger(1967) extended the range of analytical solutions to Type B and Type C melting where latent heat effects occur in a melting zone between the liquidus and solidus. The essential conclusions of all these studies are that when a system involved in a heat-transfer process under- goes a phase change, the total transfer process can be greatly altered. Even though the phase transition occurs locally, the energy absorbed or released directly affects 17 the temperature distribution throughout the material. For adequate treatment of practical situations, it is therefore necessary to obtain solutions subject to realistic configurations and boundary conditions. As a result, the first step in the solution of a melting problem is the selection of the most realistic melting model for the system. It is possible to use plots of percent melt versus temperature as a guide to the type of melting model applicable. A Type A melting situation is one in which 100% melt is produced at the melting temperature. A Type B melting relationship is characterized by a linear relationship between percent melt and temperature. A Type C melting model produces a substantial amount of melt at the eutectic temperature, and then the amount of additional melt is linearly related to temperature. In the case of a eutectic melting situation with the composition of the initial solid far removed from the eutectic composition, Type C approaches solid solution melting. If the composition of the system is equal to the eutectic composition, Type C melting is identical to pure phase melting. 18 Using this criteria, it is possible to choose a melting model for natural rock systems reported in the literature. Shaw(l969) presents a plot of percent melt versus temperature for a basalt, and Piwinskii(l968) presents a similar plot for a hydrous granodiorite(Figure 1). 0n the basis of these plots, one would expect that a Type B melting relationship is adequate for the basalt, and a Type C melting relationship is applicable to the hydrous granodiorite. There are no similar plots which correspond to Type II melting of lower crustal material. The hydrous granodiorite may be used as an initial approximation to this melting behavior. Using information taken from Robertson and wyllie(l97l), this may be corrected for water deficient melting. In the water deficient case, the amount of liquid produced as a function of temperature is considerably less than the amount produced in the saturated system considered by Piwinskii(l968). In addition, quartz and feldspar are stable with liquid over a much greater temperature interval. These points suggest that the pattern of melting displayed by the hydrous granodiorite is primarily due to the presence of the water, and in the water deficient case, melting 100 Percent crystals 90 80 70 601 50 40 30 20‘ 10< 19 III l Tsolidus Figure 1. Temperature Tliquidus Plot of percent crystals versus temperature: Curve I is for hydrous granodiorite(Piwinskii, 1968); Curve II is for basalt(Shaw, 1969); Curve III is linear relationship typical of solid solution melting. 20 of a granodiorite would more closely resemble the basalt melting behavior. Therefore, it is suggested that melting in the water deficient lower crust can be realistically modeled as Type B melting. As will be discussed below in detail in the solid solution melting model, slow temperature rise between solidus and liquidus can be regarded as an apparent increase of specific heat, reducing the problem of melting to one of temperature—variable thermophysical properties. SOURCE OF HEAT FOR MELTING Figure 2 shows the conditions of melting as determined experimentally for'water saturated, water deficient, and anhydrous systems. The normal con— tinental geothermal gradient as determined by Roy et. a1. (1968) is also plotted on the graph. The temperature gradient in the crust is mainly a function of the distribution of radioactive heat sources in the upper crust, and a second component due to sources in the lower crust and upper mantle. The curve plotted is for a region which has undergone little, if any penetrative convection, and might be regarded as typical of the stable portions of continents(Blackwell, 1971). One point is clear from an inspection of the graph. Melting is not a steady-state process in a normal continental crust. There is no depth at which the geothermal gradient approaches the conditions necessary for incipient melting. The situation dis- played on the graph might even be an optimistic one. Lachenbruch(1968) calculated maximum geotherms in the Sierra Nevada region under two assumptions: (1) Mantle heat flow was the same as now observed; and (2) Uniform 21 22 .Ao>aavom>m can asoum scum :oxwu mcfiuaofi mo mcowufiocoo .Amomavmuonuo can mom Scum powwowum Haemonuoou .mcauHoE no woman moan» Mom msfiuaofi mo mcofluwpcoo one powwomum Hmeuosuoom no uon .m ousmwm onsumuooema coma coda oooa com com com com com can com com oma F1 T l. p l. b bi _ .