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Geodesy in the Year 2000 (1990)
Commission on Physical Sciences, Mathematics, and Applications (CPSMA)

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If One y We Had Better Gravity Data. . . Marcia McNutt Department of Earth, Atmospheric, and Planetary Sciences Massachusetts Institute of Technology Cambridge, Massachusetts INTRODUCTION The Earth science community has entered an exciting new era in which, for the first time, the goal of understanding the full 3-dimensional structure of mass and energy transport within the Earth appears to be attainable. This revolution in Earth science, which will integrate the 2-dimensional surface kinematic pattern of plate tectonics with a 3-dimensional dynamic model, is largely the outgrowth of advances in global digital networks, supercomputing, and satellite geodesy. There is no question but that progress has been hindered by the lack of a high-resolution, extremely accurate, truly global gravity field. In compiling the following list of important problems that could be addressed with better gravity data, we did not confine ourselves to what might be achievable with any particular instrument or mission design. We recognize that a variety of approaches will be necessary, and that in many cases, improvements in the gravity field will be scientifically more significant if coupled with other geophysical and geological observations of similar quality. OCEANIC LITHOSPHERE Our knowledge of the gravity field over -the oceans took a quantum leap forward with the advent of satellite altimetry in the 1970s. Over some areas of the oceans, we actually have better resolution in the gravity field than in the bathymetry. Information on the marine geoid from Geos-3 and SEASAT has led to a significant increase in our understanding of the thermo-mechanical structure and evolution of oceanic lithosphere from the midocean ridges where it is formed to the trenches where it is consumed. Nevertheless, a number of important problems remain to be solved because presently-available altimetric geoids lack sufficient accuracy, resolution, and/or continuity at shorelines. A sampling of some of these problems is given below. Midocean Ridges. According to the theory of plate tectonics, midocean ridges (MORs) are a 2-dimensional volcanic line along which magma rises and accretes to the trailing edges of spreading plates in order to create new lithosphere. With the development of multi-beam swath mapping systems, we now view MORs as complex 3-dimensional structures (Figure 1) consisting of whole new classes of topographic features such 53

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54 as propagating rifts, overlapping spreading centers, 200 km undulations in axial relief, and more minor departures from axial linearity. It is thought that many of these features are the topographic expression of distinct, ephemeral magma chambers (Macdonald et al., 1987), which would produce gravity effects both by virtue of their density contrast as well as via their elastic deformation of the overlying plate (Madsen et al., 1984~. Gravity data would provide key information on the origin and evolution of the features, but are, so far, unavailable at the requisite 1 to 2 mgals accuracy and 2 to 100 km resolution. Fracture Zones. One of the more intriguing observations to emerge from analysis of the altimetric geoid is the failure of the simple plate model to describe the density structure of adjacent lithospheric plates of different ages across fracture zones. For example, Figure 2 shows the size of the geoid step across the Eltanin Fracture Zone as a function of average age of the contiguous lithosphere. Theoretical thermal models predict a constant geoid step at all ages for the half- space cooling model of the lithosphere, with the step gradually decreasing with increasing age for plate models such as that of Parsons and Sclater (1977~. Contrary to these predictions, the observed geoid step rapidly decreases at young ages and suddenly reappears at older ages. A similar pattern has been observed on the Udintsev, Ascension, and Falkland-Agulhas fracture zones (Cazenave, 1984; Driscoll and Parsons, 1988; Freedman, 1987~. In addition to conductive cooling of thermal plates with differing ages, several other factors undoubtedly contribute to the geoid signature of fracture zones. Based on geoid, gravity, seismic, or topography studies, the effects of lithospheric flexure (Sandwell and Schubert, 1982), thermal stress (Parmentier and Haxby, 1986), crustal structure (Detrick and Purdy, 1980), peridotite intrusions (Fox et al., 1976), small-scale convection (Craig and McKenzie, 1986) and hot spot volcanism (McNutt et al., 1989), have all been suggested as significant. The best present geoid data do not have the accuracy or resolution to sort out the various contributions of these processes to the density structure at fracture zones. We need a gravity field accurate to 1 mgal at resolution of 50 km or less. To realize the full potential of such data, gravity field modeling must be also constrained by better topographic data from the oceans and seismic information on crustal structure. Until such data is forthcoming, we must question the adequacy of the thermal plate model in describing the density structure of fracture zones. Subduction Zones. The largest gravity anomalies on Earth occur at trenches where oceanic lithosphere is subducted into the mantle. These zones are responsible for creating the greatest thermal, seismic, and geochemical anomalies found within the upper mantle. The underthrust plate is flexed and deformed by a number of loads, including stresses from motion relative to the convecting mantle, the weight of the overlying plate, the negative buoyancy of its own cold mass, thermal stress, and the density changes associated with phase changes in the mantle. With seasurface gravity we have observations (Watts and Talwani, 1974) and altimeter observations (McAdoo and Martin, 1984), we

