Dynamics of Magma Storage in the Summit Reservoir of Kilauea Volcano, Hawaii

Johnson, D.J., Dynamics of magma storage in the summit reservoir of Kilauea Volcano, Hawaii, Journal of Geophysical Research, 97, 1807-1820, 1992.

Copyright 1992 American Geophysical Union. Further electronic distribution is not allowed.

Abstract. An eruption of Kilauea Volcano, Hawaii, normally results in a decrease in the internal pressure of a summit magma reservoir as it partly drains. The interior of the volcano responses to the decrease in pressure (1) by elastic expansion of remaining magma and gas, (2) additional exsolution of gas dissolved in the magma, and (3) by contraction of the volcanic edifice. This process is modeled here using gravity, geodetic, and observational data for recent events at Kilauea. During magma removal, the ratio of pressure change in the magma reservoir to the volume of associated summit subsidence ranges from less than 0.22 Pa/m^3 to more than 0.43 Pa/m^3. Lower ratios occur during large subsidences because of a large effective volume of the reservoir. Small events may involve source volumes of only 2 km^3. In contrast, a volume of near 13 km^3 is associated with larger events because the boundary between plastic and elastic behavior may migrate outward with increased time and strain. The aggregate compressibility of Kilauea's reservoir is significantly increased by volumetric changes of the CO2 gas phase by bulk compression and solution with pressure. This effect is more pronounced for relatively shallow sources because the bulk modulus of gas is proportional to pressure. The average reservoir CO2 weight fraction may be near 0.0005 to 0.0009. CO2 appears to accumulate in the upper portion of the reservoir where the concentration reaches 0.0030 weight fraction. Gradual long-term subsidences are different from the short-term deflations associated with specific eruptions. During long-term subsidence, no net change in mass or pressure occurs within the summit reservoir. Rifting of the summit area, which may tend to shorten the reservoir as it widens, or slow degassing and contraction of stored magma may cause long-term subsidence.


Active Hawaiian shield volcanoes contain a fluid-filled summit reservoir. Magma, buoyantly rising from a mantle source [Eaton and Murata, 1960], accumulates within the reservoir where its further ascent by buoyancy alone is prevented by the low density of the overlying crust [Ryan, 1987]. The reservoir itself may consist of a plexus of dikes and sills separated by screens of solid rock [Fiske and Kinoshita, 1969; Davis et al., 1974]. Surrounding the fluid- filled region is likely a zone of high-temperature material, possibly containing pockets of partial melt. The volume of fluid and high-temperature (hence plastic) material associated with Kilauea's magma storage region is large enough to produce a detectable aseismic zone [Koyanagi et al., 1976] and seismic low-velocity zone [Thurber, 1984]. Source locations from inversion of vertical surface displacement data [Fiske and Kinoshita, 1969; Dvorak et al., 1983] are generally within the seismic anomaly zone. Migration of the apex of inflation or deflation with time is thought to reflect shifts of magma transfer between discrete areas (presumably individual dikes or sills) [Fiske and Kinoshita, 1969; Dvorak et al., 1983]. The seismic and deformation data define the reservoir region from 2 km down to 6 km below the south rim of Kilauea Caldera.

Shallow magma transfer to and from Kilauea's central reservoir is accompanied by crustal deformation, as the surrounding solid edifice is inflated or deflated to accommodate volume changes of magma [Mogi, 1958; Eaton, 1962]. Magma accommodation may also be by bulk compression or decompression of the entire chamber magma and gas content [Sanderson et al., 1983; Eggers, 1983; Johnson, 1987]. These processes solve the "room problem" associated with magma transfer. The balance between the role of each process, crustal deformation and magma compression, hinges on the relative elastic properties of crust and magma [Johnson, 1987]. Whichever component is more deformable takes the lead role in making space for new magma. Subsurface magma transfer also changes internal magma pressure and external crustal stress distribution [Mogi, 1958]; the magnitude of the pressure and stress change depends on the elastic moduli of the edifice and magma reservoir.

This research was motivated by an interest in determining variations in pressure and volume of the reservoir, CO2 content of magma, and effective volume of the portion of the reservoir that serves as the source of surface deformation. Previous studies of Kilauea geodetic data have been directed at resolving the geometry and location of the sources. This study focuses on the mechanical properties of the magma reservoir and surrounding edifice; properties responsible for the key observations of uplift or subsidence and gravity change. Gravity monitoring is used as a means of detecting mass changes in the summit magma reservoir. This may be verified in some cases of deflation by comparison with the volume of lava and intrusives reaching the surface and rift zone. Geodetic monitoring of surface displacement measures crustal strain associated with magma transfer.

My analysis is restricted to periods of rapid summit deflation accompanying rift zone eruptions and intrusions. These events are brief and have a locus of eruption or intrusion sufficiently distant from the monitoring sites located above the summit reservoir such that the specific effects of magma withdrawal and summit subsidence are isolated. The November 1975 deflation [Jachens and Eaton, 1980] is not considered here to avoid modeling the complex effect of anomalous horizontal extension produced by a major earthquake [Lipman et al., 1985] and near-surface dike intrusion and eruption above the summit deflation source [Tilling et al., 1976]. Analyses of gravity and geodetic data from several brief summit deflations associated with the eruption at the Pu'u O'o vent have been previously published [Johnson, 1987]. This study sup-plements these earlier data with observations from later episodes, as well as data for major Kilauea summit subsidences in August 1981 and January 1983.


Analysis of crustal deformation and gravity changes is based here on a point source model approximating a spherical source. Such a model is used because (1) it generally gives satisfactory fits to short-term vertical displacement data [Dvorak et al., 1983]; (2) there is no seismic or geodetic evidence for shallow dike injection above the Kilauea central reservoir during the selected deflation intervals; and (3) use of a more complex model is not justified by the available data. Davis [1986] attributes the general success of the point source model to the dynamics of the reservoir region that behaves as a fluid-filled cavity because of deformation of high-temperature plastic and strain-fractured solid elements. With time the pattern of deformation from a source of any geometry may appear more like that of a larger spherical source because of outward migration of the plastic deformation zone.