- m . ov wsowaom oouousuom moduOH. A. IS \ mocmansuo msofiHOm macho»: undao D 23 distribution of heat sources. At the base of the crust, he postulated a maximum temperature of only 2500 C. prior to the onset of magmatic activity. From these results, it can be concluded that if melting in the crust occurs, it is a thermal accident re- quiring transient heat sources. Many different mechanisms have been suggested for producing crustal melts in light of the above apparent temperature discrepancies.. A number of authors, for example, Brown(1973), suggested that in regions of calc-alkaline batholithic activity, the continental crust is thickened to the extent of supporting the pressure-temperature regime necessary for melting. Lachenbruch(1968) considered this possibility for the Sierra Nevada region, and dis- missed it because it would require massive amounts of rapid erosion in order to permit a former crustal thickness of 50 kilometers. The metamorphic assem- blages present in batholithic areas do not support a model of formation under such high pressure conditions. In general, there is a lack of correlation of crustal thickness with batholithic activity indicating that in most regions, unreasonable levels of erosion would 24 be required to make crustal thickening a viable mechanism for crustal fusion. In a similar fashion, other authors have suggested that granitic magmas formed as thick accumulation of geosynclinal sediments are downwarped, eventually reaching fusion temperature because of the concentration of radio- activity in sediments(Bateman and Eaton, 1967). Many authors(Ichikawa et. al., 1968; Matsumoto, 1968; Hamilton and Myers, 1967) have since shown that large scale magmatic activitiesare not preceded by eugeosynclinal subsidence, and that there is no apparent correlation between geosynclines and batholiths. It has also been suggested that melting occurs as a response to unusual concentrations of radioactivity. Sheinmann(197l) suggested that if such a mechanism were responsible for melting, the resultant magmas should be abnormally rich in radioactive materials since these materials would have fractionated into the first melt. Such unusual enrichment of radioactive elements is not observed and this suggestion must be discarded. Clearly none of the above mechanisms can adequately account for widespread occurence of calc-alkaline batho- liths. The plate tectonics model has stimulated new 25 interest in relating the origin of granitic batholiths to plate boundaries. The widespread occurrence of Mesozoic batholiths around the Pacific basin strongly suggests that generation of batholiths is related to subduction zones and corresponding magmatic activity. The crust overlying an active subduction zone would be subject to repeated episodes of penetrative convection. The thermal structure of the crust would be altered, perhaps to the point of producing crustal melts. The following section discusses two models of such penetra- tive convection and evaluates their role in crustal fusion. PENETRATIVE CONVECTION AS THE SOURCE OF HEAT In regions of extensive penetrative convection, analysis of the movement and behavior of individual magma bodies involves many interacting variables. Some of the magma diapirs make it to the surface, while others are undoubtedly emplaced at various levels in the crust. In order to assess the role of penetrative convection of mantle derived magmas in the production of crustal melts, two models are evaluated: The static model (Model I) and the dynamic model (Model II). The static model has as its essential feature the intrusion of a basaltic or andesitic magma derived from the upper mantle, into crustal material and the subsequent cooling and crystal- lization at a given depth. The potential for producing crustal melts in the surrounding rock by this mechanism is evaluated. In the dynamic model, the effect of rapidly rising magma diapirs on the thermal structure of the crust is evaluated. As envisioned, melting in the crust is a response to a period of penetrative convection in a region over- lying a subduction zone. Model I and Model II as dis- cussed above might be regarded as end member models. A likely scheme of crustal melt production involves 26 27 extensive preheating of crustal material via Model II, Vfollowed by emplacement of a mantle derived magma as suggested in Model I. Each of the component processes will be considered individually thereby placing meaning- ful thermal constraints on crustal melt production. STATIC MODEL The simple model envisioned is that a mantle derived basaltic or andesitic magma intrudes crustal material, has its upward movement arrested, and cools by conduction. The liquidus temperature of the magma ranges from 14000 C. to 12000 C. and its solidus temperature from 12000 C. to 10000 C.(Maaloe, 1973). If the magma rose adiabatically from the source region, an additional 2000 of superheating might be expected. The initial water content is undoubtedly low and the latent heat of crystallization is approximately 100 cal/gm (Jaeger, 1968). The thermal properties of basalt in- cluding conductivity(K), diffusivity(k), and specific heat(C) are listed in Clark(l966). The surrounding country rock has an initial temperature which is a function of its depth and the amount of preheating. Melting is assumed to take place along the cotectic trough in the system Ab-An-Or-HZO-Qtz. The bulk of the water in the system is assumed to be tied up in the hydrous minerals(Brown, 1973). Following Wyllie's definition of Type II melting, the first melt will form with the breakdown of biotite. 28 29 At a depth of 35 kilometers, the temperature of incipient melting would be about 8000 C.(Figure 2). The melting interval is approximately 3000 giving a liquidus temperature of 11000 C. The latent heat of fusion for granitic material is roughly 50 cal/gm. values for the other thermophysical properties are given in Clark(l966). A magma in the earth's crust would be expected to undergo vertical convection(Kadik and Yaroshevsky, 1972). This convection would result in an extremely efficient vertical transfer of heat compared to transfer of heat in the horizontal direction. One might therefore expect the thermal effects of intrusions to be con- centrated at the top of the magma body. Mathematically, this allows consideration of a one-dimensional heat transfer problem, thereby simplifying the calculations necessary. The primary variables influencing the crystal- lization and melting behavior are: a. pluton size expressed as half-width; b. temperature; c. specific heat and conductivity of the magma; d. crystallization interval; e. latent heat of crystallization; f. ori- ginal temperature of country rock; 9. conductivity 30 and specific heat of country rock; h. latent heat of fusion of crustal material; and i. melting tempera- tures of crustal materials. To simplify the analysis, the following assump- tions are made: 1. The temperature varies along the x-direction only; a one-dimensional problem is being considered. 