A steady state model for the distribution of stress and temperature on the San Andreas Fault
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Turcotte, D. L.↗
Engineering topics
Turcotte, D. L.
Publications and source records attributed to Turcotte, D. L..
Stress accumulated mechanisms on strike-slip faults
The tectonic framework causing seismicity on the San Andreas and North Anatolian faults can be understood in terms of plate tectonics. However, the mechanisms responsible for the distribution of seismicity in space and time on these faults are poorly understood. The upper part of the crust apparently behaves elastically in storing energy that is released during an earthquake. The relatively small distances from the fault in which stress is stored argue in favor of a plate with a thickness of 5-10 km. The interaction of this plate with a lower crust that is behaving as a fluid damps the seismic cycling in distances of the order of 10 km from the fault. Low measured heat flow also argues in favor of a thin plate with a low stress level on the fault. Future measurements of stress, strain, and heat flow should help to provide a better understanding of the basic mechanisms governing the behavior of strike-slip faults.
Turcotte, D. L.↗
Geoid anomalies and the thickness of the lithosphere
By using accepted crustal density distributions and either error function or linear temperature distributions the difference in geoid height between stable continental areas and deep ocean basins has been determined as a function of the continental lithospheric thickness. If the continental lithosphere were greater than 200 km thick, the geoid anomaly over the continents would be systematically negative in relation to that over the ocean basins. By using the GEM 9 satellite geoid the mean geoid anomalies over ocean basins and stable continental areas have been obtained. No systematic difference between continental and oceanic geoids is observed. It is concluded that the thickness of the continental lithosphere is near 180 km. This is in good agreement with various interpretations of the surface heat flow observations.
Turcotte, D. L.↗
Parameterized convection within the moon and the terrestrial planets
For a fluid layer or a self-gravitating fluid sphere uniformly heated from within, the internal temperature can be parameterized in terms of the appropriate Rayleigh number. The heat generation term includes both radioactive heat release and transient heating or cooling. This parameterization has been verified by comparisons with laboratory experiments. Thermal history calculations have been carried out for the earth, Venus, Mars, Mercury, and the moon. The results for the earth and Venus indicate that two scales of convection are occurring, one including the surface plates and the second occurring beneath the surface plates. In all cases the present heat flows are between seven and twelve per cent greater than the values obtained assuming a steady state balance between heat flow and internal heat generation.
Turcotte, D. L.↗
On isostatic geoid anomalies
In regions of slowly varying lateral density changes, the gravity and geoid anomalies may be expressed as power series expansions in topography. Geoid anomalies in isostatically compensated regions can be directly related to the local dipole moment of the density-depth distribution. This relationship is used to obtain theoretical geoid anomalies for different models of isostatic compensation. The classical Pratt and Airy models give geoid height-elevation relationships differing in functional form but predicting geoid anomalies of comparable magnitude. The thermal cooling model explaining ocean floor subsidence away from mid-ocean ridges predicts a linear age-geoid height relationship of 0.16 m/m.y. Geos 3 altimetry profiles were examined to test these theoretical relationships. A profile over the mid-Atlantic ridge is closely matched by the geoid curve derived from the thermal cooling model. The observed geoid anomaly over the Atlantic margin of North America can be explained by Airy compensation. The relation between geoid anomaly and bathymetry across the Bermuda Swell is consistent with Pratt compensation with a 100-km depth of compensation.
Haxby, W. F.↗
An elastic-perfectly plastic analysis of the bending of the lithosphere at a trench
A number of authors have modeled the flexure of the lithosphere at an oceanic trench using a thin elastic plate with a hydrostatic restoring force. In some cases good agreement with observed topography is obtained but in other cases the slope of the lithosphere within the trench is greater than that predicted by the elastic theory. In this paper the bending of a thin plate is considered using an elastic-perfectly plastic rheology. It is found that the lithosphere behaves elastically seaward of the trench, but that plasticity decreases the radius of curvature within the trench. The results are compared with a number of observed trench profiles. The elastic-perfectly plastic profiles are in excellent agreement with those profiles that deviate from elastic behavior.
Turcotte, D. L.↗
Geoid Anomalies and the Near-Surface Dipole Distribution of Mass
Although geoid or surface gravity anomalies cannot be uniquely related to an interior distribution of mass, they can be related to a surface mass distribution. However, over horizontal distances greater than about 100 km, the condition of isostatic equilibrium above the asthenosphere is a good approximation and the total mass per unit column is zero. Thus the surface distribution of mass is also zero. For this case we show that the surface gravitational potential anomaly can be uniquely related to a surface dipole distribution of mass. Variations in the thickness of the crust and lithosphere can be expected to produce undulations in the geoid.
Turcotte, D. L.↗
Magma production and migration within the moon
Partial melting is likely to have occurred throughout much of the moon due to heating during accretion and the volumetric heating of radioactive isotopes. Important problems that have received relatively little attention concern the migration of the resulting magmas to form surface or near surface volcanic rock. In the paper the basic mechanism for the migration of the magma through the lunar asthenosphere is considered. A porous flow model is proposed. The magma behaves like a liquid flowing through a porous matrix. The volume fraction of liquid present determines the saturated porosity. The differential buoyancy of the magma drives it upwards. It is shown that the per cent partial melt in the lunar interior will only slightly exceed that required to provide interconnecting porosity. Assuming that the radioactive isotopes are preferentially segregated into the magma, the time dependence of the partial melting of the lunar interior is found. It is shown that the total degree of partial melting of the deep lunar interior is likely to be between five and ten per cent.