Gravity monitoring will detect accumulation or loss of mass (presumably magma) from reservoirs within the crust if corrections are applied for (1) vertical movement of the observation point in the Earth's gravity field (the free-air effect) and (2) deformation-induced density change of the crust surrounding a reservoir plus vertical displacement of mass (the Bouguer effect). A free-air gradient of -0.3273 [mu]Gal/mm was determined by recording the gravity change associated with a 930-mm height change at three sites within the Kilauea Caldera. Free-air adjusted data residuals are indicated as g*. A positive Bouguer gravity anomaly of +320 [mu]Gal in the summit region of Kilauea [Kinoshita et al., 1963] is probably the source of this abnormally high gradient [Hammer, 1970]. The density change correction of 2 was assumed to be zero. This is theoretically valid for a hydrostatically inflated sphere, or point source of dilatation [Rundle, 1978; Walsh and Rice, 1979] and for multiplepoint sources [Sasai, 1986] embedded in an elastic medium. Note that there is a gravity correction (2) for other, nonaxisymmetric source geometries, such as vertical and horizontal cracks in which the component double forces are not equal [Savage, 1984; Sasai, 1986].

The inflation of a spherical source in a homogeneous isotropic elastic half-space (which simulates a reservoir source within Kilauea) causes vertical displacement of a point on the surface (modified from Mogi [1958])

[image of equation]     (1)

where Z is the source depth, X is the radial distance of the point from the source epicenter, and [delta]Ve is integrated volume of uplift. Ve is a measure of the source strength and is given by

[image of equation]     (2)

where [delta]P is the pressure change, Vr is the volume of the source, and [nu] and [mu] are the Poisson's ratio and shear modulus of the edifice.

My gravity data have poor areal coverage so there is insufficient information to solve for both location and magnitude of mass change at depth from gravity changes alone. Therefore, additional information from surface displacement measurements is used to determine [delta]M. Combination of equation (1) for vertical surface displacement and the familiar equation for the gravity effect of a point mass [Dobrin, 1960, p. 374] gives

[image of equation]     (3)

which relates magma mass accumulation or loss and deformation to gravity change and uplift. Because the functional form of the equations for gravity change and uplift are identical, the geometrical parameters cancel when the two equations are combined. The value of [gamma] is 6.67 x 10-11 N m2 kg-2.

A good spatial correlation between gravity and elevation change has been found at Kilauea [Jachens and Eaton, 1980; Dzurisin et al., 1980]. This supports the validity of the modeling procedure utilized here. Poorer correlation would be observed if the mass change and dilatation source were not coincident, if the source were to behave much differently than a sphere of uniform dilatation, or if there were significant lateral variation in crustal elastic properties. My data are too sparse to evaluate the spatial integrity of the gravity to height change correlation. The correlation is assumed to be good such that relative changes may be considered proportional to absolute changes.

The deformation source may coincide with the entire reservoir region or it may be only a small portion of the whole reservoir. Davis [1986] envisioned the magma chamber as a tangle of dikes and sills within a matrix of solid rock. Although the solid matrix may have a short-term ability to support shear strain, eventual failure and creep effects lead to an outward migration of the plastic-elastic boundary, that is, the hydrostatically equilibrated source region Vr becomes progressively larger.

Vr is that subvolume of the entire reservoir which behaves as a fluid (or plastic) over the time interval of the deformation event. Vr, in addition to a melt phase, contains subsolidus rock; its aggregate bulk modulus, however, is assumed equal to that of the melt. This assumption is valid because the effect of the melt phase is to reduce the aggregate bulk modulus to near that of melt [Brown and Korringa, 1975; Ryan, 1980]. External to the fluid source region, behavior is elastic.

Magma arriving in Kilauea's central reservoir from the mantle was estimated by Greenland et al. [1985] to contain 0.0032 CO2 by weight. This value was derived by comparing measurements of the sum of CO2 (in noneruptive summit fumaroles, eruptive plumes, and trapped in lavas) with the total lava output. Gerlach and Graeber [1985] give a value of 0.0065 by weight, derived from volcanic gas analysis of sustained summit lava lake activity and residual concentrations in fountain spatter.

A separate CO2 gas phase may be found in pockets of magma within the 3-km-deep reservoir because CO2 has a low solubility at the corresponding pressure. Harris [1981] measured the concentration of CO2 in vesicle-free glass separates from submarine tholeiitic basalts quenched at pressures of as much as 50 MPa. He found the limiting weight fraction n of CO2 that may be dissolved in a basalt melt as a function of pressure P is

[image of equation]     (4)

where the solubility constant b is 5.9x10-12 when pressure, P, is given in units of Pa. Exsolved CO2 gas m in the case of a saturated melt is given as the total CO2 N minus the portion that remains in solution n; there is no gas phase if N is less than the saturation limit . These relations are given by

[image of equation]     (5)

where the relatively small constant in the solubility equation (4) has been neglected.

The ideal gas law is adequate to calculate the volume of exsolved gas at the pressure found in 3-km-deep reservoirs. Mass fraction values for CO2 are multiplied by the source volume Vr and magma density [rho] to obtain the total volume of gas in the source

[image of equation]     (6)

The mass of 1 mol of CO2, [omega], is 0.044 kg. R is the gas constant, equal to 8.314 m^3 Pa/mol deg.K, and T is the temperature, assumed to be equal to magmatic temperatures at reservoir conditions, 1420-1470deg.K for Kilauea (M. Garcia, personal communication, 1989). The volume of gas changes with pressure as a result of bulk compression and solution effects. This relation is found by taking the derivative of equation (6)

[image of equation]     (7)

Three mechanisms that change the volume of the source region are added together; the total change is

[image of equation]     (8)

Each term on the right-hand side of (8) represents a particular physical contribution to the volume change [delta]Vr of the reservoir: the first term is the magma accumulation or withdrawal, which may be detected gravimetrically; the second term is bulk compression (or expansion) with pressure of the magma with bulk modulus K; and, finally, the third term is the volume change with pressure of the gas phase (by both change with volume compression or expansion and solution in the melt). A value of 11.5 GPa, determined for gas-free Kilauea 1921 olivine tholeiite [Murase et al., 1977], is assumed for K; the density of Kilauea basaltic melt has been measured near 2600 kg/m^3 [Fujii and Kushiro, 1977].