2. Conduction is the only heat transfer mechanism. 3. The volume change during the solidification and melting process is negligible. 4. Melting and crystallization occur over a range of temperatures. 5. In both the crystallization and melting processes, the latent heat effect occurs uniformly throughout the melting interval between the liquidus and solidus. 6. The liquid does not separate from the solid in the country rock during the melting process. 7. There is no internal heat generation except for the latent heat of fusion released when the basalt crystallizes. 8. The initial temperature is uniform and at time t = 0, a magma of uniform temperature to is intruded. 31 MATHEMATICAL STATEMENT OF THE MODEL The calculation of cooling histories of igneous intrusions is the subject of a series of papers by Jaeger(l957; 1959; 1961) and Lovering(l936). Following Jaeger's notation, the above geological model can be formulated in mathematical terms. The initial conditions can be described by a temperature distribution: T in region -1 4 x 4 l I To in region ix) 7 l T(x,0) = with the boundary condition: T(oO,t) = T0 for all t where t - time x - position ratio = y/a where y - distance from center of intrusion a - half-width of intrusion TI - initial temperature of magma T0 - initial temperature of country rock T(x,t) - temperature as function of x and t. The region -l<:x<.l corresponds to the magma body and the region lxl>l to the surrounding country rock. Without latent heat of crystallization and melting effects in the country rock, the temperature history of 32 the region could be written immediately from Carslaw and Jaeger(l959, p. 54). The effects of latent heat of crystallization and latent heat of fusion for solid solution melting can be adequately treated by using temperature variable specific heat as suggested by Jaeger(l969). Slow temperature increase between solidus and liquidus can be regarded as an apparent increase of specific heat. If the latent heat is assumed to be uniformly consumed throughout the melting interval, the equivalent specific heat is defined by equation 1. C2' = C2 + L (l) where C2' — equivalent specific heat C2 - true specific heat L - latent heat of fusion T1 - liquidus temperature T2 - solidus temperature A similar relationship applies to the solidification within the basaltic magma. An additional modification of the analytical solutions described by Jaeger is temperature-variable conductivity. Melting in the earth's crust is assumed 33 to take place at the grain boundaries between quartz and feldspar. Since the conductivity of a liquid is generally less than the conductivity of a solid, it is to be expected that as melt accumulates prior to separation of liquid and solid residue, the bulk con- ductivity of the system should be lowered. Such a change in conductivity will alter the heat transfer effects in the country rock adjacent to the intrusion. With the above modifications, the geological model can be classified as a one-dimensional, transient, variable property, heat transfer problem. The general Fourier heat conduction equation for this problem is: 3 [Knit]: flCAiI (2) dr ax M where x - position coordinates - temperature - density " area T ,0 c - specific heat A t - time K - conductivity For this case, both c and K are functions of temperature. Exact analytical solutions are not an adequate approach in such a situation, and we must resort to numerical techniques. Finite differences is a widely 34 used technique which approximates derivatives in terms of differences. The finite difference equation equivalent to equation 2 is: (PC)M AOX CITM :- A- (Km-[4KM.TM c‘i 401' 2 _ Kmd+2KM+Kmu~T~u (3) + KmeKmel .T'm“) 2 where m refers to the nodal point number. The cooling history of the flash injected magma must satisfy the above equation as well as the following boundary conditions: a. at the center x = 0 dT = 0 di' b. at the contact between the magma and the country rock qm = qcr where gm is heat flow our of magma qcr is heat flow into country rock c. as x—r-O T(x,t)-r To The boundary conditions plus the set of equations describing the energy balance at interior nodes lead to a set of simultaneous equations which can be solved for temperature as a function of position and time. A computer program written by Dr. J. V. Beck of the Mechanical Engineering Department of Michigan State 35 University has been used to solve the problem. In this program, the modified Crank-Nicolson finite difference form of the equation is used. Because of the tremendous temperature dis- continuity at x = 1, the Newman analytical solution described by Jaeger(l957) for a semi-infinite intrusion was used to obtain a set of T(x,t) at a small non- zero time. The solution was used as the starting solution for the finite difference calculations. The analytical solution accurately describes the thermal history of the region until cooling reaches the center of the pluton or the melting front advances into the country rock. The numerical