Turcotte, D. L.↗
On the gravitational potential and field anomalies due to thin mass layers
The gravitational potential and field anomalies for thin mass layers are derived using the technique of matched asymptotic expansions. An inner solution is obtained using an expansion in powers of the thickness and it is shown that the outer solution is given by a surface distribution of mass sources and dipoles. Coefficients are evaluated by matching the inner expansion of the outer solution with the outer expansion of the inner solution. The leading term in the inner expansion for the normal gravitational field gives the Bouguer formula. The leading term in the expansion for the gravitational potential gives an expression for the perturbation to the geoid. The predictions given by this term are compared with measurements by satellite altimetry. The second-order terms in the expansion for the gravitational field are required to predict the gravity anomaly at a continental margin. The results are compared with observations.
Ockendon, J. R.↗
On the evolution of the lunar orbit
It is generally accepted that the earth-moon separation is at present increasing due to tidal dissipation. Values for the corresponding lunar deceleration and the related slowing of the earth's rotation are obtained from astronomical observations and studies of ancient eclipses. Extrapolation of these values leads to a close approach of the earth and moon 1-3 b.y. BP. Periodicities in the Precambrian stromatolites may yield the number of solar days in a lunar month prior to 500 m.y. BP. These data combined with dynamic constraints on the number of solar days in a lunar month indicate a close approach of the earth and moon at 2.85 plus or minus 0.25 b.y. BP. Mare volcanism on the moon and high-temperature Archean volcanism on the earth prior to this date may be due to tidal heating. Strong tidal heating during a close approach could have contributed to the formation of the first living organisms.
Turcotte, D. L.↗
Lithospheric instabilities
In this paper we define a mantle geoid. This is the height that hot solid mantle rock from the asthenosphere would attain if it were not confined by the lithosphere. The mantle geoid lies 3.25 km below the hydrogeoid (sea level). Hot mantle rock cannot entirely penetrate the continental lithosphere. One consequence of this partial penetration is rifting; as a result of rifting an accreting plate margin may be created. Hot mantle rock from the asthenosphere can penetrate through the oceanic lithosphere if the sea floor lies below the mantle geoid. Penetration of the oceanic lithosphere by this solid mantle rock is a necessary condition for the initiation of subduction. We argue that the same processes that are associated with rifting in continental lithosphere will be associated with behind arc spreading and the initiation of subduction in the oceanic lithosphere.
Turcotte, D. L.↗
Numerical calculations of the cross-section for the accretional capture of the moon by the earth
If a primary body is increasing in mass the hyperbolic orbit of a secondary body can become an elliptic orbit. In order to determine the cross-section for the accretional capture of the moon by the earth, a series of numerical calculations has been carried out. Calculations have been carried out for various orbital ellipticities and separations and for various accretion rates. Accretional capture is favored if significant accretion occurs in a period of less than 100 yr. A window for accretional capture occurs if the minimum initial separation of the earth and moon (in astronomical units) is nearly equal to the initial heliocentric lunar eccentricity.
Nordmann, J. C.↗
Accretional capture of the moon
The effectiveness of accretional capture is studied with the aid of a simple model involving a small secondary body in a hyperbolic orbit which approaches a large primary body. When the separation is a minimum, the mass of the primary body increases. An investigation is conducted regarding the conditions under which this change in mass will result in an elliptic orbit with capture.
Clark, S. P., Jr.↗
Evolution of the Moon's orbit and the origin of life
Indications about the past history of the lunar orbit that are yielded by palaeontological data derived from periodicities in fossil corals are shown to suggest that the moon approached the earth 2,850 plus or minus 250 Myr BP. Convergent evidence in the geological record indicates that a pulse of high temperature volcanism occurred about 2800 Myr BP. The implied catastrophe roughly coincides with the first records of life. It seems within the realm of possibility that a global thermal event might have been involved in the origin of life.
Turcotte, D. L.↗
Convection in the earth's mantle
The computer is used to solve for thermal convection within the earth's mantle. A review of the knowledge of surface displacements and of the present understanding of the mantle and its relevant physical and chemical properties is contained in the paper. Applicable equations assume a Newtonian fluid layer heated from below and within, with gravity acting downward. The numerical method employs finite differences and was constructed with a view toward the faithful simulation of coupling mechanisms. It enables surveying the effect of a parameter using a relatively coarse computing mesh. Some of the results obtained are presented.
Turcotte, D. L.↗
Thermal structure of the moon.
Numerical calculations for the structure of convection cells within a self-gravitating, fluid sphere are used to determine the temperature distribution within the moon. The distribution of surface heat flux is also given. The results are compared with the temperatures deduced from magnetic induction within the moon and with the surface heat flow measurement carried out on Apollo 15.
Turcotte, D. L.↗
Finite-amplitude thermal convection within a self-gravitating fluid sphere.
Finite-difference calculations have been carried out to determine the structure of finite-amplitude thermal convection within a self-gravitating fluid sphere with uniform heat release. For a fixed-surface boundary condition, single-cell convection breaks up into double-cell convection at a Rayleigh number of 30,000, at a Rayleigh number of 500,000 four-cell convection is observed. With a free-surface boundary condition only single cell convection is obtained up to a Rayleigh number of 5,000,000.
Hsui, A. T.↗
Phase changes and mantle convection
Rayleigh and phase change instability for olivine- spinel mantle convection
Schubert, G.↗