Volcanic tremor and short-term prediction of eruptions

Journalof volcanology and gcothcnnal reseatch

ELSEVIER Journal of Volcanology and Geothermal Research 77 (1997) 305-311

Volcanic tremor and short-term prediction of eruptions

Bruno Martinelli *

Swiss Disaster Relief Unit, Obseruatorio VulcanoEgico de Pasta, AA 1795, Pasta, Colombia

Received 1 February 1996; accepted 16 October 1996

Abstract

Short-term prediction in volcanology, i.e., the reliable estimation of (1) an appropriate time window during which an eruption can take place and (2) the kind and magnitude of the eruption expected, needs to be examined, focusing research interest on physical aspects of volcanic activity. The problem consists of deducing the internal structure of the volcanic complex and the dynamic properties of the fluids involved from the associated physical and physico-chemical phenomena observed during the pre-eruptive phase. Geological and petrological investigations, as well as the analysis of volcanic gases, represent substantial sources of information in accomplishing this task, but they are not substitutes for physical examination.

To solve this problem, adequate observations and experiments should be performed. Today’s geophysical approach in the investigation of volcanic activity allows at best the reconstruction of the internal structure of the volcanic complex. Methods to detect and to quantify the dynamics of the processes suspected of triggering eruptive activity are practically nonexistent.

In solving the short-term prediction problem through the understanding of processes triggering volcanic eruptions, the estimation of the state of the fluid system represents a crucial point. In order to improve our knowledge of the dynamical properties of the underlying fluid system, the comprehension of seismic-source mechanisms is of paramount significance. Mechanisms generating some types of observed seismic activity and originating from variations in the fluid-conduit pressure field are an invaluable aid toward the reconstruction of the internal state of the volcano. Attention must be centered on the influence of a free gas phase in magma upon the generation of ‘not-earthquake-like’ ground vibrations in volcanic areas. A mixture composed of liquid containing gas bubbles (gas + liquid mixture> can likely cause large pressure fluctuations which, when transmitted to the confining rock structure, are radiated as seismic waves, the characteristics of which are carriers of the state of the fluid system. To fully estimate the state of the magma dynamics, detectable changes of non-seismic field variables must be considered as well.

Keywords: physical volcanology; volcanic tremor; volcanic hazard parameters; short-term prediction of eruptions

1. Introduction present knowledge of volcanic activity is mainly

Critical times related to different aspects of vol-

canic activity range from billions of years for certain geological processes to fractions of a second for the triggering mechanisms of volcanic explosions. Our

acquired in investigations carried out in the geologi-

cal and petrological fields, as well as from gas analysis, where the main interests are related to phenomena displaying critical time behavior at least in the range of years.

* E-mail: [email protected]

Today’s efforts in understanding eruptive processes by means of physics are confined to the

0377-0273/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved.

PII SO377-0273(96)00101-l

investigation of the eruption itself (Vergniolle and

Jaupart, 1986; Toramaru, 1988; Bruce and Huppert, 1989; Turcotte et al., 1990; Woods and Bower, 1995). Eruptive mechanisms on the basis of quantifi-

able preeruptive signals have not yet been investi-

gated systematically, although some isolated at-

tempts have been carried out (Schick, 1988; Chouet et al., 1994). The current geophysical tools for moni-

toring purposes are designed mainly to detect possi-

ble phenomenological correlations between preeruptive signals and the eruption itself. They are not

designed to discern the character of the physical processes triggering volcanic eruptions. The achieve-

ment of practical results by the phenomenological

approach is limited by different factors. such as the

shortness of the observation period and the difficulty of transferring acquired knowledge to other volcanoes. From this point of view, short-term prediction.

i.e., the estimation of (1) an appropriate time window during which the volcano is in a critical state

and (2) the kind and magnitude of the expected eruption, is still underdeveloped in terms of agree-

ment concerning what signals we should look for and which way of proceeding will lead to the identi-

fication of an appropriate framework for analysis.