solution was started at some small value of T depending on pluton size. The time increment ( 6 t) was chosen so there would be at least 100 time steps before complete solidification of the pluton. Nodal point position was selected so that in regions of large temperature gradients(i.e. - near the contact), the _distance between adjacent points was smallest. About fifty(50) points were used between x = 0 and xq = 7, where x = 0 is the center of the pluton and x = 7 is a distance of seven times a half-width from the 36 center. The location of xq was based on Gray's(197l) work which showed that near x = 7, the temperature remained constant. The modified Crank-Nicolsen finite difference methods as employed by Beck are unconditionally stable. The main requirement for an accurate solution is that the intervals J t and Jx be sufficiently small so that the higher order terms neglected in the approxi- mation be negligible. Temperatures obtained for the case of no latent heat effects were found to differ by no more than 30 C. from the exact analytical solution given by Jaeger. 37 GENERAL RESULTS; STATIC MODEL Figures 3, 4, and 5 illustrate the main results of the static model approach. They are graphs of temperature versus position for a series of times up to complete solidification of the intrusion. The position variable is non-dimensional with a value of x = 1 corresponding to the contact between the pluton and country rock, while x = 0 corresponds to the center of the pluton. Temperatures corresponding to the solidus and liquidus temperatures of both the intrusive bOdy and the country rock are indicated on each graph. Out- side the pluton, the area between a curve and the solidus line gives an indication of the amount of melt produced at that time. Similarly, within the pluton, the area represents the amount of liquid remaining. For purposes of this study, the primary variables of interest are pluton size, temperature of the country rock, conductivity of the country rock, and the amount of superheating of the magma. Pluton size was allowed to vary between .5 and 2 kilometers for the half-width value; original temperature of the country rock was varied between 2500 C. and 5000 C.; conductivity was 1300 1100 Temperature 900 700 500 300 38 liquidus solidus T’ magma country rock fill- 1 I 1 1 1 11 1 1 11 1 1 1 1 1 .4 .8 1.2 1.6 2.0 2.4 Figure 3. Position Plots of temperature versus position for magma(ha1fwidth - 1 km.) with initial temperature of 14000 C. intruding cantry rock with initial temperature of 400 C. 39 00 yrs. 1300 * 1i uidus 40000 ygs. 'd _ 80000 y 900 .- o 3 solidus .p v— m H o gmo .. a 500 - ‘*f 300 r- magma country rock d!- 1 1 11 1 1_ 1 1 1 E 1 1 1 l .4 .8 1.2 1.6 . 2.4 Position Figure 4. Plot of temperature versus position for a magma of halfwidth A km. with an initial temperature of 1400 C.ointruding country rock of temperature 500 C. 40 Temperature fir- 00 yrs. 1300 P liquidus 000 mil 1100 \ liquidus 80000 yrs. solidus 900 - _ 59.11.1111; 700 - 500 F 300 ' magma country rock qu— l L l L l l l l l L J l l l .4 .8 1.2 1.6 2.0 2.4 Position Figure 5. Plot of temperature versus position. Specifica- tions are same as Figure 4 except for temperature- variable conductivity in the country rock 41 allowed to change as a function of temperature; and the effect of superheating of 00 C. and 2000 C. was evaluated. The other variables mentioned above were held constant across the runs. Effect of the temperature of country rock: Figures 3 and 4 represent the intrusion of a pluton of half-width of l kilometer into country rock with temperatures of 4000 C. and 5000 C. respectively. Initial temperature of the magma was 14000 C., and the crystallization interval was from 12000 C. to 11000 C. Two-hundred degrees of superheating would be expected if the magma rose adiabatically from the underlying mantle(Presnall and Bateman, 1973). These graphs show clearly that percent partial melting and aerial extent of melting depend strongly on the initial temperature of the country rock. Effect of variable conductivity: Figures 4 and 5 correspond to constant conductivity and variable conductivity respectively in the country rock for the case of a pluton of halfwidth l kilometer and initial temperature 14000 C. invading crustal rocks of temperature 5000 C. Two differences are apparent. The 42 contact temperature reaches a higher value for the variable conductivity case indicating that percent partial melting is higher in the region directly adjacent to the contact. The total amount of melt is however, greater in the constant conductivity case. In both cases, the effects are relatively minor, and the assumption of constant conductivity is justified for the melting process. Effect of pluton size: Several runs were made varying pluton halfwidths from .5 kilometer to 2 kilometers for a country rock temperature of 5000 C. As expected, the total amount of melt produced is greater for the larger plutons. However, in terms of non-dimensional distance, the melting fronts advance to a similar position roughly one(l) halfwidth into the country rock. Effect of superheated magma: Several runs were made to evaluate the effect of superheating of the magma body. As might be expected, the superheated pluton produces more melt in the sur- rounding country rock, but the results in the case of 43 superheating are not dramatically different. This reflects the tremendous effect of latent heat of crystallization on the melting process. DISCUSSION: STATIC MODEL Results of the above analysis are as follows: 1. a significant amount of crustal melt can be produced by the emplacement of a mantle derived magma 2. the amount and extent of melting is a function of the original temperature of the crust, size of the magma body, and temperature of intruding magma. 