As the source expands or contracts, the ground surface is displaced with magnitude given by [Johnson, 1987]

[image of equation]     (9)

Equation (8) is rearranged to solve for [delta]M, and each term divided by [delta]Ve, or the equivalent as given by equations (2) or (9)

[image of equation]     (10)

Equation (10) shows that for a given mass change at depth, a relatively strong edifice (e.g., large [mu]) implies more magma and gas compression and hence less uplift volume [delta]Ve. Conversely, stiff magma with little CO2 (e.g., large K and small N) compresses less and forces the edifice to deform more, thus producing more uplift. The role of CO2 in accommodating volume change of magma, thereby limiting crustal deformation, is greater at low pressure.

The intrinsic shear modulus of Hawaiian basalt, determined by laboratory experiment, averages 25 GPa with a range of 4.7 to 40.5 GPa [Manghnani and Woollard, 1968]. Ryan [1987] found a shear modulus of 26 GPa for a sample of olivine tholeiite basalt. The effective shear modulus of Hawaiian volcanic edifices should be less than the above laboratory values because the volcanoes are built of many vesicular, commonly rubbly lava flows with abundant void space [Ryan et al., 1983]. Detailed studies of seismic wave velocities provide some information about the rigidity of large parcels of crust. A shear modulus of approximately 9 GPa is suggested by the P wave velocity of near 3500 m/s in the upper few kilometers of Kilauea [Crosson and Koyanagi, 1979], using a density of 2300 kg/m^3 [Kinoshita et al., 1963], and a Poisson's ratio of 0.25. Again, this specific value may not be appropriate for applications in crustal deformation modeling. First, it is a dynamic value; crustal response to a static stress imposed over periods of days to years may be different. Second, there are large lateral and vertical variations in crustal strength within the edifice. Seismic velocities and hence rigidity determined from P wave arrival data from earthquakes and explosions increase with depth and vary laterally [Thurber, 1987; Hill and Zucca, 1987], reflecting the compressive reduction of porosity with increasing depth and the contrast in strength between solidified intrusive zones and country rock.

Laboratory values of [mu] are considered to be an order of magnitude larger than values for large fractured rock masses loaded in situ [Rubin and Pollard, 1987]. A [mu] of less than 3 GPa is proposed by Davis et al. [1973, 1974] and Davis [1986] to explain the absence of a piezomagnetic effect during periods of observed crustal deformation at Kilauea. They surmized that anelastic failure of crustal material within the summit of Kilauea, such as by earthquakes during periods of intense deformation, produces a low value for [mu] and prohibits significant storage of elastic shear stresses.

Sufficient gas may be present in Kilauea's reservoir to be an important factor in determining source compressibility. A previous estimate of the shear modulus of Kilauea's edifice by Johnson [1987] was determined for summit subsidences associated with Pu'u O'o eruptions assuming no gas present in Kilauea's reservoir. This assumption was based on an interpretation by Greenland et al. [1985] that CO2 is lost from the magma as soon as it reaches shallow crustal levels. The value for m of 23 GPa by Johnson [1987] is similar to laboratory estimates and is probably too high considering the evidence given above that structural defects should result in an effective shear modulus of the volcano that is less than the intrinsic shear modulus of hand samples. If a lower value for crustal [mu] is used, then the effective K calculated is lower than the gas-free K by Murase et al. [1977], which indicates the presence of a separate compressible gas phase.


Two types of rapid deflation are analyzed here: (1) small, rapid deflations, with relatively shallow source depth, such as occurred during the early growth stages of Mauna Ulu and Pu'u O'o and (2) large, rapid deflations, with relatively deeper source depth, such as the August 1981 and January 1983 events. A third type, continuous, slow subsidence which has occurred since January 1983, is discussed in the interpretation.

This section has two parts. In the first part, [delta]M/[delta]Ve is determined for each deflation type. In the second part, observations of the height of the surface of lava lakes and eruptive events are used to estimate [delta]P/[delta]V e for a range of eruption types.

An important value needed to determine mechanical properties of Kilauea's summit is the ratio of reservoir mass loss to surface subsidence, [delta]M/[delta]V e. This is derived using equation (3) and the [delta]g*/[delta]h relation observed during each event. The values derived from the gravity changes are checked against observations of the volume of newly injected rift zone dikes and lava flows (to approximate summit mass loss) and the volume of summit subsidence. These independent values, given as [delta]M*/[delta]V e, will be shown to be in agreement. A density of 2600 kg/m^3 is assumed for molten basalt intruded in rift zone dikes [Fujii and Kushiro, 1977]. The density of solidified lava flows has been estimated at 2300 kg/m^3 [Wolfe et al., 1987].

Gravity Observations

P1, shown in Figure 1, is the gravity base station and HVO34 is the principal monitoring site. Gravity surveys before 1984 consist of at least three closed loops on separate days with a single gravimeter. Surveys done after January 1984 were made using two gravimeters run over two or more closed loops on the same day, usually within a few hours. Gravity readings are corrected for tidal effects [Longman, 1959] using a compliance factor of 1.16. Calibration functions with linear and periodic terms were determined from calibration ranges and applied to the data. A least squares procedure was used to simultaneously solve polynomials to approximate time-dependent changes in the reading level of the gravimeters (gravimeter drift), offsets of the reading level (tares) as needed, and relative gravity g at each surveyed station. At least a second-order polynomial was selected if a sufficient number of redundant observations were made. Anomalous Earth tides, ocean tides, and variations in atmospheric pressure, presuming that they are more or less uniform over the relatively small network areas, will appear as a gradual change in reading level at all stations and will be removed by the drift correction. No attempt was made to correct the gravity data for water table changes because base and monitoring sites at Kilauea are located within a short distance of each other, in areas of similar rainfall intensity.

