Modeling of Volcanic Processes

In this review I describe results from experiments conducted by the U.S. Geological Survey in diverse volcanic environments to image velocity anomalies in the crust and upper mantle using teleseismic P-wave residuals. The linear least-squares inversion technique of Aki et al. (1976, 1977) is extensively used in these studies. The seismic models thus obtained are synthesized with available geologic and geophysical data to infer plausible models of magma genesis in these regions. The three-dimensional velocity model beneath Yellowstone Plateau shows a large low-velocity body of approximately 100 km diameter centered on the caldera and extending from the crust to a depth of about 250 km. This is interpreted to be a massive magma body which is responsible for the volcanism during the past 2 m. y. in Yellowstone. Teleseismic S-wave residuals, Raleigh-wave dispersion data, heat-flow, gravity, Curie isotherm depths, and magnetotelluric data, all support the existence of a temperature near granite solidus beginning at a depth of 5-10 km beneath the Yellowstone caldera floor. In the Eastern Snake River Plain (ESRP) a low-velocity anomaly is present in the upper mantle but not in the crust, leading to the speculation that ESRP is the healed track of a northeast propagating volcanic center whose present position is Yellowstone. The seismic model for the ESRP-Yellowstone volcanic system, though unable to distinguish between different models of origin of the system, clearly shows that basaltic magma rises from the mantle, melts the lithosphere and yields massive quantities of rhyolitic magma.

The seismic velocity structure beneath Hawaii, an oceanic hot spot, shows a complex crustal structure with no evidence for a large magma chamber in the crust. However, in the upper mantle there is an elongate north-south trending low-velocity zone, 200 km wide and traceable to a depth of 165 km. Thus, similar hot-spot generation models in the asthenosphere may be applicable to Yellowstone and Hawaii, though the chemistry and volume of surface volcanism is greatly different in the two areas.

In all the six intra-plate silicic volcanic centers which we have probed using the teleseismic-residual technique, low-velocity anomalies, inferred as crustal magma chambers have been found. In at least one such volcanic center, Long Valley in California, uplift and S-wave attenuation measurements support that the magma chamber delineated by tele-seismic residuals is real. The suggestion of a root to the magma chamber extending into the upper mantle supports the geologic model for magma genesis in these centers, namely, infusion of basaltic magma from the asthenosphere into the lithosphere and crust, and resulting partial melting. In contrast to the silicic volcanic centers, none of the andesitic Cascade volcanoes show evidence for crustal magma chambers detectable using the teleseismic technique. Teleseismic-residual data in two volcanoes, Newberry in Oregon, and Medicine Lake in California, show massive high-velocity intrusions in the crust beneath the volcano edifice. A high-resolution seismic imaging experiment has revealed the presence of a low-velocity anomaly which could be a dike-like molten magma pocket within the high-velocity intrusive in Newberry volcano. On a regional scale, the teleseismic residual experiments using long profiles have successfully delineated high-velocity anomalies, possibly related to subduction, in the Oregon Cascades, and a low-velocity anomaly due to asthenospheric upwarp beneath the Rio Grande Rift.

