Richard L. Carlson

On modeling the thermal evolution of the oceanic upper mantle: An assessment of the cooling plate model

The plate cooling model for the thermal evolution of the oceanic upper mantle has been widely accepted to explain observed variations of depth to oceanic basement and conductive heat flow with the age of the seafloor. Several estimates of “best fitting” plate model parameters, derived from depth, heat flow, and age data, have been proposed, but the viability of the plate model itself has not been rigorously evaluated. We have used published mean depths and depths to basement at Deep Sea Drilling Project/Ocean Drilling Program (DSDP/ODP) drilling sites to test the plate cooling model based on two criteria: First, viable plate models must have coefficients that are consistent with the slope of the corresponding root t line because the half-space (or root t) subsidence of young seafloor is implicit in the plate model (i.e., the slope of the root t line can be calculated directly from the coefficients of the plate subsidence model). Second, any viable physical model must fit the data with an acceptable degree of systematic misfit; large systematic misfits indicate that the model cannot explain the observations. Fits of half-space (root t) models to depth versus age data for young (< ∼80 Ma) seafloor indicate basal temperatures in the range 1300 to 1370°C. Based on the age at which the depths deviate from the root t line, the minimum plate thickness that is compatible with the best fitting half-space models for young seafloor is 120 km. In contrast, all best fitting plate models yield systematically higher temperatures (1450 to 1470°C) and thinner plates (102–118 km). The plate model can explain the depth to basement at DSDP/ODP drill sites with a satisfactory degree of systematic misfit, but we find that there is no plate cooling model that can explain the variation of the mean depths (derived from the DBDB5 database) with age over the entire range of ages (0 to 165 Ma). Models that “best fit” the entire data set have unacceptably large systematic misfits over the entire range of seafloor age, whereas models that minimize the systematic misfit for young seafloor (0 to 81 Ma) fail for older seafloor. The plate model clearly fails to explain the observations. The cooling history of old seafloor is not simply an extension of the cooling history of young seafloor according to a simple plate cooling model. Previous studies have suggested, as an alternative to the plate model, that observed variations of basement depth with age are best explained by the combined effects of a “normal” half-space cooling process and the dynamic and/or thermal effects of hot spots or mantle plumes. Our results are entirely consistent with the half-space cooling model, and we find that the best reference model for “normal” subsidence is d(t) = (2600±20)m + (345±3)m (m.y.)−½ t½. We also find that the heat flow predicted by this half-space model is consistent with the most reliable average heat flow values from the Pacific.

Subduction hinge migration

Abstract It has been argued that back-arc tectonics is controlled principally by the “absolute” motion of the overriding plate and the migration of the hinge of the downgoing plate. Thus, hinge migration (rollback) is fundamentally important to understanding the geodynamics of back-arc regions, but even rates of hinge migration are unknown. The rate of hinge migration can be estimated if the rate of back-arc extension and the motion of the overriding plate are known. Rates of rollback in a hotspot reference frame range from near zero in the case of the New Hebrides Arc, to 50–70 mm/a at the South Sandwich Arc, and may be as high as 100 mm/a at the Tonga Trench, but the hinge is actually advancing along the Izu-Bonin Trench, as evidenced by the fact that there is no significant active extension behind the Izu-Bonin Arc. The rate of hinge advance increases from north to south along the Izu-Bonin Trench, and correlates well with the dip of the subducted slab. Active spreading in the Mariana Trough may be attributed to a rate of hinge advance which is lower than the rate of retreat of the Philippine plate. All of the possible motions of overriding plates and subduction hinges which might give rise to back-arc opening are represented among the examples considered. Thus, there is no unique circumstance in which back-arc extension occurs. Finally, there appears to be no clear correlation between hinge motion and the age of the subducted lithosphere.

Anomalous crustal structures in ocean basins: Continental fragments and oceanic plateaus

Plateau-like features in ocean basins exhibit crustal structures which differ markedly from the relatively simple, three-layer model which applies to most of the oceanic crust. While some plateaus are known or thought to be fragments of continental crust (e.g. Rockall Bank, Lord Howe Rise), others appear to be of oceanic origin (e.g. Shatsky Rise, Broken Ridge), and their seismic structures, though variable, are significantly different. Continental fragments are similar in structure to continental shield areas: Depth to Moho is typically about 30 km, and the lower crust consists of a 6.8–7.0 km/s layer, 14–18 km thick, overlain by a 5.8–6.4 km/s layer of variable thickness, while velocity structures are variable at upper crustal levels. By contrast, the Moho apparently occurs at shallower levels beneath oceanic plateaus, which are characterized by the presence of a 7.3–7.6 km/s layer, 6–15 km thick at the base of the crust. This basal layer is commonly overlain by units having velocities typical of oceanic layers 2 and 3. Refractors having velocities which correspond to layer 3 tend to occur at deeper levels in continental fragments than they do beneath oceanic plateaus. That high-velocity basal layers have been detected at the base of normal oceanic crust and in some ophiolites suggests that oceanic plateaus are truly marine in origin. Upper and middle crustal levels probably consist of basaltic and gabbroic rocks, respectively. The nature of the basal layer is difficult to assess. Olivine gabbro, mafic garnet granulite, and epidote amphibolite all exhibit velocities in the appropriate ranges, as does a mixture of mafic and ultramafic lithologies. Partially serpentinized peridotite cannot be ruled out on the basis of shear and compressional wave velocities alone.