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55 have been able to calibrate the rheology of the deformed lithosphere. Earthquake hypocenters (e.g., Isacks and Barazangi, 1977) and travel time anomalies (Creager and Jordan, 1984) provide maps of the geometry of the downgoing plate. Thermal plate models allow us to calculate the load associated with the cold slab (Toksoz et al., 19711. If we had a gravity or geoid map continuous from the undeformed seafloor, across the outer rise, trench, forearc, and island arc to the overriding plate, we would be able to calculate the stresses acting on the underthrust plate, and thereby learn much about lithosphere/asthenosphere interaction and aspects of mantle rheology, such as the degree to which the lower mantle resists slab penetration (Hager, 1984~. The large amplitude of the anomalies leads to accuracy requirements of only 5 to 10 mgals at 100 to 200 km resolution for studying plate interactions, and 5 mgals at 1000 to 3000 km resolution for investigating mantle rheology. The necessity of having a field that spans the transition from ocean to continent leads to the requirement that at least some of the data be obtained using non-altimetric techniques. Midplate Swells and Plateaus. The world's ocean basins contain more than 100 areas of elevated seafloor which extend at least 1000 km and stand more than 2 km above the adjacent oceanic crust. These features are generally classified as either oceanic swells, which are capped by active hot spot volcanoes, or plateaus, which display steeper margins and flatter tops. Gravity data collected by geodetic satellites are one of the primary means of studying the thermal and mechanical perturbations that occur when midplate swells or plateaus form. For example, the amplitude of the geoid high over midplate swells has been the key observational constraint used to argue that the base of the lithosphere has been reheated by an upwelling mantle plume since the compensation depth is 60 to 70 km (Crough, 1978; McNutt, 19871. The large amplitude (10 m) and long wavelength (~1000 km) of the geoid signature from the thermal anomaly responsible for uplifting swells is more than adequately mapped by the altimetric geoid data presently available over the oceans. However, more precise gravity data with better resolution would contribute to studies of midplate swells in an indirect, but significant way. Gravity anomalies with an accuracy of a few mgals and with wavelength of 30-SO km have been the principal observational constraint used to measure the flexural rigidity or elastic plate thickness of the oceanic lithosphere (Figure 3) supporting the individual hot spot volcanoes capping these swells (Watts, 19781. Because the base of the elastic plate corresponds to an isotherm near 500°-600°C (McNutt and Menard, 1982), by measuring the elastic plate thickness as a function of distance along the subsiding thermal swell as it moves past the hot spot, we can chart the depth to the 500°-600°C isotherm as a function of time (McNutt, 1984~. This view of the evolution of one isotherm provides a strong constraint on the details of the thermal structure imposed by the hot spot that cannot be resolved by the more general integral constraints on low density provided by the longer wavelength geoid anomaly over the long swell. A thorough

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56 understanding of the mechanism by which the hot spot reheats the lithosphere requires such knowledge of the vertical and lateral structure of reheating. The more numerous oceanic plateaus have the following characteristics: Lack of focussed seismicity, non-lineated magnetic anomaly patterns, (generally) calcareous sediment caps, crustal thickness in excess of 15 km, and topographically-correlated geoid anomalies (Carlson et al., 1980; Nur and Ben-Avraham, 1982; Sandwell and Renkin, 1987~. In total area, oceanic plateaus cover more than 3% of the seafloor. Therefore, they must play a significant role in both the evolution of the ocean basins and the formation of collision-type margins (Vogt, 1973; Ben-Avraham et al., 19819. Nevertheless, the origin and subsurface structure of these features remain enigmatic. Are they continental fragments or oceanic in origin, formed by excess volcanism at or near midocean ridges? The thick pelagic caps make direct sampling by dredging and even drilling difficult. Seismic refraction data are not always available, and in at least one case (Ontong-Java), the same set of travel times have been used to argue for both continental and oceanic origin. Since continental-type plateaus would have deeper isostatic roots than oceanic ones, gravity data provide important information as to the origin of plateaus. Satellite altimeter data have been used to estimate depths of compensation for a number of plateaus from the slope of geoid height versus topography (MacKenzie and Sandwell, 1986~. For smaller plateaus, the accuracy of this procedure is limited by the accuracy and coverage of existing satellite altimeter data. A complete gravity/topography study requires a field accurate to 1 mgal at resolution of 50 km and greater. Distribution of Volcanoes. Although the most prominent islands and seamounts occur as chains (on fast-moving plates) or clusters (on slow-moving plates) formed by hot spots, we suspect that the vast majority of oceanic volcanoes are smaller features erupted in a less organized, but still non-random, manner (Jordan et al., 1983~; Smith and Jordan, 1987~. Several factors control the distribution of oceanic volcanism. First, there must be a large supply of magma beneath the lithosphere. Second, the lithosphere's density and thermal structure must be such that the magma has enough hydraulic head (Vogt, 1974) and latent heat to penetrate it without freezing during ascent (Spence and Turcotte, 1985~. Finally, the lithosphere must remain over the magma pool long enough for the volcano to develop (Gass et al., 1978~. Since the rate at which such seamounts are erupted onto the seafloor is related to the thermal state of both the lithosphere and the deeper mantle, seamount distribution contains information on both thermal properties of the plate and the temporal evolution of the convecting mantle. Almost all oceanic volcanoes lie beneath the ocean surface and thus most remain uncharted. At the present exploration rate, it will take several centuries to map significant portions of the seafloor using ships. It has already been demonstrated that gravity/geoid data can be