Magma Transfer During the August 1981 Southwest Rift Zone Intrusion

A magmatic event began August 10, 1981, and lasted 2 days. It drained magma from the summit reservoir into the southwest rift zone [Pollard et al., 1983; Dvorak et al., 1986; Klein et al., 1987]. Approximately 45 x 10^6 m^3 of summit subsidence, reflecting magma withdrawal, have been estimated by Dvorak et al. [1986] from height changes between level surveys conducted June 1 and August 13. Tilt changes at Uwekahuna (UWE) that indicate inflation between the first leveling survey and onset of deflation suggest that the actual collapse volume may be near 56 x 10^6 m^3. The pattern of vertical deformation in the southwest rift zone measured during this period has been interpreted by Pollard et al. [1983] to indicate shallow dike intrusion. The dike is estimated [Dvorak et al., 1986] to be within 250 m of the surface, with a width of about 1 m and a height of 3 km. The injection volume is 75 x 10^6 m^3 if the dike extends with these dimensions for the full 25 km length of the associated seismic swarm [Klein et al., 1987].

This volume together with the density of the injected magma of 2600 kg/m^3 gives an estimated [delta]M*/[delta]Ve ratio of 3480 kg/m^3 for this August 1981 summit subsidence. In comparison, [delta]M/[delta]Ve estimated from the residual gravity and height change data gives 3050+/-1645 kg/m^3. This value is derived using equation (3) and the [delta]g*/[delta]h relation of 0.128+/-0.069 [mu]Gal/mm given by a least squares fit to the equally weighted data in Figure 2a.

Magma Transfer During the January 1983 East Rift Zone Intrusion and Eruption

A significant summit subsidence event began on January 2, 1983, and lasted 6 days. A dike was intruded in the middle east rift zone area and erupted to the surface [Wolfe et al., 1987; Dvorak et al., 1986]. The volume of summit subsidence from inversion of tilt data (obtained measuring differential elevations between three nearby benchmarks) is 72 x 10^6 m^3 [Dvorak and Okamura, 1987]; from level data it is 61 x 10^6 m^3 [Dvorak et al., 1986]. Again tilt changes at the continuously recording meter at UWE between the time of the geodetic surveys and the deflation indicate that the actual subsidence volume may have been greater than that recorded by the geodetic surveys by a factor of 1.37 (Hawaiian Volcano Observatory (HVO), unpublished data, 1983). So, [delta]Ve is estimated at -83 x 10^6 m^3 (level data) to -98 x 10^6 m^3 (spirit level tilt data). Dvorak et al. [1986] modeled horizontal displacements observed in the vicinity of the affected segment of the east rift zone and estimated an intrusive volume of 98 x 10^6 m^3 for the dike. Wolfe et al. [1987] estimate a dike volume of 120 x 10^6 m^3 based on observed surface extension of one distance monitor across the dike trace and extent of the intrusive earthquake swarm. With a dike length equal to that of the eruptive fissure the volume is 60 x 10^6 m^3. An additional 14 x 10^6 m^3 of lava reached the surface [Wolfe et al., 1987] which must be added to the intrusive volume in calculating [delta]M*.

Using an average of the two subsidence volume estimates for [delta]Ve (1.37 x (61 + 72) x 10^6/2 = 92 x 10^6), and with [delta]M* as given by the sum of the intruded [Dvorak et al., 1986] and extruded volumes times their respective density (98 x 10^6 x 2600 + 14 x 10^6 x 2300), [delta]M*/[delta]Ve is an estimated 3170 kg/m^3. The unweighted residual gravity versus height change spanning the major January 1983 deflation of Kilauea's summit is [delta]g*/[delta]h = 0.110+/-0.018 [mu]Gal/mm (Figure 2b). The [delta]M/[delta]Ve ratio implied by this and equation (3) is 2625+/-430 kg/m^3.

Magma Transfer During 1983-1986 Pu'u O'o Eruption

The Pu'u O'o vent is located in the middle of Kilauea's east rift zone and began its activity following the January 1983 summit subsidence and rift zone intrusion. During subsequent activity the summit of Kilauea showed a pattern of cyclic inflation and deflation superimposed on a long-term trend of collapse [Johnson, 1987; Wolfe et al., 1987]. Summit tilt as recorded at UWE (see Figure 1 for location) is given in Figure 3; on this graph increasing values of tilt generally accompany inflation. Each episode of vigorous lava effusion is marked by rapid deflationary tilt. Summit inflation during the repose intervals and rapid deflation during lava effusion at the vent are widely regarded as evidence for significant magma transfer from the summit reservoir to the rift zone at the time of each of the eruptive events [Dvorak and Okamura, 1985; Johnson, 1987; Wolfe et al., 1987].