An asperity-deformation model for effective pressure

Abstract Variations of the mechanical and transport properties of cracked and/or porous rocks under isotropic stress depend on both the confining pressure ( P c ) and the pore-fluid pressure ( P p ). To a first approximation, these rock properties are functions of the differential pressure, P d = P c − P p ; at least for low differential pressures. However, at higher differential pressures, the properties depend in a more complicated way upon the two pressures. The concept of effective pressure, P e , is used to denote this variation and it is defined as P e ( P c , P p ) = P c − n ( P c , P p ) P p . If n = 1 (and therefore, is independent of P c and P p ), the effective pressure is just the differential pressure. We have used an asperity-deformation model and a force-balance equation to derive expressions for the effective pressure. We equate the total external force (in one direction), F c , to the total force on the asperities, F a , and the force of the fluid, F p , acting in that same direction. The fluid force, F p , acts only on the parts of the crack (or pore-volume) faces which are not in contact. Then, the asperity pressure, P a , is the average force per unit area acting on the crack (or grain) contacts P a = F a /A=F c /A−F p /A= P c − (1 −A c /A)P p , where A is the total area over which F c acts and A c is the area of contact of the crack asperities or the grains. Thus, the asperity pressure, P a , is greater than the differential pressure, P d , because P p acts on a smaller area, A − A c , than the total area, A . For elastic asperities, the area of contact A c and the strain (e.g., crack and pore openings) remain the same, to a high degree of approximation, at constant asperity pressure. Therefore, transport properties such as permeability, resistivity, thermal conductivity, etc. are constant, to the same degree of approximation, at constant asperity pressure. For these properties, the asperity pressure is, very accurately, the effective pressure, P c . Using this model, we find that the dynamic (undrained) elastic modulus ( M cr ) of saturated cracks (rocks) at low effective pressure is given by M cr = (1 − P p A′ f )M a + (1 − A f )M f = − w dP c /d w , where M a is the (dry-matrix or crack-) asperity modulus, M f is the fluids modulus, A f is the fractional area of contact ( A f = A c / A ), A ′ f =d A f /d P a and w is a measure of the crack or pore openings. This simple model accounts for the dependence of the rock modulus (and elastic velocity) on: (1) the elastic properties of the fluid, (2) the elastic properties of the dry rock, and (3) the pore-fluid and confining pressures. Explicit expressions depend upon the choice of the asperity- (or grain-) deformation models and their contact distribution functions. The effective pressures for transport properties are different than the ‘effective pressure’ for the mechanical properties. Calculated results based on the ‘bed-of-nails’ model having power-law (or fractal) asperity-height distribution functions can be fitted quite well to experimental data with a minimum of fitting parameters.

Variation of sea floor depth with age: A test of models based on drilling results

Previous analyses of the variation of depth with age in oceanic basins have demonstrated a systematic square root of age dependence in crust younger than 80 Ma. These studies used depths determined from marine seismic data, which have uncertainties due to the assumed sediment velocity. As an alternative, we compiled the basement depths from all DSDP and ODP drill sites that sampled ‘normal’ ocean crust in the Atlantic, Pacific and Indian Oceans, up to recent drilling (Leg 136). We applied further criteria to the data, rejecting any site not formed at a mid ocean ridge, or that did not penetrate extrusive basalts of MORB composition. The remaining high quality data set is small (77 sites), but adequate to test models of the thermal structure of the upper mantle. Our new results also show that the square root of age (t½) variation incorrectly estimates the observed depth for crustal ages older than 90 Ma. However, our data suggest a plate thickness of 104 ± 9 km and a basal temperature of 1400 ± 140 °C, and agree, at all ages, with the recent inversion by Stein and Stein, 1992.

An experimental test of P-wave anisotropy in stratified media

In theory, stratified media in which the layers are elastically homogeneous and isotropic approximate transversely isotropic media with an axis of symmetry perpendicular to layering when the seismic wavelength is sufficiently longer than the layer spacing. The phenomenon has apparently been observed in field measurements, and acoustic anisotropy in deep‐sea sediments, measured in the laboratory, has been attributed to fine‐scale bedding laminations. However, to the best of our knowledge, no rigorous test of the theory has been made. We have made a partial test by making laboratory measurements of compressional‐wave velocities parallel and perpendicular to layering in fabricated samples consisting of glass and epoxy. We found no statistically significant difference between observation and theory in this limited test. Further, having used several frequencies, we found that the velocities progressively change from the long‐wave values toward those predicted by the time‐average relation, as expected. Finally,...

