Herbert R. Shaw

Mantle Convection and Volcanic Periodicity in the Pacific; Evidence from Hawaii

The thermal-feedback theory of mantle melting proposed by Shaw in 1969 is found to be quantitatively consistent with data pertaining to the evolution of the Hawaiian Ridge. Applicable rate factors are estimated from relations between lava volumes and position along the ridge given in this paper and the radio-metric age distributions given by Jackson and others in 1972. Rate curves derived from these data provide a new method of age extrapolation or interpolation; results indicate that previous methods used to estimate the age of the Hawaiian-Emperor Bend are in error. No definite age is established, but calculations suggest an age greater than 50 m.y. Much more extensive radiometric data are required to define kinematic relations between the Hawaiian Ridge and Emperor Seamount chain. It appears to be firmly established from the work of Jackson and others and from the present study that the evolution of the Hawaiian Ridge has been episodic, with episodes of several different time scales. Average growth rates of the entire ridge system are divided into two regimes with a discontinuity at a position roughly 1,000 km northwest of Kilauea; the estimated age of this discontinuity is about 10 m.y. Other episodes relate to the durations of eruptive sequences along individual or contiguous lines of volcanoes within the en echelon set of locus lines defined by Jackson and others. The latest of these episodes, beginning about 6 m.y. ago, is marked by accelerating volume rates of eruption and accelerating rates of ridge propagation; this episode appears to be approaching a culminating stage represented by the present activity of Kilauea Volcano. The calculated rate of eruption of Kilauea (0.11 km 3 per yr) is virtually identical with a rate independently estimated by Swanson in 1972 using different data. Calculated durations for older locus lines are generally greater than 6 m.y., but major time overlaps occur that are not adequately understood. Episodic behavior of shorter durations also exists relative to growth of individual shields or to synchronous activity on neighboring shields (for example, Mauna Loa and Kilauea). Some of these shorter term effects are partly explained in terms of isostatic factors acting on the lithosphere and asthenosphere. The longer episodes are explained in terms of variations of melting rates in the asthenosphere, governed by viscous heating produced by the interaction of lithosphere translation and both vertical and horizontal shear flows in the subjacent mantle. Accelerations of eruption and propagation rates are explained by melting instabilities in the upper zones of the asthenosphere as a result of thermal feedback. During the latest melting episode, shear stresses in the asthenosphere derived from the rate data as interpreted by the thermal feedback model are in the range 100 to 200 bars; apparent viscosities range from 2 × 10 21 to 4 × 10 20 poise, decreasing with increasing melting rate. In general, a thermomechanical model is shown to be consistent with the idea that oceanic melting spots can be fixed relative to the deep mantle, although this invariance is not completely established. The thermal plume model of Morgan is not definitely ruled out but does not seem to be required for internally consistent interpretations of oceanic chains of volcanism. It is concluded that motion vectors of the Pacific plate cannot be inferred directly from rates of propagation of volcanic chains, because these rates reflect local, not average, relative velocities of lithosphere versus mantle flow. During growth of the Hawaiian Ridge, propagation speeds calculated on the basis of rate data for the southeastern Hawaiian Islands ranged from less than 1 cm per yr near the Hawaiian-Emperor Bend to nearly 30 cm per yr at the present ridge front.

Fractal properties of tremor and gas piston events observed at Kilauea Volcano, Hawaii

We study the fractal properties of shallow volcanic tremor and gas piston events associated with magma degassing at Kilauea Volcano, Hawaii, using data from two dense short-baseline arrays of seismographs deployed near the active crater of Puu Oo on the east rift of the volcano. We found an upper bound on the fractal dimension of a strange attractor common to phase portraits of both tremor and gas piston activities in the range of 3.1–4.5 with a mean of 3.75 over a scale length of the wave field of the order of 100 m. The dimension of the attractor fluctuates over the course of tremor and gas piston episodes within a range comparable to the spatial variations of fractal dimensions found in the wave field. The existence of a categorically stable attractor characterizing both types of activities strongly suggests that the excitation mechanism of tremor is similar to that of gas piston events, which in turn are correlated with visual observations at the volcanic vent. The low value derived for the dimension of the attractor in phase space points to significant self-organization in the process of generation of tremor and offers general constraints on the dimensionality of attractors derived from models of acoustic emission associated with magma flow, vesiculation, and degassing.