An alternative approach is to design short-term prediction methods on the basis of knowledge re-

garding the processes triggering the eruptive phase. The understanding of processes displaying critical

times in the range of fractions of a second to minutes requires the emphasis to be shifted from the chemi-

cal to the physical aspect of a volcanic eruption. In an attempt to advance our physical knowledge of eruptive mechanisms, particular attention should be paid to processes leading to anomalous increases of

pressure in complex fluid systems (see, for instance.

Wohletz, 1986: Friihlich, 1987; Zimanowski et al., 1991). When trying to develop a strategy in this direction, the following aspects should be investi-

gated in depth: (1) the estimation of overpressure in the fluid system, caused by the overall activity; and (2) the estimation of the amount of volatile components in the fluid system, together with their own physical states.

A fairly promising way to address these fluid dynamic aspects of physical processes in a volcanic conduit is through seismology. Seismic signals caused by variations in the fluid-conduit pressure

field are commonly named ~lcanic tremor. Knowl-

edge of the tremor-source mechanisms is crucial for the investigation of gas/liquid interaction within a

magma conduit and therefore for the investigation of

eruption-triggering mechanisms.

The aim of this note is to make a few remarks and

to present a number of questions related to the behavior of gas + liquid mixtures inside magma con-

duits. Under certain dynamic regimes, flow undergoes periodic density and velocity oscillations. These

oscillations generate large pressure fluctuations

which, when transmitted to the confining rock struc-

ture. are radiated as seismic waves, the characteristics of which are carriers of the state of the fluid

system.

In addition, some geophysical problems related to shallow magma activity and deserving more atten-

tion by the volcanological community are mentioned in the hope of stimulating further investigations in

the field and of acquainting researchers with physical processes related to eruption-triggering mechanisms.

2. The concept of state

Any discussion of short-term prediction must rec-

ognize that processes related to volcanic activity are strongly nonlinear. This is evident both from instru-

mental observation and from theoretical knowledge

of the assumed underlying physico-chemical phenomena. Therefore, the terminology used must consider this nonlinear context and be carefully defined. This will undoubtedly follow in due time. The fol-

lowing discussion simply represents an attempt to describe in this manner the expressions state and

critical state.

Complex natural phenomena, like volcanic activity, are characterized by interactions both among their components and with their environment. The

ability to deal effectively with complex phenomena is one of the main characteristics of mathematical system theory, which is defined as the theory of mathematical models (Kalman et al., 1969; Casti, 1992). The part of system theory which provides models for dynamic phenomena, using for the most part differential or difference equations, is called the theop of dynamical systems. Following this disci- pline, the concept of state used in this paper is

B. Martinelli/ Journal of Volcanology and Geothermal Research 77 (1997) 305-311 307

defined as being some attribute of the volcanic activity at the present moment, which is relevant to the determination of present and future external effects of this activity. Roughly, the state may be regarded as a kind of information storage (or memory) built of past observations. Therefore, the problem is to represent the observable world at a volcano by a set of state variables, the nature of which will be essen- tially contained in the relationships linking the chosen variables (equation of state). The choice of an appropriate state space and of the related equations of state can be inferred from physical and physico- chemical considerations and must, of course, be able to synthesize all information needed to predict the effect of the past upon the future.

What do recorded data tell us about the state of the volcano? This question is related to the definition of the observability of the underlying system. A system is said observable if the information contained in the recorded data allows the determination of the instantaneous values of its state variables. Therefore, observability must be considered as the concept underlying all questions of identification and has extremely far-reaching implications in practice, for example in the design of monitoring systems for volcanoes.

For the short-term prediction problem and for characterizing external activity, the concepts of critical state and of eruptive state are of paramount significance. A volcano can be defined to be in a critical state when a small perturbation of its state variables is capable of putting it in an eruptive state. Defining an eruptive state is not as easy as one may think and requires careful consideration with regard to the dynamical behavior of the set of variables that ‘drive’ the eruptive activity. To be sure, each volcano will have its own class of eruptive states, and therefore, its own class of critical states.