3. little melting will occur unless there has been substantial preheating of the crust above the 2500 C. temperature in- dicated by Lachenbruch(1968) for the lower crust. These results can be directly applied to the generation of batholiths. Batholiths involve a spectrum of rock types, mainly intermediate in com- position. As many authors have pointed out, neither simple anatexis of crustal rocks alone, nor fractional crystallization of a basaltic magma can provide a satisfactory explanation of their petrogenesis. Partial 44 fusion of crustal material yields liquids richer in silica than the major rock types in batholiths. Fractional crystallization of basaltic magma would not yield suf- ficient quantities of intermediate rock types to ade- quately account for the petrogenesis of batholiths. Combination of partially fractionated mantle derived magmas with anatectic crustal magmas may provide a more reasonable explanation. Such a mechanism is sup- ported by lead, strontium, and rubidium isotope studies which indicate that mantle source material is involved in the petrogenesis(Hurley, Bateman, Fairbairn, and Pinson, 1965). Hurley and others(1965) showed that the initial Sr87/Sr81 ratios for granitic rocks of the Sierra Nevada Batholith are intermediate between those of mantle and crustal material. They suggest that a mixture of 1/3 mantle with anatectic melt could produce the observed ratios. Piwinskii and wyllie(1968) give further support to this mixing model by suggesting that hybridization of partially crystallized basalt with anatectic crustal melt would produce liquids of intermediate compositions, sim- ilar to those in the batholiths. The thermal calculations of this study support the feasibility of such a mechanism 45 by showing that significant amounts of crustal melt coexists with differentiated basaltic magma through- out a substantial portion of the crystallization interval. This process is illustrated in Figure 4. At a time 40,000 years after emplacement, the basaltic magma is only 75% crystallized. In the country rock at the same time, an approximately equivalent amount of melt has been produced. At the contact, percent partial melting is about 70%. The melting front at this time is at a distance of l kilometer away from the contact. Depending on the amount of convection in the magma chamber, the relative viscosities of the two magmas and the ability of the crustal melt to separate from the solid residue, it might be expected that mixing of magmas would result(Wager and others, 1965). Once mixing occurred, the hybrid magma could then rise and be emplaced at a shallower level in the crust. This model requires substantial heating of the crust above the normal levels, prior to the emplacement of the basaltic magma. Without preheating, little melting would occur and there would be no possibility for mixing of magmas. The next section suggests a mechanism for such preheating and shows the relation- ship between calc-alkaline batholith activity and plate dynamics. DYNAMIC MODEL Clearly the region directly above the sub- duction zone in island arc regions is one which has undergone extensive penetrative convection. Turcotte(l973), Oxburgh and Turcotte(l97l), Toksoz, Minear, and Julian(l97l), and Uyeda(l970) in discussions of the thermal structure of island arcs relied on extensive penetrative convection in order to account for the high surface heat flows. As the buoyant magmas rise toward the surface, they are slowed as they enter regions of higher viscosity, and lose part of their original heat content to the surrounding rocks. It has been suggested that semi- continuous eruptions in such a zone would eventually heat the lower crust to the point of partial melting (Presnall and Bateman, 1973). The purpose of this section is to test the feasibility of such a mechanism for producing crustal melts, and to thereby evaluate the role of penetrative convection in altering the thermal structure of the crust. The amount of heat lost in transit by an individual magma body is a complex function of the initial magma temperature, the size of the individual 46 47 magma bodies, the rate of ascent, and the temperature of the surrounding crust. While the exact nature of the heat transfer is not amenable to solution, it is possible to estimate the heat lost by comparing the temperature of the magma when it penetrates the base of the crust to the temperature of the magma at the time of eruption. Combination of such estimates with estimates of the volume of magma ascending through a unit horizontal area per unit time(magma flux) in island arc regions makes it possible to evaluate the effect of extensive penetrative convection on the thermal structure of the crust. Al- though these estimates are a first approximation, such calculations should provide meaningful thermal con- straints on crustal temperature. Figure 6 provides the essential features of the calculations described above. Magma generated in the subduction zone or mantle directly above the sub- duction zone penetrates the base of the crust. Presnall and Bateman(l973), from an analysis of Green's data on crystallization of hydrous andesite, estimate that the andesite magma reaches the lower crust superheated with a temperature of approximately 14500 C. This assumes the 48 Ls TART I { , Magma generated in sub- _ duction zone under water Tempegature deficient conditions E23: :02- Magma rises adiabatically _Tempegature» + C(l450°) and penetrates crust 1450 C. 5:2: :02: At eruption - 20% of 1Tempe5ature + C(llSOO) magma is crystallized 1150 C. Estimate of magma flux yields total number of grams per unit time contents yields estimate Difference in heat J ‘of heat lost per gram Heat lost/gram coupled which passed with number of grams per through the unit time yields heat area generation per unit time Duration of ‘ volcanic activity re- lated to plate dynamics f Heat generation per unit time coupled with specific heat + duration of volcanic activity yields temperature rise ,_1_. ‘ END Figure 6. Flow chart for dynamic model calculation 49 magma is water deficient(l% water) and rises adia- batically through the upper mantle. If the andesite was water saturated, it could exist at lower tem- peratures, but such a situation must be rejected be- cause upward movement of water saturated magma is difficult(Cann, 1971). In addition, it is unlikely that much water is carried down to the depths of andesite magma generation(Wyllie, 1973). Upon eruption as island arc volcanics, the magma has typically between 10% and 20% phenocrysts indicating it has cooled somewhat below the liquidus temperature(Ewart and others, 1973). For a magma deficient in water, the temperature at eruption is therefore close to 11500 C. A reasonable estimate of temperature loss of andesite magma during ascent through the crust is 3000 C. The heat content of a magma is given by equation 4: H = L + c To (4) where L - latent heat of crystallization c - specific heat T - temperature H - heat content per gram 50 This equation can be used to estimate the amount of heat loss per gram of magma as it passes through the crust. Using accepted values of specific heat and latent heat of crystallization, the heat content at the base of the crust is given by equation 5: Hbase = 100 cal/gm + .25(Tmagma) (5) where H - heat content per gram at base base of crust At the time of eruption, the heat content is given by equation 6: = 13 -+ .25(T ) (6) Heruption erupt where Herupt - heat content at eruption Terupt - temperature at eruption L' - amount of latent heat of crystallization left If the magma has partially crystallized, L' is given by equation 7: L' = T - T 1 S x L (7) T - T s where T1 - liquidus temperature TS - solidus temperature T - temperature 51 This assumes that percent crystallization is linearly related to temperature throughout the crystallization interval. The total heat lost is then the difference between the heat content at the base of the crust and heat content at the surface. This loss of heat might then be regarded as an internal source of heat similar to that generated by radioactive decay. From the above analysis, it is possible to compute the amount of heat generated within the crust per gram of magma. In order to translate this into heat generation per unit volume, it is necessary to estimate the magma flux in a region of extensive penetrative convection. Sugimura, Matsuda, Chinzei, and Nakamura(l963) have made such an estimate for the Japanese Islands. They estimate that in the early Neogene, the total amount of magma reaching the surface was approximately 150,000 km3 over an area of 360,000 kmz. Since this is based on a volumetric estimate of the amount of magma reaching the sruface, it is clearly a minimum value for the quantity which penetrates the lower crust. This translates into approximately .41 km of magma passing through each square kilometer over a period 52 of five million years. Using an average density of 2.8 gm/cm3, the total number of grams of magma passing through an area can be estimated. Combining this with estimates of the heat lost by each gram of magma on its ascent through the crust, the total heat generation per unit volume and unit time can be calculated. For the magma flux reported by Sugimura and others(l963), and a temperature drop during ascent of 3000 C., the heat generation is approximately .3 x 10‘13 3 cm -sec calorie. The average value of heat generation in the lower crust by radioactivity is 13 in contrast, about .5 x 10' calorie(Blackwell, 1971). cm3- sec The temperature at any point in the crust is given by equation 8, assuming temperature independent thermophysical properties. T(xrt) = TO (X) + T1(X,t) (8) where T(x,t) - temperature at depth x and time t To(x) - temperature at depth x prior to onset of volcanic activity T1(x,t) - temperature at depth x and time t due to heat generation by volcanic activity 53 Since To is the known geothermal gradient as given by Blackwell(197l), in order to solve for T(x,t), it is necessary to find the solution Tl(x,t). The heat transfer equation for a one-dimensional transient, constant heat production problem is given by equation 9: K)‘T,(x.o + c“ _-_- [Manual ax.‘ a: where K — conductivity q1 - heat generation ,0 - density c - heat capacity Boundary conditions are: x = T1(O,t) = o x ._, co “3.11.9 o ax The solution to this problem is given by Carslaw and Jaeger(l959). Utilizing this solution, it is possible to assess the effect of varying levels of magma flux on the thermal structure of the crust. Figure 7 demon- strates the temperature profile for three levels of magma flux. The temperature profile for all three cases is shown for comparison. Magmatic activity on the 54 level of that observed in Japan does not significantly raise the temperature of the crust. Indeed, at a depth of 35 kilometers, the temperature is raised only 100 - 150 C. after five million years. The lava flux observed by Sugimura and others(l963) is a minimum value for flux through the lower crust since not all magma would reach the surface. In order to bring the lower crust up to the temperature of incipient melting, it would be necessary to have magmatic activity at