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57 used to locate uncharted seamounts (Dixon et al., 1983; Dixon and Parke, 1983; Sandwell, 1984), and for those of known dimensions, the age of the lithosphere at the time of emplacement of a seamount can be inferred from the gravitational signature of the flexural response of the lithosphere caused by loading of seamount (Cazenave et al., 1980; Watts and Ribe, 1984~. Thus, high quality global coverage would allow a more accurate census of the age distribution of seamounts. Such a data set would place constraints on thermal evolution of the lithosphere and the time variability of mantle convection. The requirements for seamount studies are an accuracy of 1 to 5 mgals and resolution of 10 to 50 km. CONTINENTAL LITHOSPHERE The potential for accurate global gravity data to improve our understanding of lithospheric properties and processes is even more apparent for the continents which are considerably more complex and less readily explained by plate tectonic concepts than the ocean basis. For example, evidence is mounting that the differences in the mechanical properties of continental and oceanic lithosphere are not simply explained by the presence of the thick, granitic continental crust, but rather require thermal and/or compositional differences extending to depths of 200 km or more. At present, gravity data accurate +4 mgals at 100 km resolution are publicly available for only 22 percent of the Earth's land area (Figure 4), with political and geographical barriers preventing further acquisition by means of standard ground surveys. In order to comprehend the origin, evolution, and resource potential of that part of the planet which we inhabit, global gravity missions are a primary scientific priority. Rifting and Continental Extension. The global distribution of continents today and the partitioning of their mineral and petroleum resources largely reflects the effects of continental rifting, and yet it is a process about which we understand very little. Does the location of rifting reflect the position of diverging currents in the mantle, a preexisting zone of weakness in the lithosphere, or both? Why do some rifting events fail after a short period of time while others succeed in leading to the formation of new ocean basins? How is the extension partitioned horizontally and vertically in the crust and lithosphere? Gravity data can bring important constraints on the problems concerning continental rifting in several ways. Gravity anomalies over rifts are sensitive to the perturbed crustal structure from lithospheric stretching and any deep thermal anomalies responsible for doming and plate thinning. An outstanding problem in the study of extensional deformation is the disagreement among various measures of extension, such as heat flow, subsidence, and gravity anomalies, as to the total amount of lithospheric thinning in a single vertical column (Royden et al., 1983a,b; Wernicke, 1985~. As compelling evidence for the discontinuous nature of extension in time as well as space (e.g., Wallace, 1984; Glazner and Bartley, 1984; Morgan et al., 1986) has continued to grow, the need for models that go beyond one

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~8 layer extension has been recognized (e.g., Royden et al., 1983 a,b; Hellinger and Sclater, 1983~. With particular reference to the Basin and Range, Wernicke (1985) proposes a simple shear model (Figure 5) for the continental lithosphere in which motion along a low angle detachment allows lithospheric thinning in regions far removed from the surface zone of normal faulting. In general, this geometrical model is capable of explaining thermal uplift on the flanks of rifted regions where no crustal thinning has occurred, although the effects of small-scale convection induced by large lateral thermal gradients have also been invoked to explain the same observations (Steckler, 1985; Moretti and Proidevaux, 1985; Moretti and Chenet, 1987~. Gravity anomalies have the potential to distinguish between these two explanations by providing bounds on the vertical and lateral extent of the low-density material providing flank uplift and by mapping out variations in flexural strength of the lithosphere caused by thermal reheating. Broad constraints on thermal structure would be obtained with gravity data accurate to 1 to 2 mgals with a resolution of 100 km. Specific information on variations in flexural rigidity, given the low elastic plate thicknesses to be expected, would require similar accuracy but a resolution of 20 km or better. Sedimentary Basins and Passive Margins. Sediment deposits in continental basins and on passive continental margins preserve a record of the Earth's geologic history. As repositories for fossil fuels, they represent the most economically significant geologic feature. The principal research topics include: Why do basins and margins subside? Why are the same basins periodically reactivated? Do sediment onlap/offlap patterns on passive margins reflect changes in eustatic sea level or temporal variations in lithospheric rheology? Gravity anomalies bear on these problems in several ways. For example, gravity maps of the Michigan Basin reveal a high-density body at the base of the sedimentary strata thought to correspond to a magmatic intrusion (Haxby et al., 1976). Cooling of this magma body may have supplied the driving force for basin subsidence. Additionally, gravity observations plus data on depths to distinct stratigraphic horizons yield estimates of the elastic thickness of the basin lithosphere as a function of time. The elastic thickness in turn constrains models of the long-term thermal evolution of the basin. Thus, gravity observations supply key information on both the driving forces for basin subsidence and the history of how those forces affect the mechanical behavior of the lithosphere. Global gravity data with ~50 km spatial resolution and accuracy of 1 to 2 mgals is required here. In order to study passive margins, it is particularly vital that we obtain a gravity data set continuous across the coastlines. Mountain Belts. Gravity observations have already played a major role recently in completely overturning the accepted notion that mountain belts on the Earth's surface are compensated by simple crustal thickening through a form of Airy isostasy. Karner and Watts (1983) noted a consistent assymetry in the Bouguer gravity field across the Alps and Appalachians. The Bouguer gravity low, which results from the