[delta]M*/[delta]Ve. Previous analysis by Wolfe et al. [1987] of early Pu'u O'o eruption and summit subsidence volume used tiltmeter data and empirical volume-to-tilt correlations from data collected before the Pu'u O'o epoch [Dzurisin et al., 1984; Dvorak et al., 1986]. One drawback to use of these factors is that they represent an average; the actual tiltmeter response to a specific deformation event greatly depends upon the source location. Tiltmeter response is found by taking the derivative of equation (1) with respect to X

[image of equation]     (11)

where [delta][tau] is the tilt change. Figure 2 of Dzurisin et al. [1984] gives the range of [delta]Ve/[delta][tau] expected for various source locations between 2 and 4 km horizontal and 2 to 4 km vertical from a tiltmeter. Factors range from 0.09 to 0.75 x 10^6 m^3/[mu]rad (in an azimuth directly radial to the source). Since sources have been previously observed at the entire range of distances and depths covered by Dzurisin et al. [1984], determining the source hypocenter is certainly a necessary prerequisite to extrapolating edifice volume change from tilt change. Estimating elevation changes, volume of summit subsidence, and source depth during each event of the Pu'u O'o eruption series is virtually impossible for the first 30 eruptive episodes after the major subsidence, as no attempt was made to bracket deformation cycles with geodetic surveys. Only four events (episodes 32, 38, 39, and 40) of the Pu'u O'o eruption series were well monitored by leveling or tilt surveys.

For episodes 2-31 of Pu'u O'o activity, tilt vectors from three continuously recording sites in the Kilauea summit area (HVO, unpublished data, 1985) point to a source of cyclic deformation below the south rim of the Kilauea caldera. The recording tilt data alone cannot be inverted because they are too few, are spatially poorly distributed, and have a high noise content. Leveling data from December 1983 to July 1984 are given in Figure 17.26B of Wolfe et al. [1987]. The center of elevation change was also at the southern margin of the caldera. Inversion of these leveling data yields a source location 3.5+/-0.24 km below the south caldera rim (Figure 4). Inversion of vertical changes between the July 1984 survey and one done on February 5, 1985 (HVO, unpublished data, 1985), gives a source 1 km north of the earlier interval and a shallower depth of 2.5+/-0.17 km (Figure 4).

The northerly migration of the short-term source continued after February 1985. By April 1985 the cyclic eruption-related displacements focused near the east side of Halemaumau Crater, while long-term collapse continued to the south. Surface displacement surveys that spanned individual short periods of deformation were begun at this time to isolate the short-term source (Table 1 and Figure 4). The first of these surveys involved leveling a profile from P-1 to HVO34 (Figure 1) just before and after the episode 32 deflation of April 21, 1985. A point source model given by equation (1) [Mogi, 1958] was used to estimate [delta]Ve, which differs from the value given by Johnson [1987] because data for a short spur route near Halemaumau crater were not considered previously. A monitoring program utilizing the spirit level tilt technique was carried out between October 1985 and January 1986 (HVO, unpublished data, 1986). Measurements were made before and after eruptive deflations at three to five sites and were supplemented by data from the two-component water tube tiltmeter at Uwekahuna. Source parameters were estimated with equation (11). The short-term spirit level tilt monitoring at Kilauea was discontinued after January 1986. Hence source parameters for episodes 41-48 are unknown, but may be inferred from a dominantly east-west direction of cyclic tilt at UWE to be from a northerly source, like that of the later 1985 events.

Values for [delta]M*/[delta]Ve for the four well-monitored deflations are given in Table 1; the average ratio is 11,180 kg/m^3. Ratios for episodes 38-40 have been adjusted by up to 30% since the geodetic surveys were done over a longer interval than the actual deflations and hence included some inflationary change as indicated by the UWE tilt. Collapse volumes are quite small in comparison to the quantity of erupted lava, a relation previously noted by Wolfe et al. [1987] for earlier Pu'u O'o deflations. Analysis of the gravity data that follows will confirm this relation.

[delta]M/[delta]Ve. Observed gravity at HVO34 relative to P1 is plotted in Figure 5 for the series of observations made from January 1984 to July 1986. Gravity differences plotted are not adjusted for elevation change. The long-term gravity trend seen in Figure 5 is an increase. Much of it may be explained by the free-air effect of progressive subsidence centered near the location of HVO34. Long-term subsidence is indicated by leveling data [Johnson, 1987; Wolfe et al., 1987] and decreasing UWE tilt (Figure 3). Separate gravity signatures of short-term and long-term deformation are apparent by plotting together the progression of gravity and tilt values (Figure 6). Figure 6 shows only values corresponding to high and low points of the deformation cycle.

The critical observation here is the relationship between gravity and tilt change for specific inflation and deflation intervals. Changes are plotted together in Figure 7; a weighted least squares fit to the data gives [delta]g/[delta][tau] values of -0.13+/-0.10 [mu]Gal/[mu]rad for all deflation intervals and 0.01+/- 0.12 [mu]Gal/[mu]rad for all inflation intervals. In general, the fits show that the observed changes at HVO34 average near zero despite up to 20 [mu]rad of UWE tilt. This pattern is not unrealistic, as the observed gravity changes reflect a composite of free-air gravity increase due to subsidence and gravity decrease ([delta]g*) due to removal of magma mass. For these data the two contributions equally offset.

A large portion of the data scatter seen in Figure 7 is due to uncertainty in the gravity observations. This is particularly noticeable in the later data, when the standard error of the observations (Figure 5) increased. To avoid bias by the poorly determined values, the data were weighted by 1/[sigma]2 while solving [delta]g/[delta][tau] . There is no evidence for a systematic temporal change in the gravity response to deformation cycles; solution for [delta]g/[delta][tau] for subgroups of data gives roughly the same result as the whole. As the data scatter is large relative to the average gravity change, differences between any specific inflation or deflation period cannot be considered significant.

Only for episode 32 was the height change of HVO34 directly measured by leveling before and after deflation. The -80 mm change accompanied -17 [mu]rad of UWE tilt, giving a [delta]h/[delta][tau] of 4.7 mm/[mu]rad. Values determined during inversion of the spirit level tilt observations for episodes 38-40 give lower changes, averaging 40 mm, in accordance with the smaller observed UWE tilt change. Fortunately, the shortage of height change data is not critical here as [delta]g/[delta][tau] is close to zero and therefore [delta]g/[delta]h is also near zero. Using 4.7 mm/[mu]rad from episode 32 as representative of the uplift rate gives [delta]g/[delta]h of -0.028+/-0.021 [mu]Gal/mm for the deflations and 0.002+/- 0.025 [mu]Gal/mm for the inflations. These figures were then adjusted for the free-air effect to obtain [delta]g*/[delta]h values (Table 2). Then equation (3) was used to derive values for [delta]M/[delta]Ve given in Table 2; the ratio for all deflation intervals is 7165+/-500 kg/m^3.