Piton de la Fournaise (Réunion Island) is a basaltic oceanic intraplate volcano. On the basis of geological and geophysical data gathered at the volcanological Observatory since its installation in 1980, and of a detailed geological survey of its activity since 1930 (Bachelery, 1981), a preliminary model of its magma supply and transfer is presented. For the period 1930–1985 the mean magma output rate was 0.34 m³/s, but for shorter time intervals this rate varied between about 0.15 and several m³/s. The cumulative output volume is represented by an irregular sawtooth curve. We distinguish a type A behavior that applies to periods of high magma output rates and a type B behavior corresponding to the intervening periods of lower output rates. The type A periods are relatively short and are associated with eruptions of oceanites and olivine basalts that are both less evolved lavas than the other lavas of the Enclos caldera. It is suggested that the type A periods mark the arrival of new batches of magma in the shallow magma storage complex. According to this model the three oceanite eruptions of 1931, 1961 and 1977, which account for at least half of the erupted volume of lavas of about 50 eruptions between 1930 and 1985, would reflect major pulses of internal magma transfer while less considerable eruptions of oceanites or olivine basalts would represent smaller pulses. The type B period observed since 1977 is analysed; the physical behavior (seismicity and deformation) of Piton de la Fournaise since 1980 and detailed petrological and geochemical studies (Boivin et al., 1984) of the lavas of the eruptions that followed the April 1977 oceanite eruption lead us to assume that these eruptions have been fed by a shallow magma reservoir that has not been replenished since 1977. Similar geophysical and petrological data are not available for the other type B periods. It is therefore not possible to assume that they also correspond to successive partial discharges of a non-replenished reservoir as suggested by the pattern of the cumulative volume curve.

The internal magma transfer to the sub-volcanic reservoir of Piton de la Fournaise appears to be a complex, discontinuous and irregular process for a period of some tens of years. This contrasts with the well-known sub-continuous supply of magma to the shallow reservoirs of Kilauea and Krafla volcanoes.

Seismic and petrological data are analyzed with reference to the eruptive phenomena at Mt. Etna from 1974–1984. Seismological data show that most earthquakes occur within the upper 16 km of the crust and very few below 30 km. Focal solutions for events at depth between 7 and 16 km show evidence of both normal and thrust faults, due to an unstable stress field, whereas at shallower levels only normal mechanisms are observed. In most cases, enhanced seismic activity preceded the beginning of adventive eruptions, but neither upward migration nor clear concentration of epicenters near the eruptive area (except for the shallowest events; h < 1 km) was observed.

Petrological analyses of the products from the various eruptions show no regular variations and suggest that slightly different magmas rose up through a complex system of fractures, having possibly resided at various levels. The results of this study suggest that tectonics strongly control the eruptive activity at Mt. Etna, allowing magmas to be stored at depth and providing ways to the surface for them.

Recent ground deformation studies in three volcanic areas of Italy are reviewed in this paper. Lipari-Vulcano complex, the andesitic volcanoes located in the Aeolian islands, southern Italy, are characterized by a quiescent stage of activity since 1890, with eruptions recurring at an average interval of the order of one hundred years. Vesuvio has been quiescent since 1944, but it must be considered as one of the potentially high risk volcanoes in the world, because of the violent type of eruptions and the high density of population (about 700,000 people live close to its foot). These two volcanoes have not shown, however, any significant ground movement in recent years. On the other hand, Campi Flegrei are characterized by remarkable ground movements, having one of the highest observed strain-accumulation rates in a volcanic area without any known eruption. A quantitative modeling of this type of ground deformation is quite a difficult task, due to the network geometry and the proximity of the sea. Current models for explaining the uplift episodes during 1970–1972 and 1982–1984 are reviewed.

First seismological results obtained for the area of Campi Flegrei show a close clustering of epicenters over an area as wide as approximately 2 × 2 square Kilometers. The main part of this cluster is located just in the northern part of the maximum ground uplift area. Depths are in the range 1–4 km. Time distribution show a clear tendency of the earthquakes to occur as swarms. The medium in which the seismic energy is released is quite homogeneous, with a half space average velocity of 2.8 km/sec. Seismic quality factor for coda waves shows an irregular frequency dependence, different from nearby and distant tectonic zones. Focal parameters, seismic moment, and stress drop scale in a roughly linear pattern. On the contrary, in most of the tectonic zones, the stress drop does not follow the moment below a certain value of magnitude. Fault plane solutions show normal faulting. The similarity of waveforms for events of the same swarm suggests a similar focal mechanism. These elements are interpreted in terms of magma ascension through cracks just beneath the zone of maximum uplift.