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so low-density material at depth compensating the excess mass of the mountains, is consistently offset towards the foreland basin to the west of the Appalachians and to the north of the Alps, while a prominent gravity high, unassociated with any topographic feature and not predicted by Airy isostasy, appears in the hinterland on the opposite side of the orogens-(Figure 6~. Karner and Watts (1983) demonstrated that this gravity pattern is consistent with a model in which the mountains are supported by a stiff elastic plate which has underthrust the mountains from the direction of the foreland in the process of continent-continent collision. The amplitude of the deflection of the elastic plate as revealed by the magnitude of the Bouguer gravity low requires loading by both the mountainous topography and by a buried high-density body in the hinterland, the mass presumably responsible for the Bouguer gravity high. This new model for the structure of mountain belts has thus established the validity of elastic flexure to describe the rheology of continental lithosphere and the existence of subsurface loads to maintain the deflection of foreland basins despite erosion of topographic loads. Despite the importance we now place on buried loads in describing the conditions of mechanical equilibrium at mountain belts, the nature of these buried loads remains obscure. Subsurface loads from cold slabs (Sheffels and McNutt, 1986), dense abducted blocks (Karner and Watts, 1983), and normal stress applied from flow in the mantle (Lyon-Caen and Molnar, 1983) have all been used to supply forces and bending moments to the lithosphere beneath mountain belts. Do all these factors contribute to the compensation of erogenic belts at different times in their geologic evolution, or do the peculiarities of plate collision lead to fundamentally different loading conditions at different locations? We require additional studies of thrust belts at all stages of evolution with a variety of pre-collision tectonic settings (e.g., presence or absence of back-arc basins, different ages of colliding plates, etc.~. A wide range exists on Earth; unfortunately, we lack observations of the gravity field over many, particularly the very youngest collision zones, due to difficult terrain and/or political problems with access. Gravity coverage over continental orogens at wavelengths of 50-100 km (i.e., less than the flexural wavelength of the lithosphere) with an accuracy of 1 to 2 mgals would allow us to test models of lithospheric rheology, mechanisms of plate loading, causes of vertical tectonics in orogens and the details of continental suturing. For example, McNutt and Kogan (1987) used statistics of gravity anomalies in Eastern Europe and Central Asia to argue that steeply plunging continental plates beneath thrust belts are characterized by a low value of elastic plate thickness even for very old lithosphere. They explain their result as the effect of massive brittle and ductile failure of the plates at high strains, as might occur for a plate which behaves according to the theological model shown in Figure 7. The unavailability of unclassified gravity profiles across the orogens used in their study prevents them from testing their hypothesis with forward modeling.

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60 Deep Structure of the Continental Lithosphere. The thickness of oceanic plates has been determined based on the cooling half space model. Generally speaking, it varies from almost zero thickness at the midocean ridges to about 100 km thick beneath old oceanic basins. However, the thickness of continental lithosphere has not yet been agreed upon. The results of seismic studies on the thickness of continental lithosphere are controversial, with maximum thicknesses ranging from no more than 200 km (Anderson, 1979) to over 400 km (Jordan, 1979a). The flexural observations from foreland basins adjacent to mountain ranges point to an asymptotic thermal plate thickness for continental lithosphere of the order of 250 km or greater, at least twice that for oceanic lithosphere. The question remains as to how such a cold continental keel can be maintained against convective destabilization. One viable hypothesis for the deep structure of continents proposes a chemically-induced density reduction in the lower continental lithosphere that offsets the density increase from cooling (Jordan, 1979b). Regardless whether the bottom of the lithosphere is defined as a thermal boundary or a chemical boundary, density anomalies will exist as a depth between 100-400 km across the boundary of a "continental root". This horizontal density variation will give a surface gravity anomaly of about 1-5 mgal. The anticipated wavelength of the gravity anomaly will coincide with the length scale of the continent. Thus, an improved constraint on the thickness of the continental lithosphere can be derived based on improved surface gravity data and proper modeling of mantle thermal structure adjacent to the roots of continents. Earth scientists do not have, at present, a precise global gravity field to search for the gravity signal from deep continental thermal structure. THE MANTLE The problem of mantle convection is fundamental to understanding the evolution of the Earth. The outgassing of the oceans and atmosphere, the differentiation of the crust, volcanism, and all tectonics-- continental as well as oceanic--are ultimately dependent on energy sources within the mantle and core, and upon the transport of this energy and material by flow driven by thermal or compositional buoyancy. The oceanic crust and lithosphere are part of this convecting system: they make up its uppermost, cold thermal boundary layer. Their motion is associated with a flow pattern coming to the surface at the midocean ridges or other rifting areas and returning to the interior at subduction zones. Most oceanic crust, as well as its associated lithosphere, is recycled to the interior. The continental lithosphere, which consists of the continental crust and sizeable pieces of sub- continental mantle, rides on top of the convective system. The velocities of the system are of the order of centimeters per year; the heat transport is an average of 0.08 W m~2. These values, together with the thermal and theological properties of rocks, indicate that the system must be more complicated than the smoothest flow necessary for the observed plate motions. Phenomena such as changes in the plate tectonic pattern on time scales of tens of millions of years, long-term