3. Two-phase flow and volcanic tremor

The presence of volatile components in a magma is an essential factor in studies of the processes which govern volcanic eruptions. This fact, widely accepted in many branches of volcanology, still has not received due attention in seismology. In a volcanological context, seismologists commonly focus

their attention on homogeneous, incompressible fluids, attributing the origin of seismic signals basically to hydrofracture phenomena or to vibrations of the fluid conduits (Aki et al., 1977; Chouet, 1988). Fluid behavior in such situations is found to play only a secondary role. Studies which show a significant participation of fluid are rare (i.e., Steinberg and Steinberg, 1975; Ferrick et al., 1982; Chouet et al., 19941, and even in these cases the contribution of a dispersed gas phase in a liquid is often underesti- mated.

Evidence for the presence of a free gas phase in magma at shallow levels can be found by exploring dyke structures appearing at the surface through erosion processes. Their presence to depths of 500- 700 m is displayed in a very impressive manner in the Valle de1 Bove at Mt. Etna, Italy.

Processes leading to the formation of a free gas phase in magma have attracted the attention of many researchers. Goranson (1936, 1937) experimentally established the solubility of water in silicate melts in two cases: (1) when the two phases are subjected to the same hydrostatic pressure; and (2) when water and silicate melt are subjected to differential hydrostatic pressure. The observations by Goranson show that water solubility in melt is drastically reduced, thus favoring the appearance of a free gas phase, whenever country rock surrounding a silicate-water solution is pervious to water and impervious to the silicate melt, for instance by fissuring. Sparks (1978) made extensive studies of bubble formation and growth in magma. He found that nucleation could occur at depths between 250 and 2500 m, depending on the chemical properties and water content of the magma itself. Although magma containing a free gas phase is of primary interest in volcanology, the role played by other fluid systems in volcanic areas needs to be mentioned. For example, two-phase systems consisting of brine and CO, may exist in geothermal fields down to a depth of 20 km (Giggenbach, 1987).

Seismic waves radiated from the volcanic conduits propagate through a heterogeneous medium. Therefore, the seismogram characteristics related to the nature of the source could be difficult to separate from path or site effects. It is obvious, therefore, that the explanation of seismogram characteristics as source, path or site effects is subject to considerable debate. However, it can be established that some of

308 B. Martinelli/ Journul of Volcunolqy and Geothermal Research 77 (19971 305-311

the observed tremor characteristics (i.e., time pattern,

some dominant frequencies, onset/offset behavior) are strongly related to the source processes.

While investigating tremor-generating processes,

emphasis must be placed on examining temporal and spatial changes of dynamic pressure in the gas phase

and/or in the condensed phase. Two-phase systems consisting of dispersed gas bubbles in liquid have

been investigated extensively in various engineering

applications. To evaluate the relationships which govern the dynamic behavior of such systems, com-

plex numerical models and powerful computers are

required (Ishii, 1975; Drew, 1983; Stewart and Wen-

droff, 1984). The application of numerical models to volcanology is particularly difficult, since the fluid-

related constitutive equations and many of the governing parameters, such as the type and quantity of

volatile components, fluid viscosity, and shape and dimensions of the conduits, are not known with

sufficient reliability. Therefore, in modeling such natural phenomena the linkage relationships between

the ‘real world’ and abstraction become extremely

difficult to establish. In order to make this problem more tractable, a

more conventional approach can be chosen, consisting of modeling the two-phase system as a homoge-

neous fluid in which any effect connected with the character of the gas phase is disregarded. except for

the compressibility (Tangren et al., 1949; Van Wijn- gaarden, 1968, 1972). This so-called homogeneous

model assumes a velocity ratio of one and a thermal equilibrium between the two phases. Thus, the mixture is treated as a single-phase fluid, and behavior

and characteristics of this fluid are obtained by

straightforward extension of the gas theory. The insights so far obtained on the dynamic behavior of

gas can be used to investigate the influence that compressibility exerts on the mechanisms that could cause some of the observed seismic signals. The

assumption that the volcanic fluid behaves as a ‘pseudo-gas’ does not necessarily reveal reality but evolves from the need of getting some insight into the role of fluid dynamics in volcanic seismicity.