Calculated geochronology and stress field orientations along the Hawaiian chain

Abstract A new method has been discovered for calculating ages of the main shield building stages of volcanoes along the Hawaiian chain from Kilauea to the Hawaiian-Emperor bend. The method is based on a graphical technique for hypothetical subtraction of distance intervals that theoretically represent regions of simultaneous volcanism along adjacent or nearly en-echelon loci of volcanism. Distances along the chain, measured from Kilauea, when progressively foreshortened by the distances of hypothetical “collapse” and plotted versus existing age data are found to give linear age-distance relationships. A calibration graph is presented that agrees closely with the measured ages in 17 of the 20 existing dated volcanoes. The criterion for simultaneous activity on different loci is based on the concept of equal azimuths of synchronous volcanic propagation within coeval segments of the chain. This is the predicted relationship when magmatic fluids inject the lithosphere along directions normal to a nearly horizontal least principal stress. It appears that the Pacific plate has been subjected to oscillatory, but principally clockwise, rotations of horizontal stress components during the last 40 m.y.

Hydrogen-Water Vapor Mixtures: Control of Hydrothermal Atmospheres by Hydrogen Osmosis

Experiments at 700�C and 800 bars total pressure demonstrate positive deviations from ideality for mixtures of hydrogen and H2O gases. The deviations are greater than predicted with Stockmayers method. The composition of the mixture and the fugacity of hydrogen are controlled by diffusing hydrogen through metallic membranes. The results give the fugacities of both H2O and oxygen.

Sierra Nevada Plutonic Cycle: Part I, Origin of Composite Granitic Batholiths

Intrusion of Mesozoic batholiths in California and the western North America Cordillera began in the Late Triassic 210 m.y. ago and ended in the Late Cretaceous 80 m.y. ago. Emplacement of granitic rocks was apparently not continuous but was accomplished during five major epochs of intrusion at approximately 30 m.y. intervals, each epoch taking 10 to 20 m.y. to complete. A progressive transgression of epicontinental seas onto the midcontinent occurred during the same interval of time as the batholithic emplacement to the west. A penecontemporaneous deformation near the loci of granitic emplacement and a temporary regression during the major progressive transgression of seas onto the midcontinent are correlated with each intrusive epoch. The locus of Mesozoic granitic rocks was a source of sediments during most of the period of time required to emplace the batholiths; the origin of the batholithic magmas cannot be related only to localized down-warping of geosynclines. The source of the major proportion of the mobile granodioritic magmas of the Sierra Nevada was within the mantle, as is indicated by Sr isotope data. All plutons now exposed in the Sierra Nevada, whether of Cretaceous age or older, were emplaced at depths of a very few kilometers, the shallowest having been emplaced at depths of 4 km or less. The spatial relationships among these synchronous geologic phenomena and the geochemical and geophysical data from the same region are accounted for by a northwestward drift of North America in the region of the western Cordillera of the United States onto and across a Mesozoic feature that had characteristics like present-day oceanic rises.

Fractal hierarchies of magma transport in Hawaii and critical self‐organization of tremor

A hierarchical model of magma transport in Hawaii is developed from the seismic records of deep (30–60 km) and intermediate-depth (5–15 km) harmonic tremor between January 1, 1962, and December 31, 1983. We find two kinds of spatial distributions of magma fractions at depths below 5 km, defined by the fractal dimension D3, where the subscript is the embedding dimension. The first is a focused distribution with D3 = 0.28, and the second is a dispersed distribution with D3 = 1.52. The former dimension reflects conduitlike structures where the magma flow converges toward a summit magma chamber and the fractal dimension tends to zero. The latter dimension reflects multifractal clustering of dendritic fractures where hypocentral domains represent subsets of fractures within spherical domains with an average radius of about 1 km. These geometries constitute a percolation network of clustered intermittent fracture and magma transport. The magma volume of the average fracture is about 2 × 104 m3. A tremor model of magma transport is developed from mass balances of percolation that are proportional to tremor durations. It gives reasonable magma fractions and residence times for a vertical drift velocity of 4 km yr−1 and yields patterns of intermittency that are in accord with singularity analyses of the 22-year time series record. According to the model, sustained tremor is generated by the relaxation oscillations of the percolation network with a dominant frequency of about 1 Hz to obtain internally consistent values of fracture geometry, fracture opening force, and magma supply rate. Calculated tremor frequencies are higher in fracture networks of small volume in harmony with the observed relation between seismic amplitude and dominant frequency of tremor. Tectonic relaxation times of rock stresses versus magma pressures are in fair agreement with the average length of tremor episodes and average period of tremor intermittencies. These observations suggest that a high degree of self-organization is characteristic of the nonlinear dynamics of fracture percolation and coupled tremor processes. Logarithms of frequencies (in hertz) of high-amplitude tremor (1-s period), mean tremor duration (28-min period), and mean onset interval (14-day period) are 0, −3.2, and −6.1, implying broadband maxima in the frequency spectrum of transport at intervals of 103. The next longer period of this sequence, which corresponds to eruptions and shallow intrusions, is about 32 years (10 −9 Hz), comparable to the average eruption intermission of Mauna Loa during the last 150 years (about 20 years). This and other evidence suggest that spatiotemporal universality extends from small to large scales in Hawaiian and other magmatic systems. The apparent universal scaling of frequencies may be more than 15 decades in time (1 s to about 60 m.y.) and 10 decades in length (0.1 mm to 103 km).

