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MAGNITUDE of DRIVING FORCES of PLATE MOTION Since the Plate

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MAGNITUDE of DRIVING FORCES of PLATE MOTION Since the Plate J. Phys. Earth, 33, 369-389, 1985 THE MAGNITUDE OF DRIVING FORCES OF PLATE MOTION Shoji SEKIGUCHI Disaster Prevention Research Institute, Kyoto University, Uji, Kyoto, Japan (Received February 22, 1985; Revised July 25, 1985) The absolute magnitudes of a variety of driving forces that could contribute to the plate motion are evaluated, on the condition that all lithospheric plates are in dynamic equilibrium. The method adopted here is to solve the equations of torque balance of these forces for all plates, after having estimated the magnitudes of the ridge push and slab pull forces from known quantities. The former has been estimated from the age of ocean floors, the depth and thickness of oceanic plates and hence lateral density variations, and the latter from the density con- trast between the downgoing slab and the surrounding mantle, and the thickness and length of the slab. The results from the present calculations show that the magnitude of the slab pull forces is about five times larger than that of the ridge push forces, while the North American and South American plates, which have short and shallow slabs but long oceanic ridges, appear to be driven by the ridge push force. The magnitude of the slab pull force exerted on the Pacific plate exceeds to 40 % of the total slab pull forces, and that of the ridge push force working on the Pacific plate is the largest among the ridge push forces exerted on the plates. The high cor- relation that exists between the mantle drag force and the sum of the slab pull and ridge push forces makes it difficult to evaluate the absolute net driving forces. However, the slab resistances appear to contribute more to cancelling the driving forces than the mantle drag force. From stress estimation, it was found that high stresses are concentrated around the leading edge of the downgoing slab. 1. Introduction Since the plate tectonic hypothesis has gained credibility in explaining a variety of geophysical and geological observations, the problem of the driving mechanism of plate motion has become an important subject, and has been closely investigated by several authors (e.g., FORSYTHand UYEDA, 1975; CHAPPLEand TULLIS,1977; RICHARDSONet al., 1976; HARPER,1978; DAVIES,1978; HAGERand O'CONNELL,1981; CARLSONet al., 1983). Plate motion may be closely related to the thermal convection in the mantle. Although mantle convection has been in- vestigated with idealized models (e.g., RICHTER,1973; MCKENZIE et al., 1974; PARMENTIER,1978; DE BREMAECKER,1977; CSEREPES,1982; JARVIS and Mc- KENZIE,1980), it seems rather difficult, at present, to understand the driving mech- 369 370 S. SEKIGUCHI anism of plate motion, in terms of thermal convection in a realistic mantle, because of the uncertainties in the distributions of temperature and viscosity in the mantle. On the other hand, the kinematics of plate motion, i.e. the configuration and the velocity of the plate, is now well understood, on the basis of the spreading rate of mid-oceanic ridges, the strike of transform faults, and the slip vectors of major earthquakes (MINSTERand JORDAN,1978). FORSYTHand UYEDA(1975) ex- amined the driving mechanism of plate motion, by making use of the kinematics of plates. They estimated the relative magnitudes of plate driving forces, on the as- sumption that each plate is in dynamical equilibrium, and obtained the following results: 1) the slab pull is an order of magnitude larger than any other force; 2) the slab pull force is nearly balanced with the slab resistance; 3) the mantle drag exerted on the bottom of the plates, which resists plate motion, is much stronger under the continents than under the oceans. However, all the magnitudes of these forces acting on plates have been treated as unknown parameters, so that the abso- lute magnitudes of these forces could not be directly determined by solving equi- librium equations. Also, in their treatment, slab pull was assumed to be propor- tional to the length of the trench, but this assumption appears simplistic. CHAPPLEand TULLIS(1977) followed an approach similar to that by FORSYTH and UYEDA(1975). They estimated the slab pull in advance, using the analytical solution of McKENZIE(1969) for temperature and density distributions in a down- going slab. They also took account of the focal mechanisms of intermediate and deep-focus earthquakes. It is also stated in their conclusions that the slab pull force is nearly balanced with a resistive force working at subduction zones, al- though it is not clear whether the slab resistance or the colliding resistance cancels the slab pull force. The main purpose of the present study is to estimate the absolute magnitude of various forces that could contribute to plate motion and for better understand- ing of