the base of the crust approximately fifty times that observed at the surface. This suggests that 2% of the total magmatic activity reaches the surface while the remainder is emplaced at various levels of the crust. Such a flux would result in a prohibitively high rate of crustal accre- tion. Uyeda(l970) using surface heat flow measurements, suggested the total magma flux through the crust is only ten to twenty times that observed on the surface. Figure 6 illustrates that 500 to 1000 of crustal heating would be achieved by such levels of activity. It is unlikely that extensive volcanic activity is able to bring all of the lower crust up to the temperature of incipient melting. Substantial 55 .omomb cw auw>wuom owomoflo> oo>nomno on» mmswu cm can .om .oa an couscouo musowooum Hmeuosuoom usomouoou v one .m .m «powwomum Hmauonuoom Hmeuos on» mm H "moowufiocoo mcwuHoE one mpoowosum Hmeuonuoom no uon onsumuooeoa OONH omHH coca ooa 0mm com com com oov com com _ _ _ _ . _ _ . .b.ousmwm OOH — e / muauoa. osoancnon msofiaom msoHHOm topmosHMm msouomncm ov om om 0H undao 56 preheating of the lower crust produces conditions where crustal fusion in the country rock surrounding a magma body is likely, as suggested in the static model. RELATIONSHIP BETWEEN PLATE DYNAMICS AND BATHOLITHIC ACTIVITY It has been established that although melting is not a steady-state phenomena in the crust, mantle derived magmas can provide the necessary heat to make it a viable process for batholith genesis. The ob- served association between batholiths and destructive plate margins suggests that upward transport of andesitic and basaltic magmas along subduction zones may produce environments where crustal melting phenomena are localized. The model of crustal magma production proposed here is one which calls for localized melting around the margins of intrusions of mantle derived magma. The amount of melt is critically dependent on the tempera- ture of the lower crust prior to intrusion. This temperature is in turn functionally related to the amount of magma which has 'passed through' the region. The probability of melting in the lower crust is there- fore unquestionably related to the total volume of mantle magma which penetrates the crust. With frictional heating as the main source of heat for melting along a subduction zone, it is to be expected that a relationship exists between rate of 57 58 plate descent and volume of magma produced(Fitton, 1971). This relationship, once established, would make it pos- sible to relate batholithic activity to the dynamics of plate movement. Different rates of motion will produce different shear strain heating effects. If it is assumed that melting in the subduction zone is at an invariant point, vast amounts of magma can potentially be generated which are uniform in composition(Presnall, 1969). Dif- ferences in heating due to shear effects will then be reflected by different amounts of magma produced. To illustrate, let us assume melting in the subduction zone takes place in a rather narrow zone of ten kilometers. This assumption is supported in both observation and theory. wyss(l973) showed that the thickness of the deep seismic zone in Tonga was about 11 kilometers. Minear and Toksoz(1970) showed that the low conductivity of the mantle coupled with the tempera- ture dependence of viscosity produce a narrow band of high deformation rates. McKenzie(l967) has shown that most of the movement in subduction zones occurs as creep, with only a small percentage being radiated as elastic waves. Most of the stress energy is therefore 59 dissipated as frictional heat within this narrow zone. It is within this zone that melting should take place. The picture of melting envisioned is that when- ever slip rate is high enough, melting takes place on the slip zone. With invariant point melting, the temperature is buffered at the basalt solidus. After this temperature is reached, all additional frictional heating goes into the production of more melt. If we assume the system behaves like a Newtonian fluid, the rate of heat production is given by equation 10(Uyeda, 1970): - 2 w = . v 7 -?r- (10) where ’2 - viscosity v - velocity of descent a - thickness of zone From this we can see that rate of heat production and therefore, rate of magma production is critically re- lated to the viscosity, velocity of plate descent, and thickness of deformation zone. To get an estimate of the relationship between amount of melt produced and velocity of plate descent, we use values of shear strain heating suggested by Minear and Toksoz(l970) for a plate descent velocity 60 of 8 cm/year and l cm/year. The values are 12 12 15.3 x 10- cal/cmB-sec and 3.29 x 10- cal/cmB-sec. Both of these values are at least two orders of magnitude higher than any of the other heating effects in the shear zone, and would therefore be the primary source of heat for the melting process. It is probable the values used for heat pro- duction are much too high through the melting interval. Because of the dependence of shear strain heating on viscosity, and dependence of viscosity on the amount of melt present, shear strain heating should be drama- tically decreased with the onset of melting. Shaw(l969) demonstrated that viscosity of solid melt systems varies from 1021 poise for the unmelted to 101 poise for the completely molten basalt. Shear strain heating should drop by a similar proportion. In the shear zone, frictional heating should therefore become negligible after small amounts of melting(‘710%). Shaw demon— strated that for relatively small amounts of melt fraction(<.5%), the viscosity remains relatively con— stant. Therefore, it is reasonable to assume that the value of shear strain heating will also remain relatively constant through small amounts of melting. 