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61 episodicity of volcanism in tectonically complex areas such as western North America, exceptionally high heat flow on the continental side of subduction zones, and higher than predicted heat flow and topography in some parts of ocean basins, all suggest that there are secondary scales of mantle flow not directly connected to the precisely measured plate tectonic pattern. Observations which see through the lithosphere and into the mantle are needed. The gravitational field provides one such observable. Viscosity of th_ Mantle. The thermal state and mechanical behavior of the mantle are strongly dependent on its viscosity structure. There are two major issues to be resolved. From laboratory creep studies of minerals under mantle conditions (i.e., high temperature and high pressure), it is inferred that mantle rock should deform according to a power law non-Newtonian rheology (Kohlstedt and Hornack, 1981~. However, a Newtonian model for the mantle has been utilized to delineate mantle viscosity structure: such a model can approximately fit both the isostatic glacial rebound data and the gravity data around Hudson Bay in Canada (Peltier and Wu, 1982~. This result can perhaps be reconciled with the laboratory data if volatiles and inhomogeneities within the mantle alter its deformation mechanism such that it resembles a Newtonian fluid. The second issue concerns the magnitude of mantle viscosity. Some studies find that the viscosity of both the upper and lower mantle is about 102i Pa-sec (Wu and Peltier, 1983), while other studies, such as the geoid plus seismic tomography study described in Figure 8, indicate that the viscosity of the upper mantle is 10~9 Pa-sec with the viscosity of the lower mantle approximately one order of magnitude higher (Hager and Clayton, 1987~. Studies utilizing non- Newtonian rheology indicate that the viscosity of the lower mantle is probably not constant but changes with a two- to three-orders-of- magnitude variation across the lower mantle (Karato, 1981~. Geoid highs over subducted slabs can also be explained using a non-Newtonian model (McAdoo, 19829. Both issues can be addressed and plausible mantle deformation mechanisms can be discriminated using a set of gravity measurements that are dense and high resolution, e.g., 1 mgal accuracy over 500 km wavelengths, together with seismic tomographic studies and convection model computations (Hager and Clayton, 1987~. Vertical Scale of Mantle Convection. The vertical scale of mantle flow is a subject of current debate. Geochemical isotopic studies have been interpreted as suggesting the existence of a multilayer structure (Jacobsen and Wasserburg, 1981~. However, geophysical arguments indicate that a single layer convective regime is more likely (Spohn and Schubert, 1982~. If multilayer convection exists, it is hypothesized that the 670 km seismic discontinuity will be the boundary between separate flow systems in the upper and lower mantle. Due to the up- welling and down-going currents associated with mantle flows, undulations or vertical displacements at this boundary will occur with a wide range of wavelengths (Christensen and Yuen, 1984~. Due to the attenuating effects of distance, the ones with most signal will be in the range of several thousand km (Busse, 1981~. The gravitational characteristics of a chemically stratified mantle are quite different

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62 than those of a mantle with uniform composition. Consequently, high resolution gravity data can be used to better delineate the competing hypotheses. The depth of slab penetration can be studied particularly effectively with better gravity data. Based on seismic investigations of travel time (Creager and Jordan, 1984, 1986), subducting slabs are thought to be able to penetrate into the lower mantle. Since seismic anomalies are directly related to density variations, the existence of deep penetrating slabs can be examined with the gravity data derived from the proposed global measurements. The gravitational signature of a deep subducted slab is particularly sensitive to the presence or absence of a chemical discontinuity at 670 km depth. If a discontinuity is present, dynamic compensation of the slab will occur at that depth, resulting in smaller gravity anomalies for a given density contrast. The current long wavelength gravity field (>4000 km) can be satisfied by either a model with normal slab density and mantle-wide flow or a model with high slab densities (caused by phase changes) and a chemical barrier to flow. The models can be discriminated using shorter wavelengths. Since subducting slabs lie beneath island arcs and typically span the ocean-continent transition, altimetric geoids are not sufficient to study this problem and gravity fields such as those obtained by a gravity-measuring satellite are required. The expected signal strength-will be above 0.1 mgal with a length scale dictated by the angle of a subducting slab and the speed of slab subduction; a typical wavelength will be about 1000 km. Small-scale Convection. The existence of small-scale convection (i.e., at horizontal scales much less than plate dimensions) beneath lithospheric plates has been predicted from the observed flattening of the depth-age and geoid-age relations for oceanic lithosphere, from laboratory experiments, and from theoretical convection calculations. For example, the fact that the slope of the geoid begins to flatten over older oceanic lithosphere (Parsons and Richter, 1981) has been one of the key observations in support of the thermal plate model (McKenzie, 1967) which does not allow conductive cooling to extend below about 125 km depth. Presumably, deeper cooling could be prevented by some sort of small-scale convection, such as the longitudinal rolls observed in a layer of constant viscosity undergoing horizontal shear in the laboratory by Richter and Parsons (1975~. Theoretical calculations suggest that longitudinal rolls can exist only if the upper mantle viscosity is extremely low (Yuen et al., 1981) and that they may have a typical horizontal wavelength of about 150 km with an amplitude of 5 mgal (Buck, 1985~. One of the major discoveries of the SEASAT altimeter mission is gravity undulations with the predicted wavelength, amplitude, and orientation in the Central Pacific (Haxby and Weissel, 19861. However, in the Indian Ocean, crossgrain features with the same wavelength but even larger amplitudes (20-60 mgal) are thought to be due to buckling of the lithosphere in response to N-S compression of the Indian plate as it