global tectonics, earthquake mechanisms, as well as the plate driving mech- anism itself. The major difference of our study from the previous studies is that we estimate the slab pull and ridge push forces as definitely as possible, before solving the equilibrium equations. Since the thermal structure of oceanic litho- spheres has been well explained in some models (e.g., PARKERand OLDENBURG, 1973 ; SCLATERand FRANCHETEAU,1970), we can calculate the ridge push force, which may be the force arising from density variations in cooling oceanic litho- spheres. The slab pull force resulting from the density contrast between the slab going down from the trench and the surrounding mantle is also calculated in advance. Since the slab resistance plays an extremely important role in the net driving force of plate motions, we investigated, in detail, several different types of the slab resis- tance, such as those exerted along the surface of downgoing slabs and around the edge of the slabs. With these improvements, we shall discuss the results obtained here in comparison with those obtained by FORSYTHand UYEDA (1975) and CHAPPLEand TULLIS(1977). The Magnitude of Driving Forces of Plate Motion 3712. Method In order to estimate the magnitude of the driving forces, we shall use the dynamic equilibrium conditions, following the previous studies (FORSYTH and UYEDA, 1975; CHAPPLE and TULLIS, 1977). The equation of torque balance for plate motions can be written in the form, (1) where subscripts i(=0, •c, N) and j(=1, 2, 3) indicate an index of a plate and a component, respectively, and repeated subscripts k indicate summation over the set of unknown parameter xk. The equation a3i+j ,k includes the geometrical and dynamical factors for the length of arms from the rotational axes of plates, the areas of plates, the length of trenches, the length of the convergence plate boundaries, the thicknesses and the length of the slab, and the relative and absolute velocities of plate motions. The equation b3i+j indicates the ridge push, and c3i+j denotes the slab pull forces. In the present study, the torques to be com- puted are the following two types. The first type is the torque whose directions and magnitudes will be calculated in advance, which includes the slab pull and the ridge push, and the second is those of which directions are calculated, leaving the magnitudes and signs unknown. If we consider 12 plates, then there are 36 linear algebraic equations for the unknown parameters xk. This set of equations can be solved by least squares (e.g., AKI and RICHARDS, 1980). Next, we formulate the magnitude and type of the forces working on all plates. Here, we consider 8 forces, i.e., the ridge push (FRP), mantle drag (FD,), continental drag (FCD), colliding resistance (FCR), slab pull (FSP), slab surface re- sistance (FSSR), slab edge resistance (FSER), and suction (FSC). We know that the first three forces are exerted on the area of plates. However, we assume that the last five forces act on the boundaries of plates, although, strictly speaking, these forces do not exactly act on the boundaries. Resistances along transform faults and pushing forces from hot spots have been neglected in this study, because CHAPPLE and TULLIS (1977) have shown that these forces produce such insignifi- cant torques on the plates. Twelve plates are incorporated in this study (Fig. 1). They are African (AF), Antarctic (AN), Arabian (AR), Caribbean (CA), Cocos (CO), Eurasian (EU), Indian (IN), North American (NA), Nazca (NZ), Pacific (PA), Philippine Sea (PH), and South American (SA) plates. The plate boundaries and the edges of the continents were digitized from Plate 1 of SCLATER et al. (1981). The ages of the oceanic plates are also taken from the same data. We refer to the absolute and relative velocities of plate motions from AM1-2 and RM2 of MINSTER and JORDAN (1978, 1979), respectively. Although AM1-2 has been derived from the assumption that hot spots are fixed at the base of the mantle, there could be an alternative approach to estimate absolute plate velocities, which is based on the assumption that no net torque is exerted on the lithosphere as a whole, and also 372 S. SEKIGUCHI some assumptions about the forces driving plate motions (SOLOMONand SLEEP, 1974). This approach gives absolute plate velocities that are very similar to those calculated on the assumption that a set of hot spots provides a fixed reference frame (SOLOMONand SLEEP,1974). For this reason, even if we use this absolute velocity, the results obtained in this paper would not be seriously affected. 2.1 Ridge push It is well known that there are close relations between the depth of the ocean floor, heat flow and the age of oceanic plates (PARSONS and SCLATER, 1977). These relations can be explained either by a plate model (SCLATER and FRANCHE- TEAU, 1970) or by a thickening model (PARKER and OLDENBURG, 1973; YOSHII, 1973; KONO and YOSHII, 1975).
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