Sierra Nevada Plutonic Cycle: Part II, Tidal Energy and a Hypothesis for Orogenic-Epeirogenic Periodicities

The dissipative power of the solid earth tides is the order of 10 19 ergs/sec, or a few percent of terrestrial heat flow. It is proposed that this energy is concentrated along oceanic ridge systems and in the asthenosphere by mechanisms of viscous dissipation involving shear melting. Tidal energy localizes and sustains sources of sea-floor spreading through the melting mechanism, convection and magmatic transfer. Components of this energy enter the continent as magmatic heat either where ridge type sources and continents interact or where lateral motions induce shear zones and viscous dissipation within the continent. Temporal maxima of igneous intrusion into continental crust and related epeirogenic oscillations, spaced at intervals of about 30 m.y., are explained in terms of periodic thermal instabilities in the process of shear melting in the mantle. That is, maxima in rates of magma production in the mantle are relieved by vertical magmatic transfer. This process is coupled with lateral motions of the continent in a way analogous to episodic creep episodes of much shorter period in motions of active fault systems. Calculated periodicities are found to be simultaneously compatible with (l) the Sierra Nevada intrusive epochs of Part I, (2) oscillations in the eustatic curve during the Mesozoic Era, (3) concepts of sea-floor spreading, and (4) the magnitude of tidal power. More profound epeirogenic oscillations, having periods of about 200 m.y., are induced by variations in proportioning of tidal energy dissipation between the solid earth and the epicontinental seas. Thus, the tidal deformations of the earth provide information that leads to a general dynamic theory where magmatism, orogency, epeirogeny, sea-floor spreading and continent migration are systematically interrelated.

Earth tides, global heat flow, and tectonics.

The power of a heat engine ignited by tidal energy can account for geologically reasonable rates of average magma production and sea floor spreading. These rates control similarity of heat flux over continents and oceans because of an inverse relationship between respective depth intervals for mass transfer and consequent distributions of radiogenic heat production.

Magmatic heat and the El Niño cycle

Large submarine lava flows with apparent volumes exceeding 10 km3 have recently been imaged on the deep ocean floor in various parts of the Pacific by means of GLORIA and SeaMarc side-looking sonar surveys. Such flows may produce thermal anomalies large enough to perturb the cyclic processes of the ocean and could be a factor in the genesis of El Nino phenomena. We find that known volume rates of mid-ocean magma production could generate repetitive thermal anomalies as large as 10% of the average El Nino sea surface anomaly at intervals of about 5 years (the mean interval of El Nino events between 1935 and 1984). Likewise, estimated rates of eruption, cooling of lava on the seafloor, and transfer of heat to the near-surface environment could reasonably produce a thermal anomaly comparable to that associated with El Nino. Larger magmatic events, associated with fluctuations in the total magmatic power and seismicity along the East Pacific Rise, are possible at longer intervals and may explain the extreme size of some El Nino events, such as that of 1982–1983.

Reply, on chaos

The letter from Foster Morrison is both provocative and much appreciated. It is a veritable syllabus for an advanced course on everything not as yet resolved by applied mathematicians. Not being one, despite my simplified application of some properties of numbers, it might be best to leave sleeping tigers alone on that score. However, I will venture some responses in the same spirit of enquiry that marks the tone of Morrisons remarks. The points I take up are fairly evident in following the sequence of paragraphs in his letter (if I have missed anything, it is either because the response is implicit in other remarks or there was nothing to add).