By low-speed flow of the mixture (i.e., A4 << 1. where M is the Mach number), pressure changes due to the flow are relatively small and accompanied by negligible density changes. In such cases, the related seismic signals may reveal at best some geometrical

properties of the source, and they can be investigated assuming mixture incompressibility.

Looking for signals with a high information content, the main interest must be restricted to high-

velocity mixture flow, i.e., flows in a velocity regime

close to Mach-number one, where large pressure

changes, accompanied by correspondingly substantial changes in density, appear. In this flow regime,

several mechanisms of instability have been detected (Jungowski and Meier, 1984: Anderson, 1989). The-

ories based on incompressibility are in such cases

wholly inadequate, and compressible-flow analysis

must be used. As already stated (Hsieh and Plesset, 1961; Kief-

fer, 19771, the presence of a free gas phase in the

liquid greatly reduces the propagation velocity of the pressure disturbances (sound speed). At a shallow

depth and at a velocity of the order of a few meters per second, fluid flow may reach the critical velocity

( M = 1). Under particular geometrical conditions, such as a conduit which undergoes cross-section

enlargement, curvature, or nozzle behavior, transonic

tlow occurs (i.e., mixed regions where M < 1 and

M > I). Under certain pressure regimes, the flow

undergoes periodic density and velocity oscillations. These self-excited oscillations generate large pressure fluctuations which are transmitted to the confin-

ing rock structure and radiated as seismic waves. The basic mechanisms which lead to the pressure oscilla-

tions are known for gas (Meier et al., 1978; Ander-

son and Meier, 1982). The analogy between gas and homogeneous-mixture behavior allows us to consider the known mechanisms in a volcanological context.

For processes involving liquids containing gas

bubbles and suspected to generate seismic signals - i.e.. collapse of the diaphragm separating two fluid

domains, propagation of pressure waves, sudden phase changes - the amplitudes of the related pressure disturbances may be finite. Such processes can-

not be treated with methods based on the infinitesi- mal amplitude of the pressure disturbances. Finite- amplitude wave propagation in a two-phase system follows nonlinear laws and may develop into a shock wave (Noordzij and Van Wijngaarden, 1974; Van Wijngaarden, 1982) or solitary waves (Oldenziel, 1979). The characteristics of finite pressure-wave propagation in gas + liquid mixtures are strongly sensitive to dissipation and dispersion effects in the


mixture and to the amplitude of the wave itself. Therefore, whenever such waves are identified, the content of the recorded signals may be used as a carrier of information on viscosity, gas distribution, and pressure conditions in the fluid conduits.

The view described above is only one of many possible ways to proceed. In a gas-liquid system, several intrinsic processes convert kinetic energy of flow into energy of compression (pressure wave emission). However, a high kinetic energy of flow is not necessarily required to increase pressure conditions. In the case of phase changes, for instance, the compressibility of the system could be altered by the inertial motions of bubbles themselves. Assuming that a pressure wave meets a collapsing bubble, then local compressibility increases. If, however, the pressure wave meets an expanding bubble, then the apparent compressibility decreases. In the limiting case that the bubble, in spite of the counteracting pressure, expands further, then the volume increases as the pressure increases (negative compressibility). The inertial energy in the liquid is transformed into compressional energy (Oldenziel, 1979; Leiber, 1990). Such a process also can release seismic en-

ergy.

4. Non-seismic field variables

Movement of magma or free gas prior to an eruption can also result in detectable changes in non-seismic field variables. Despite their importance, non-seismic field variations are not adequately considered in short-term prediction. Several reasons can be given. Non-seismic field variations, for instance, are extremely difficult to correlate with magma movements because of the unknown time delay between dynamic and observed anomalies. Moreover, external influences (e.g., meteorological conditions) are difficult to separate from the internal magmatic processes under observation. Nevertheless, in conjunction with tremor analysis, the behavior of an appropriate set of non-seismic field variables could be relevant for the identification of the processes triggering volcanic eruptions.