61 Frictional heating will occur in the top few kilometers of the descending slab. The temperature in this zone is raised to the basalt solidus at about 150 kilometers. The exact depth is dependent on the rate of descent. The temperature is buffered at the basalt solidus, and any subsequent heat available is consumed in the melting process. After small amounts of partial melting(4(5%), shear strain heating would be reduced by several orders of magnitude, and little additional melt is produced. Following Weertman's(l972) analysis of bubble coalescence in the shear zones, the magma bubbles will coalesce into fewer bubbles which are of sufficient size to rise buoyantly into the over- lying mantle and crust. Following removal of the melt, the viscosity of the system is again raised to the level where significant shear strain heating occurs and the process repeats itself. In order to assess the effect of variable rates of plate descent on this process, we can look at the length of time required to produce a given amount of melt under the two rates of plate descent discussed by Minear and Toksoz(1970). With a plate descent of 8 cm/year, 5% melt in the shear zone would be achieved 62 in approximately 1150 years. With a plate descent of l cm/year, this same amount of melt would be produced in 4600 years. Therefore, it can be concluded that differing rates of plate descent dramatically affect the volume of volcanic materials which pass through a portion of the crust per unit time. we might then define two critical rates of plate descent. The first is a threshold value, necessary in order for shear strain heating to raise the tem- perature of a portion of the subduction zone to the basalt solidus. The second critical rate of plate descent might be defined as that rate producing an intensity of magmatic activity, sufficient to trigger crustal melting and the subsequent development of batholiths. More detailed analysis of the production and collection of magmas in the subduction zone will be necessary before realistic estimates can be made of these critical rates. CONCLUSIONS Results of this study support a lower crustal origin for batholiths such as those of the western United States. Temperatures required for partial melting under water deficient conditions can easily be reached by repeated penetration of the lower crust by mantle derived magmas. Providing the crust has been preheated by a period of magmatic activity, emplacement of a magma body has been shown to be capable of generating crustal melt. The potential for production of hybridized liquids of intermediate com- position was verified by demonstrating the coexistence of fluid phases which can undergo mechanical mixing. The following steps chronologically summarize the series of events as envisioned above: 1. Long periods of volcanic activity preheat the lower crust about 1000 C. (Heating above this level would require volcanic activity many times greater than that observed in Japan.) 2. Magmatic activity is directly tied to rates of plate descent in subduction zones, and therefore variable through time. 63 64 After a period of preheating via volcanic activity, a mantle-derived magma intrudes crustal rock and subsequently cools. Emplaced magma undergoes vertical con- vection and heat is efficiently transferred to the top of the chamber. Melting occurs in the region directly above the magma chamber. The amount and extent of crustal melt produced is a function of the size of the magma body, temperature of incipient melting, and original temperature of the crust. I A potential for mixing of magmas occurs as significant amounts of crustal melt coexist with differentiated basaltic magma through- out a substantial portion of the crystallization interval. Hybridization of the coexisting melts via mechanical mixing produces liquids of inter- mediate composition, similar to those observed in batholiths. These hybridized magmas subsequently may rise and be intruded as plutons beneath the cover of volcanic material. These hybridized magmas may be joined by un- differentiated magmas from the mantle. Crustal melts which did not mix with differentiated 65 mantle magmas could also be incorporated, producing the range of compositions charac- teristic of batholithic terrains. The above sequence of events is substantiated by field relationships. Modern examples of batholiths are elongated parallel to consumptive plate margins. A period of volcanism is commonly observed at the start of any orogenic cyc1e(Badgley, 1965). This period is reflected in the ubiquitous occurrence of calc-alkaline mantle- derived volcanics in close spatial association with the granitic plutons. The coastal batholith of Peru is an excellent example(Pitcher, 1972). Over much of its length the batholith is emplaced into a thick layer of volcanic rocks. Individual plutons range in composition from gabbro to potash granite, but the vast majority are intermediate in composition, necessitating magma mixing in their petrogenesis. There is a direct relationship between plate dynamics and the formation of both mantle and crustal melts which lead to batholith formation. There are 66 two critical rates of plate descent; the first rate is that rate necessary to bring the upper portions of the subduction zone to the basalt solidus; the second is defined as that rate which produces an intensity of magmatic activity sufficient to trigger crustal melting and the subsequent development of batholiths. 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