Magma Transfer During 1969 Mauna Ulu Eruption

The character of the first stage of eruption in 1969 of Mauna Ulu [Swanson et al., 1979] was similar to that of Pu'u O'o until 1985. In particular, both eruptions had alternating periods of magma accumulation when the summit reservoir gradually inflated and brief summit deflation accompanying eruption when previously stored magma supplied a vigorous spray of lava. One difference noted by Wolfe et al. [1987] is an almost twofold difference in volume of erupted lava per unit deflationary tilt at UWE. Deflations are reconsidered here in terms of the specific subsidence volume given by inversion of tilt data from a network of tilt sites because the apparent difference may partly relate to a change in the source location between the two periods and hence a change in the sensitivity of the tiltmeter to deformation.

[delta]M*/[delta]Ve. The lava mass versus summit subsidence volume is determined for the 12 fountaining episodes that characterized the first phase of Mauna Ulu activity in 1969. Overall uplift accompanied this activity as indicated by inflationary tilt change at UWE [Swanson et al., 1979, Figure 2]. Net uplift, measured by leveling surveys between March 1969 and February 1970 (HVO, unpublished data, 1989), was greatest in the southern margin of Kilauea Caldera. However, tilting during individual subsidence events accompanying Mauna Ulu eruptions focused at a center located at the east rim of Halemaumau Crater, north of the long-term inflation source. Spirit level tilt observations were made at four to five sites on Kilauea just before and just after episodes 5, 7, 9, and 12 (HVO, unpublished data, 1989). Inversion of three of these data sets (no stable solution could be found for episode 5 data) gave an average 0.14 x 10^6 m^3/mrad of summit subsidence UWE tilt measured on a N60deg.W azimuth. The ratio of north tilt to east tilt at UWE [Swanson et al., 1979, Figure 2] remained roughly the same for each deflation event of the first stage of the Mauna Ulu eruption, suggesting that the volume-to-tilt relation for the three events is representative of all events.

Lava volumes and tilt changes for episodes 2-12 of 1969 Mauna Ulu activity are given by Dzurisin et al. [1984] as 0.36 x 10^6 m^3/mrad N60deg.W tilt. A slightly higher lava density of 2400 kg/m^3 is appropriate here to account for higher density of the portion of the Mauna Ulu lavas that filled Alae crater [Swanson et al., 1979]. Combination of the lava versus tilt ratio and subsidence to tilt ratio gives an estimate for [delta]M*/[delta]Ve of 6000 kg/m^3. This is roughly 50% less than the average value found for the sample of four Pu'u O'o eruptions considered above but significantly larger than the August 1981 and January 1983 events.

Summary of magma transfer observations. Table 2 is a compilation of all [delta]M*/[delta]Ve and [delta]M/[delta]Ve estimates, along with additional parameters for source depth and deflation volume which are used for modeling. The major observation is that the Pu'u O'o and Mauna Ulu eruptions were accompanied by limited subsidence relative to reservoir magma withdrawal. In comparison, collapse during the August 1981 and January 1983 events were larger in terms of both absolute and relative volumes. An important constraint is that the source depths of both the 1981 and 1983 subsidences was greater than those for the smaller events. A possible exception is the 1984 to April 1985 Pu'u O'o events for which the short-term source depth is unknown.

Evidence of Summit Reservoir Pressure Variations, [delta]P/[delta]Ve

Uplift from a Mogi [1958] point source model as given by equation (2) is proportional to source pressure change as well as volume; these parameters cannot be separated by analysis of the surface displacements alone [McTigue, 1987]. The height of the surface of lava lakes and eruptive vents, however, give independent information that may be used to model reservoir pressure.

Pressure change during large deflations. Epp et al. [1983] show that the amount of summit collapse at Kilauea indicated by tilt change at UWE during periods of rapid deflation is inversely proportional to the elevation of the eruption site. Deflation reflects a pressure drop within the summit reservoir if the height and, therefore, weight of the magma column is reduced in proportion to the vent elevation. Pressure drop in the central reservoir is greater for eruptions at lower elevation in distant parts of the rift zone several hundred meters below the summit elevation, thus allowing a larger reduction of the magmastatic head (or weight) of the magma column.

Deriving [delta]P/[delta]Ve from vent height and magma density versus deflation data here implies (1) each deflation begins with roughly the same initial summit source pressure and (2) source pressure drops to that of the magmastatic pressure of a lava column with height equal to the elevation of the vent site. The three largest summit deflations (1955, 1960, and 1961) are associated with low elevation (46-399 m, 30 m, and 396-792 m) flank eruptions [Epp et al., 1983, Figure 1]. The 1955 event followed months of summit inflation [Dzurisin et al., 1984], and summit eruptions actually preceded the 1960 and 1961 cycles. Hence if we define the initial pressure as summit pressure sufficient to produce a summit eruption, requirement (1) above is satisfied for two of the three low elevation dis-charges. Another event in 1977 began with very little summit inflation in the preceding 6 months [Dzurisin et al., 1980], suggesting that summit pressure may have been low at the time of the eruption onset. The volume of subsidence in fact falls slightly short of the general correlation given by Epp et al. [1983, Figure 1]. Assumption (2) is probably never satisfied, particularly for eruptions on the distant portions of the east rift zone (several tens of kilometers from the summit) because flow resistance in the conduit system may stop magma motion before pressure equilibrium is reached. In addition, the infrequently intruded and, hence, relatively cool lower east rift zone is an especially poor environment for long lasting eruption [Hardee, 1987]. Dike-shaped conduits that feed surface vents are prone to closure by rapid cooling against wall rock and are inefficient for magma transport. Therefore the source pressure drop is most likely less than implied by the vent height and the [delta]P/[delta]Ve ratio so calculated represents a maximum value.