To look into shallow magma activity, contribu- tions could be made from the detection of micro- gravimetric changes (Rymer and Brown, 1989) re-

sulting from the exsolution of gas dissolved in the silicate melt or to magma intrusion from deep regions. The process discrimination could be performed in conjunction with deformation measurements. The information obtained is of particular interest in relation to shallow magma activity with- out associated seismic activity.

To detect if magma processes or hydrothermal boiling of groundwater causes the observed seismicity, an effort in collecting and examining concomi- tant non-seismic information is also required. Vol- canic gases, for instance, contain ultrafine aerosol particles. By means of photoemission techniques applied to particles in the nanometer size range, a fingerprint of the shallow magmatic activity is obtained which is related to the degassing process (Ammann, 1992). Detection of a correlation with the seismic activity, for instance, would help explain the origin of this seismicity.

Magma transport through cracks and hot gases rising through water-filled cracks could cause measurable conductivity changes. Therefore, geophysical sounding methods which respond to strong contrasts in electrical conductivity (Schnegg and Fischer, 1984; Di Maio and Patella, 1994) could be deployed not only to ascertain the volcanic structure but also to follow rising - and possibly seismically silent - material near the surface.

Indirectly, the influence of magma movements can be perceived by studying electromagnetic field changes. The amplitude and spatial scale of electromagnetic effects due to magma dynamics is still difficult to quantify, but the detection of some of the measurable changes will supply significant information in estimating the internal state of the volcano. Particularly strong changes of magnetic field anomalies, for instance, could indicate magma temperatures that are near the Curie point of the ferromagnetic mineral phases (around 650-680 K).

5. Discussion and suggestions

The investigation of eruption-triggering mechanisms is among the most urgent aspects of the short-term prediction problem. The identification of the magma dynamics on the basis of quantifiable

310 B. Martinelli/ Journd of Volcanology and Grothernrul Research 77 (19971 305-31 I

signals will constitute a significant contribution to-

wards solving this problem. To fulfil this task, theoretical work, laboratory experiments and appropriate

field observations must be performed which are related to the dynamic properties of the fluids in-

volved, The investigation of the tremor-source mech-

anisms offers an effective tool to examine the short-

term prediction problem. It should be emphasized.

however, that progress in the field can only be achieved if one integrates other domains of physical

volcanology in the interpretation of the seismic sig-

nals. Additionally, the following points should be con-

sidered in seismology when studying the mecha-

nisms that trigger volcanic eruptions: - Today’s recording, description and interpreta-

tion of volcanic seismic signals are based mainly on

instrumentation and concepts that were developed to

study tectonic earthquakes, where the main interest is the investigation of wave path or site effects. This

approach must be critically reviewed, particularly when the signals collected are used to model their

source mechanisms. - When trying to solve source problems, seismol-

ogists should focus their efforts from the tendency to

link the observed signals towards a unique source mechanism to the investigation of all possible solu- tions. At this stage of knowledge, the development

of a qualitative understanding is far more significant than the quantification of an ‘a priori’ assumed --

and not verifiable - process. Once a satisfactory

general solution has been constructed, quantitative details could be gained through the development of

appropriate identification procedures. - Monitoring and research purposes on active

volcanoes by means of seismology are quite difficult to integrate because of their different objectives.

Breakthroughs in both fields can only be achieved by clearly defining the goals of an observation before-

hand. To summarize, for modeling processes leading to

seismic wave generation, seismology applied to volcanic activity should emphasize the need for theoretical ideas to be used in conjunction with observation and experimental data, as well as the experience of individuals. Furthermore, the appropriate use of theoretical ideas will suggest what parameters (signals) can most usefully be measured.

Acknowledgements

I am grateful to Gordon Woo, John Stix and

Jiirgen Neuberg for reading the manuscript and offer- ing valuable suggestions for its improvement.

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Volcanic tremor and short-term prediction of eruptions