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~3 collides with Asia (Weissel et al., 1980; McAdoo and Sandwell, 1985~. Even lithospheric boudinage, a pinch and swell instability resulting from platewide tensile stresses (Froidevaux, 1986; Zuber et al., 1986), might be capable of producing some of the crossgrain lineations. Therefore, before crossgrain lineations are used to constrain models of small-scale convection, we must map them with greater accuracy and in more detail to determine their origin. Do these features contain information concerning asthenospheric viscosity, or are they indicative of lithospheric stress and rheology? An improved gravity data set not only will be able to verify the existence or absence of such structures, it will also be able to delineate where such rolls begin and where they terminate as a function of plate age and spreading velocity. An accuracy of 1 mgal at 100 km resolution would allow these features to be traced to 20 percent of their amplitude. Beneath the continents there is direct observational evidence from seismic tomography that small-scale convection also occurs. For example, below the Transverse Ranges in Southern California a curtain of high-velocity material extending down to a depth of 250 km is evidence of convective downwelling of the cold thermal boundary layer at the base of the lithosphere (Humphreys et al., 1984~. This feature may explain the dynamics of the Big Bend of the San Andreas Fault. The gravity signature of this feature is calculated to be up to 15 mgal in amplitude with a wavelength of about 150 km. A model of the local gravity field (Sheffels and McNutt, 1986) indicates that this feature is, to a large extent, compensated from above by flexure of the overlying plates. In this particular instance, both gravity observations and velocity anomaly maps from seismic tomography were necessary in order to understand the interaction of the lithosphere with the asthenosphere. Once we have this system response well calibrated, it may be possible to identify regions of downwelIing beneath continents from gravity and the surface geology alone. Mantle Plumes. While the volcanoes associated with mantle plumes are lithospheric features, the source and ultimate cause of hot spot activity lies in the mantle below. Candidates for the formation and feeding of hot spots include chimney-like thermal plumes (Morgan, 1972), isolated hot blobs (Olson and Nam, 1986), and stripping away of the base of the lithosphere by convective instability (Richards et al., 1987~. For each of these models, it is possible to predict a dynamic gravity model which could then be tested by observation. The depths of origin of hot spots can be addressed by looking at the long wavelength gravity variations. In order to separate the dynamic topography due to deep circulation from crustal and lithosphere effects, understanding the shorter wavelength variations is essential. To do this would require gravity data with an accuracy of 1 mgal at spatial resolution on the order of 100 km. TEMPORAL VARIATIONS IN GRAVITY A less obvious but equally important use of gravity data is the detection of time variations in the field. In most geophysical and

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74 Richter, F. M., and B. Parsons, On the Interaction of Two Scales of Convection in the Mantle, J. Geophys. Res., 80, 2529-2541, 1975. Royden, L., F. Horvath, A. Nagymarosy, and L. Stegena, Evolution of the Pannonian Basin System. 2. Subsidence and Thermal History, Tectonics, 2, 91-137, 1983a. Royden, L., F. Horvath, and J. Rumpler, Evolution of the Pannonian Basin System 1. Tectonics, Tectonics 2, 63-90, 1983b. Rundle, J. B., Deformation. Gravity and Potential Changes Due to Volcanic Loading of the Crust J. Geophys. Res. 87 10 729-10 744 ~ , ~ ~ , ~ 1982. Sandwell, D., A Detailed View of the South Pacific Geoid From Satellite Altimetry J. Geophys. Res. 89 1089-1104 1984. , . . . Sandwell, D. T., and M. L. Renkin, Compensation of Swells and Plateaus in the Northern Pacific: No Direct Evidence for Mantle Convection, J. Geophys. Res., 4, 2775 - 2783, 1988. Sandwell, D., and G. Schubert, Lithospheric Flexure at Fracture Zones, J. Geophys. Res., 87, 4657-4667, 1982. Savage, J. C., Local Gravity Anomalies Produced by Dislocation Sources, J. Geophys. Res., 89, 1945 - 1952, 1984. Sheffels, B., and M. McNutt, Role of Subsurface Loads and Regional Compensation in the Isostatic Balance of the Transverse Ranges. California: Evidence for Intracontinental Subduction, J. Geophys. Res., 91, 6419-6431, 1986. Smith, D. K., and T. H. Jordan, Seamount Statistics in the Pacific Ocean, J. Geophys. Res., 4, 2899-2918, 1988. Spence, D. A., and D. L. Turcotte, Magma-Driven Propagating Cracks, J. Geophys. Res., 90, 575-580, 1985. Spohn, T. and G. Schubert, Modes of Mantle Convection and the Removal of Heat From the Earth's Interior, J. C-~^¢h~rs. yes 1982. ... . . --., 87, 4682-4696, Steckler, M. S., Uplift and Extension at the Gulf of Suez - Indications of Induced Mantle Convection Nature 317 135-139 1985 , . . . . Toksoz, N. N., J. W. Minear, and B. R. Julian, Temperature Field and Geophysical Effects of a Downgoing Slab, J. Geophys. Res., 76, 1113- 1138, 1971. Vogt, P., Subduction and Aseismic Ridges, Nature, 241, 189-191, 1973. Vogt, P., Volcano Height and Plate Thickness, Earth Planet. Sci. Lett., 23, 337-348, 1974.