Decker et al. [1983] infer a pressure change of 0.085 MPa/[mu]rad of N60deg.W UWE tilt from the Epp et al. [1983] vent elevation versus tilt correlation; implicit is a magma column density of 2550 kg/m^3. Adjusting values to an east tilt at UWE (assuming that N60deg.W is a radial vector to the average source epicenter) gives [delta]P/[delta][tau] of 0.098 MPa/[mu]rad. With an average [delta]Ve/[delta][tau] factor of 0.45 x 10^6 m^3/[mu]rad for east-west tilt [Dvorak and Okamura, 1985], [delta]P/[delta]Ve is 0.22 Pa/m^3.

A separate calculation of pressure change and subsidence volume is made for a large subsidence event which, because of its size, strongly influences the overall [delta]P/[delta]Ve relation given above. The summit eruption in December 1959 was at a 1100-m elevation vent and was followed by eruption at sea level in January 1960. The reservoir pressure drop [delta]P corresponding to a 1100 m drop in the magma column (of density 2600 kg/m^3) is a maximum of 28 MPa. For the January 1960 deflation, Eaton [1962, Figure 12] found [delta]Ve=150 x 10^6 m^3, determined by visual fit of a point source model to observed tilts in the Kilauea summit region. Therefore [delta]P/[delta]Ve is 0.19 Pa/m^3.

Pressure change during small inflations and deflations. One half of the 18 deflations considered by Epp et al. [1983] produced deflationary tilts larger than 45 [mu]rad (N60deg.W tilt at UWE) with the largest deflation in January 1960 totaling 310 [mu]rad. Therefore the pressure estimate given above is appropriate for the larger deflations.

During the 1972-1974 Mauna Ulu activity, Tilling [1987] noted a positive correlation between lava lake surface elevation and level of summit inflation, as measured by tilt at UWE. He interpreted this to imply that Kilauea's magmatic system was fully engorged and open so that as the reservoir expanded the lava lake expanded too. It can also be considered in terms of a pressure link. A pressure increase within the summit reservoir would raise the elevation of the lava lake and, hence, the magmastatic head. Eruptions and intrusions at rift zone sites near Mauna Ulu tapped magma from the Mauna Ulu system and reduced pressure locally. In response, the elevation of the lava lake dropped and magma flow from the summit increased. Flow continued until the pressure gradient between summit reservoir and rift zone returned to an equilibrium value, leaving the summit partly deflated. Therefore, as a first approximation, summit pressure variations may be estimated from changes in the Mauna Ulu lava lake height.

Two of the larger 1973 summit deflations and lava lake draining episodes and intervening reinflation described by Tilling [1987] are reexamined here. Summit subsidence accompanied a Mauna Ulu lake-draining event, which also included brief lava effusion at nearby Pauohi and Hiiaka craters on May 5, 1973. The lake emptied of lava within 2 hours leaving a 200-m-deep crater floored by rubble, a change of more than 160 m; it is unknown how far the column retracted below the rubble cover. Lava began to refill the crater of Mauna Ulu on May 8, and 150 m were added between May 8 and 25. Filling of the Mauna Ulu lava lake and summit inflation continued to June 9 when a second deflation event occurred, this time noneruptive and not as severe as the first.

Unfortunately, only the gradual inflation interval between the deflations is well characterized by geodetic data [Tilling et al., 1987, Figure 16.41C]. The source locations for the two rapid summit deflations are unknown; hence volumes of deflations cannot be calculated with much certainty. Inversion of the inflationary tilt data using a point source model gives an uplift volume of 2.3x10^6 m^3. The source is below the northeast rim of Halemaumau Crater at a depth of about 2.8 km. The summit pressure change estimated from the lava lake filling with a density of 2600 kg/m^3 and summit uplift between May 7 and 25, 1973, is [delta]P/[delta]Ve=1.66 Pa/m^3. If the source position for the two periods of rapid deflation centered near the position of the intervening inflation, then the UWE tilt changes given by Tilling et al. [1987] suggest collapse volumes of 2.5 x 10^6 and 1 x 10^6 m^3 for the May and June events, respectively. The May 5 deflation event gives a minimum (as the total lava level change is unknown) pressure change of 1.63 MPa/m^3. Pressure change is an estimated 2.39 Pa/m^3 for the June 9 event.

Between 1984 and 1986, repetitive periods of summit inflation at Kilauea were associated with an increase in level of the lava column filling the vertical eruptive vent within the Pu'u O'o cone [Wolfe et al., 1987; HVO, unpublished data, 1989]. At the end of an eruptive episode, lava disappeared below a depth of 50 m (lava could generally not be seen at depths greater than this) for a period of a few days to three weeks. The period of conduit refilling and summit reinflation culminated in 1 or 2 days of spectacular fountaining at Pu'u O'o. Following episode 34, lava was sighted 3 days after the eruption at a depth of 100 m [HVO, unpublished data, 1989]. A 50- to 100-m rise in height of a column of magma (density 2600 kg/m^3) produces a hydrostatic pressure increase of 1.3 to 2.5 MPa. This is a minimum pressure increase for the summit reservoir because the lava column may descend to greater depths within the conduit and because additional pressure is required to overcome the yield strength threshold of the rift zone magmatic system before resuming flow. This range of pressure change, with inflation volumes of 3 x 10^6 m^3 give a rate of reservoir pressure change with uplift of at least 0.43 Pa/m^3 and possibly more than 0.83 Pa/m^3.

Summary of pressure change estimates. Table 3 summarizes the reservoir pressure estimates given here. The smaller Mauna Ulu and Pu'u O'o events have a high rate of pressure change compared to the rate for flank eruptions given by Decker et al. [1983] which is sensitive to larger-sized events.