A seismic station was operated on the island of Stromboli during 1983-1984. More than 100,000 volcanic “Strombolian” eruptions were recorded. Histograms of interval times between successive eruptions and the associated seismic amplitudes are given. The shape of the histograms is correlated with the visually observed crater activity. Histograms of inter-eruption times Δt approach normality when a logarithmic transformation is applied: The additive term a appears to be associated with the strength of volcanic activity. No significant periodicities at the 95% level can be found in the eruption sequences. The observations are compared with studies from fluid mechanics, and an eruption model is discussed in which the turbulent boundary layer of the uppermost part of the magma conduit gives rise to randomly occurring velocity “bursts” in the magma flow which trigger the eruptions.

Sketch maps of the crater terrace are presented.

We present Finite-Difference solutions to the equation of balace of heat for one dimensional viscous flow in conduits with finite thermal conductivity. For reasonable contrast in thermal characteristics between the fluid and the walls, the results show that the steady state is not achieved and the characteristic times for the onset of instability are much shorter than in the isothermal case.

Formulas relating the activity concentration under the ground surface, the rate of emanation from the ground surface and the activity concentration in the air, of natural Radon gas, were derived in terms of the common parameters such as soil porosity, Radon diffusion coefficient, soil gas flow velocity and the so-called effective turbulent diffusion coefficient of the air. The formulas were verified by taking some numerical examples.

The mathematical theory of attractors is reviewed descriptively. An attractor can be thought of as a map of the characteristic dynamic states of an evolving system, whether the form produced is continuous or discontinuous, regularly periodic or stochastic. Graphical examples of attractors showing dynamic bifurcations in the evolution of magma transport from the mantle to the surface are developed in terms of a model of nonlinearly pumped volumetric capacitors. Dynamic bifurcation means that the system alternates regularly or irregularly between two or more volumetric states. The potential for a volume domain (whether a plexus or a magma chamber) to store and discharge increments of magma is the basis for calling the system a volumetric capacitor. Pumping is represented by percolation and/or extensional fracture mechanisms of variable magma transport from a mantle source. Steady, oscillatory, and pulsatory flow regimes are predicted which qualitatively simulate the behavior of near-surface inflation/deflation cycles and volcanic eruptions. Buildup to catastrophic pyroclastic eruptions of silicic magma during the growth of caldera-forming ash-flow systems is described as attractor evolution produced by convergences of multidimensional rate processes. Such convergent behavior is analogous to the dynamics of slaved systems described by synergetic feedback, such as Haken’s (1979) theory of the optical laser. In the magmatic context, slaving refers to a condition where focused volumetric states of the system are outgrowths of cooperation among transport paths originating from multiple volumetric states (e. g., the net effects on heat flow and magma transport paths of basaltic fields surrounding an evolving silicic system). The multiple states, in turn, have arisen as bifurcations of magma transport from a source system of primitive magma in the mantle. In a metaphorical sense, culminating stages of silicic volcanism are laser-like. The metaphor is based on parallelism with the idea that energy (in the form of protons or magma) is pumped into the system in multi-mode states which ultimately feed a single state. In the optical analogy this is the distinction between the laser mode and multiple modes of ordinary light. In the magma system it is the distinction between a central evolved silicic chamber and the multimode field of basaltic injections of the crust that supports its evolution (the “basaltic shadow” of Smith and Shaw, 1973; 1975). Synergy is expressed by the cooperative effects which create the centralized chamber. Entirely new kinds of energetic states are thereby made possible (e. g., crustal melting, convection, chemical zonation, and large-scale eruptive pulses). The synergetic process is self-organizing in the sense that the composite system is slaved to an effectively single culminating mode of eruption leading to the caldera-forming stage of ash-flow magmatism. Other eruptive styles occurring both before and after such an episode represent detuning of the optimally slaved state. Attractor models show features that resemble Smith’s (1979) concepts of the evolution of silicic magmatism.