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75 Wagner, C. A., and D. C. McAdoo, Time Variations in the Earth's Gravity Field Detectable With Geopotential Research Mission Intersatellite Tracking, J. Geophys. Res., 91, 8373-8386, 1986. Wahr, J. M., Effects of_the Atmosphere and Oceans on the Earth's Wobble, Geophys. J. Roy. Astro. Soc., 70, 349-372, 1982. Wallace, R. E., Patterns and Timing of Late Quaternary Faulting in the Great Basin Province and Relation to Some Regional Tectonic Features, J. Geophys. Res., 89, 5763-5770, 1984. Walsh, J. R., and J. R. Rice, Local Changes in Gravity Resulting From Deformation, J. Geophys. Res., 84, 165-170, 1979. Watts, A. B., An Analysis of Isostasy in the World's Oceans 1. Hawaiian-Emperor Seamount Chain, J. C7~-onhv-~ Red 1978. --r-J ~., 83, 5989-6004, Watts, A. B., and N. M. Ribe, On Geoid Heights and Flexure of the Lithosphere at Seamounts, J. Geophys. Res., 89, 11152-11170, 1984. Watts, A. B., and M. Talwani, Gravity Anomalies Seaward of Deep-Sea Trenches and Their Tectonic Implications, Geophys. J. R. Astron. Soc., 36, 57-90, 1974. Weissel, J. K., R. N. Anderson, and C. A. Geller, Deformation of the Indo-Australian Plate, Nature, 287, 284-291, 1980. Wernicke, B., Uniform-Sense Normal Simple Shear of the Continental Lithosphere. Caned ~Forth .Rr; 92, 108-125, 1985. Williamson, R. G., and J. G. Marsh, Starlette Geodynamics: The Earth's Tidal Response, J. Geophys. Res., 90, 9346-9352, 1985. Wu., P., and W. R. Pettier, Glacial Isostatic Adjustment and the Free Air Gravity Anomaly as a Constraint Upon Deep Mantle Viscosity, Geophys. J. Roy. Astro. Soc., 74, 377-449, 1983. Yoder, C. F., J. G. Williams, J. O. Dickey, B. E. Schutz, R. J. Eanes, and B. D. Tapley, Secular Variation of Earth's Gravitational Harmonic J2 From LAGEOS and the Nontidal Acceleration of Earth Rotation, Nature, 303, 757-762, 1983. Yuen, D. A., W. R. Peltier, and G. Schubert, On the Existence of a Second Scale of Convection in the Upper Mantle, Geophys. J. Roy. Astro. Soc., 65, 171-190, 1981. Zuber, M. T., E. M. Parmentier, and R. C. Fletcher, Extension of Continental Lithosphere: A Model for Two Scales of Basin and Range Deformation, J. Geophys. Res., 91, 4826-4838, 1986.

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76 120°W 1 10° 100° 90° 80° I I ~ To l I I I~ South ~V Am. - ~; ~ ~ 162 mym ,.( ~ 20°40'S area a I I I ACCRETIONGRY PLATE BOUNDARIES Overlopping spread) ng centers and propagati ng rif ts ~1 Transform faults Axis ~ Depth Profi Me Long Wavelength Undulation of the Axis: ~ . ~ Short Wavelength Undulations of the Axis - ~ ~_ _~_ . , SADDLE SADDLE 2500 ~OSC I ~OSC I LARGE 3000 3SOO IRK NS ~ A I Bl C b+~ I ~ PRO PAG ATt NG D I E \\ ~ _elt Segregation Events A- E Need Not Be Synchronous_ | 1 ~ ~ ~50- tOOkm 1 1UPWELLING ~ ~ ~ ~ ~ , ~ ~ ~ , ~ , . ASTHENOSPHERE 1 l 10° 2408 Figure 1. (a) Overlapping spreading centers (OSCs) and propagating rifts on southern East Pacific Rise. Smaller ridge-axis discontinuities such as saddle points, devals, and small, non-overlapping offsets are not shown here. (b) Model for midocean ridge segmentation. Major episodes of melt segregation occur near regions A-E in upper mantle, leading to replenishment and swelling of axial magma chamber. Magma migrates downhill along-strike, away from sources of melt. Small ridge- axis discontinuities occur at distal ends of these magma pulses. OSCs occur where magma pulses have misaligned such that they produce overlapping en echelon offset. From Macdonald et al. (1987~.

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77 200. 150. _ O 100. CO 2 o L1J CD 50. O. 20Q. 150. - LL 1 O 100. u' 50 O. ELTANIN WEST _ `_ _, \ _ ~ Thick plate 1 1 1 it_ 1 a 10. 20. 30. 40. 50. 60. 70. AVERAGE AGE ACROSS FRACTURE ZONE (MY) ELTANIN EAST to ~ 90-km-thick plate - _ _ 60 km ~ . ,1_ 1 ~ 1 b 10. 20. 30. 40. 50. 60. 70. AVERAGE AGE ACROSS FRACTURE ZONE (MY) Figure 2. Geoid slope estimates across the Eltanin Fracture Zone system. The dots represent the observed change in geoid across the fracture zone divided by the age contrast plotted as a function of the average of the ages on both sides of the fracture zone. The continuous curves give the expected relationship between geoid slope and average age for thermal plate models with lithospheric thicknesses of 90 km and 60 km. (a) Data for the western (Antarctic) limb of the fracture zone. (b) Data for the eastern (Pacific) limb. After Driscoll and Parsons (19879.

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78 r Zi am p m id. w Figure 3. Schematic cross section of a midplate swell. The volcano with height ht and density PO loads an elastic plate of thickness Te, which corresponds to the depth to the thermal-controlled elastic/ductile transition. The flexure of the elastic plate is superimposed on a broader midplate swell of height w buoyed up by some low-density anomaly P of thermal origin at depth z. The average depth of the bathymetry below the sea surface and the depth to the oceanic Moho are zig and Zm, respectively. The density of seawater and mantle material are Pw and Pm, respectively. Prom McNutt and Shure (1986~.