Subduction hinge migration along The Izu-Bonin-Mariana arc

Abstract Hinge migration or “rollback” is thought to have a significant influence on the tectonics of trench-arc-backarc systems. Where the backarc region is actively opening, the hinge is usually either stationary or retreating in a mantle (hotspot) frame of reference. The Izu-Bonin-Mariana system represents a highly anomalous case in which the hinge is reportedly advancing behind the retreating eastern edge of the overriding Philippine Sea plate. We have re-evaluated the motion of the subduction hinge using the best available estimates of the motion of the Philippine Sea plate and estimated maximum rates of extension within the Izu-Bonin Arc: if the plate motions have not changed appreciably, the subduction hinge of the Izu-Bonin Trench has advanced over the last 5 Ma. The approximate average rate of hinge advance is 0–6 mm a−1 at the north end of the Izu-Bonin Arc, increasing to 24–30 mm a−1 at 27°N. The rate of advance of the Mariana hinge (at 18°N) is 10–20 mm a−1. The dip of the subducted slab is strongly correlated with the motion of the Philippine Sea plate, suggesting that the rapid retreat of the overriding plate affects mantle flow. We have found a tentative hinge-advance mechanism in a simple Newtonian-viscous corner flow model. Though the model has severe geometrical and rheological limitations, it suggests that the retreat of the overriding plate gives rise to excess uplift pressures acting on the top surface of the subducted slab. If the hinge is not assumed to be fixed, the excess pressure will tend to rotate the slab arcward, steepening the slab and advancing the subduction hinge. Thus, the westward motion of the Philippine Sea plate may explain both the advance of the subduction hinge and the observed relationship between the motion of the Philippine Sea plate and the dip of the subducted slab along the Izu-Bonin-Mariana Trench.

How crack porosity and shape control seismic velocities in the upper oceanic crust: Modeling downhole logs from Holes 504B and 1256D

Mounting evidence from Holes 504B and 1256D suggests that porosity is the principal factor affecting velocities in the upper oceanic crust. Spheroidal inclusion and asperity compression models based on reprocessed sonic velocity logs and apparent fractional porosities estimated from deep resistivity logs reveal how both porosity and the geometry of the pore space affect seismic velocities in Layer 2. Models that best match the data indicate the following: First, there are three populations of cracks in Hole 504B; most of the transition zone and the dike section are populated by low concentrations of weak cracks, while the upper part of the transition zone and the extrusive pile contain a higher concentration of stiffer cracks. Similarly, the deepest part of the dike section in Hole 1256D can be modeled by a dilute concentration of thin or weak cracks, while the overlying dikes, the transition zone, and the extrusive pile contain a higher concentration of stiffer cracks. Second, in a striking confirmation that porosity controls velocities throughout Layer 2, 90% or more of the variance of sonic velocities logged at both sites is explained by porosity in these models, while third, the effect of pressure on the variation of sonic velocity is essentially negligible. Fourth, while there is no direct correlation between crack populations and igneous lithostratigraphy, some changes of crack population do correspond to metamorphic transitions, and fifth, velocities typical of Layer 3 are reached when the porosity falls to low values (0.2% in Hole 1256D and 0.6% in Hole 504B).

Characteristics of back-arc regions☆

A compilation is given of the geophysical and geological characteristics of 21 back-arc regions published before April, 1982.

The effect of hydrothermal alteration on the seismic structure of the upper oceanic crust: Evidence from Holes 504B and 1256D

It has long been argued but never demonstrated that alteration “fronts” should be recognizable features of the seismic structure of the oceanic crust. The abrupt transition from crust affected by low-temperature hydrous alteration to crust affected by high-temperature hydrothermal alteration must arise from a stepwise reduction of porosity and permeability that should correspond to a seismic boundary. In Holes 504B and 1256D, the sudden downhole appearance of hydrothermal minerals corresponds to a increase of the velocity gradient that is caused by a change of porosity within the lava-dike transition zone, and models of the downhole variation of permeability computed from apparent porosity logs show a corresponding stepwise change of permeability (by a factor of ∼20) that is sufficient to account for the onset of hydrothermal alteration. In principle, the coincidence of the seismic structure with the alteration boundary can be used to interpret the seismic structure of the oceanic crust. In particular, the onset of hydrothermal alteration proves to be a viable candidate for the transition from Layer 2A to Layer 2B, which also occurs within or near the lava-dike transition zone. There is also a systematic decrease of permeability with increasing sonic velocity in both the lavas and the dikes (log(κ) ∼ a + bv). Remarkably, the extrapolated trend for the lavas is in excellent agreement with in situ permeabilities measured in very young crust, ranging in age from zero to 3.5 Ma. To a good approximation, the permeability of Layer 2A can be estimated from its seismic structure.