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79 o o e~ ~ :L, To to a _ ~ o 0 a 0 it: o SO O O ~ 0 ,,l o o 3 , - O O ,= ~ U) ' - A U] ~ 5 O ~ a' , U O · ~ ~ ~ O C5> O SO N by .,4 O in, fU O O CU to ID a,

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80 'mime" Normal Fruiting ~. ~ Moho ~=~- ~ ~Ductilc' Stre~d~ng He-'~;~~ i Dilation by l~ru Astheno~e ,~l ~- ', ,~~8rime-Ductik Tronsiffon 1 ~ ~ ~ Con pectins (0J Asthenosphere Incipient Detoc~men1 ~\'':~;~- _It~e _ Ash Surfoce mbr~cote Norma Faulting ~. /~\/,'/~/''`~/'1//`,~7 ~ , , , , ~ . . ~ __ ~ ~ ~_ ( b ) Ast~ ___ Figure 5. End-member models of strain geometry in zones of lithospheric extension. (a) 'tPure Shear' model, in which crust and mantle lithosphere are attenuated uniformly along any given vertical reference "Simple-shear" model, in which relative extension of crust along any given vertical line is non-uniform. line. (b) and mantle lithosphere From Wernicke (1985~.

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81 Gravity anomaly Model of f I exure Subsurfoce loading Outer Outer gravity high gravity low \ \ Flexural oulge F lexural basin 1 __ 1 t/ 1 Augur c' // ~MSL / ~, ~/ ~I - I l ~/ , . o km 200 Sub or intro crystal load (P - 3 4 ) ~ me ~ 1 1 Overt Trust length Obducted Crustal ~-~-~~- O l Block L (id- 2 8 gm/c~3 ) Inner gravity high Igloo Lo to - 10 - 20 - 30 4o ad i meets - 2 5 ) Crust (lo- 2 8) km Figure 6. Schematic model of the crustal structure and the predicted (Bouguer or free air) gravity anomaly over a completely eroded orogen. The flexure of the elastic plate on the left side is maintained by the weight of either an abducted block from the overriding plate or some intracrustal load. The gravity anomaly is characterized by a positive- negative couple in which the low in the foreland is due to flexural depression of the basement and the high in the hinterland is caused by the excess mass of the buried load. From Karner and Watts (1983~.

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82 Example of a Continental Rheological Mode] a (low curvoturecese) compress) on quartz flow \~ I 1 olivine flow low ~ | Depth b (high curvature case Stress compression tensl on - Byerle. s Law -: - oho \\ tensl on Byerle's Low ----t1oho Depth Figure 7. Example of how a section of continental lithosphere, if bent to high curvature, can behave as a very thin elastic plate. Elastic stresses for the case of low plate curvature (a) and high plate curvature (b) are superimposed on a possible model for the strength of continental lithosphere as a function of depth. The strength in the upper crust and upper mantle is controlled by frictional sliding according to Byerlee's law. Strength in the lower crust and at the base of the elastic plate is limited by ductile flow laws for quartz and olivine, respectively. For the case of low plate curvature (a), the strength of rocks in the lower crust is not exceeded, and the plate flexes as one unit of relatively large thickness. For the case of high plate curvature (b), the strength in the lower crust is exceeded~so that the plate decouples, flexing as two thin plates. Even though the depth to the elastic/ductile transition is the same for the two plates, the effective elastic thickness for case (b) is only half that for case (a).

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83 Observed Geoid: degree 2-9 a .~ _ ~1 ~ ~ contour lnter~al: 20 m Static Geoid: degree 2-6 contour lntcrvel: 100 m CC-I.M, Slab, T-UM Predicted Geoid: degree 2-9 ~ K~ condom lateral: 20 m Figure 8. Example of how geoid data can constrain the viscosity structure of the Earth. (a) The observed geoid at spherical harmonic degrees 2-9; (b) the predicted geoid from converting seismic velocity anomalies derived from mantle tomography to density anomalies, assuming that they are statically maintained within a rigid Earth. This geoid has the right pattern but the wrong sign. (c) The geoid predicted assuming that the density anomalies used in (b) drive convection in the mantle with an order-of-magnitude viscosity increase between the upper and lower mantle. The total geoid is now the sum of the effects of the density anomalies themselves plus the deformations they induce on the Earth's free surface and the core/mantle boundary. The model provides a remarkably good fit to the observed geoid. Open circles show locations of hot spots. From Hager and Clayton (1987~. i

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84 Geoid Change from Glacial Rebounc} (cm a') it/ Act' _ ~ . ,, -it) +0.035 ,J~7 1' ~ ~ Figure 9. Geoid change predicted from simplified model of postglacial rebound. Units are cm/yr. From Wagner and McAdoo (19869. 10 in - -= 6 8 3 4 Cal c, a: 2 r ; Oceanic Lithosphere Continental Lithosphere Oceanography\ Mantle \. ~ ~ ~\ Convection Rheology I I 1 000 1 00 1 0 1 Horizontal Resolution in km Figure 10. Summary of requirements for gravity measurement accuracy as a function of spatial resolution for the problems discussed here.

Representative terms from entire chapter:

continental lithosphere