A difference in [delta]M/[delta]Ve (and [delta]M*/[delta]Ve) is apparent in comparing summit deflations for Pu'u O'o and Mauna Ulu eruptions with those of August 1981 and January 1983 (Table 2). The Pu'u O'o and Mauna Ulu events also had smaller deflation volumes and shallower source depths. Mechanisms that might produce this difference in [delta]M/[delta]Ve include (1) change in abundance, N, of comagmatic CO2 gas between or during eruption, (2) decrease in effective crustal shear modulus, [mu], for larger events, and (3) greater volume change of CO2 gas phase with pressure change for events with shallow source depth because of lower lithostatic pressure at that level or upward migration and concentration of CO2 at shallow levels of the reservoir. I propose that mechanism (3) is the cause of varying [delta]M/[delta]Ve. First, I explain why mechanisms (1) and (2) are unlikely.

Mechanisms That Might Produce Difference in [delta]M/[delta]Ve

Changing abundance of CO2 gas. Variation of [delta]M/[delta]Ve for different events is probably not the result of a net change in the abundance N of comagmatic CO2 gas during repose. For a fixed reservoir depth in the 2.5-3.5 km range appropriate for Kilauea, an increase in N of between 0.002 and 0.004 is necessary to produce the magnitude of change of [delta]M/[delta]Ve observed between January 1983 and the later Pu'u O'o events. This is too large a change relative to the estimated CO2 content to be reasonable. The arrival of fresh mantle magma to Kilauea's reservoir, which is the source of CO2, is thought by Dzurisin et al. [1984] to have been relatively constant during the past two decades, varying between 5 x 10^6 m^3 and 11 x 10^6 m^3 per month. Degassing of the summit reservoir since measurements began in 1979 is also a reasonably steady process [Casadevall et al., 1987].

It is unlikely that preferential leakage of exsolved gas from the reservoir during larger events is responsible for decreasing [delta]M/[delta]Ve. CO2 degassing at a rate two orders of magnitude greater than measured by Greenland et al. [1985] in December 1983 and February 1984 is required to explain the excess of collapse in 1981 and 1983 compared to the Pu'u O'o events. There are no data on the specific rate of CO2 emission at Kilauea at the time of the 1981 and 1983 events. For 2 months following the January 1983 eruption, however, geochemical data for Kilauea summit fumaroles (HVO, unpublished data, 1983) do not indicate a surge of CO2 emission, in particular from the ratio of carbon to sulfur or from emission rates of SO2 [Casadevall et al., 1987].

Variation of crustal shear modulus [mu]. Diminishing [mu] lowers both [delta]M/[delta]Ve (equation (10)) and [delta]P/[delta]Ve (equation (2)). A reduction of the effective crustal shear modulus m could result from creep effects with time or anelastic failure at high stress. The value for [mu] (in equation (10)) appears to be unrelated to the magnitude of strain and time. Both short deflation and considerably longer inflation intervals of the Pu'u O'o eruption produce similar [delta]g/[delta][tau] (Figure 7) and hence derived values for [delta]M/[delta]Ve (Table 2). This is supported by gravity and tilt observations at a summit site of Mauna Loa volcano during the 1984 eruption [Lockwood et al., 1985]. These data showed a constant ratio of gravity to tilt change for the duration of the 3-week deflation, with the exception of the first day which was affected by the initial shallow dike injection.

Increased role of CO2 gas at shallow levels. The Mauna Ulu and Pu'u O'o (at least after April 1985) deflations had source depths of 2.2-2.8 km, while the 1981 and 1983 events were 3.5-4.0 km (Figure 4). A prefered explanation for differences in [delta]M/[delta]Ve (Table 2) is greater volume change of CO2 gas with pressure change at shallow, low pressure levels of the summit reservoir during Pu'u O'o and Mauna Ulu related summit deflations. During these events, more pronounced volume increase of CO2 gas replaced drained magma, which limited edifice collapse. Two mechanisms may increase the role of CO2 gas at shallow levels. First, [delta]M/[delta]Ve is related to the internal reservoir pressure (1/P2 in equation (10)), which controls volume changes of exsolved CO2 that partially fills the source volume Vr. This term reflects a combination of the volume of the exsolved gas phase (inversely proportional to P) and its bulk modulus (essentially P). As pressure P increases with depth, exsolved CO2 volume changes with pressure change will be most pronounced for shallow reservoir depths. Second, upward migration of exsolved CO2 gas leads to increased concentration in shallow levels of the reservoir.

A Mechanism That Might Produce Difference in [delta]P/[delta]Ve

Variation of the effective source volume might produce a difference in [delta]P/[delta]Ve. The volume of the source, Vr, does not affect [delta]M/[delta]Ve in equation (10). It does affect the source pressure change [delta]P, as shown by equation (2). Assuming constant [mu], observed differences in [delta]P/[delta]Ve indicate a relatively big source volume for the larger subsidence events as compared to smaller Mauna Ulu and Pu'u O'o ones (Table 3). Variation of Vr in this context does not relate to volume changes by simple inflation and deflation, but to migration of the boundary between elastic and fluid behavior. This is essentially a transition to viscoelastic behavior after a certain yield stress is exceeded in the high-temperature, high-strain zone surrounding the pressure source [Davis, 1986]. A viscoelastic material under constant stress will increase in strain with time or, if strain is constant, stress will decrease with time. Hence such a behavior implies that Vr is a function of stress and time.

The spatial pattern of vertical surface displacement is virtually identical for a spherical source of any size [McTigue, 1987], and so Vr can not be determined from geodetic data. Some systematic trends in the history and distribution of deformation at Kilauea, however, support the idea of a changing source size. Some leveling or tilt data span brief time intervals, and identify discrete source hypocenters [Fiske and Kinoshita, 1969; Dvorak et al., 1983; Figure 4]. These may correspond to small, distinct source volumes, such as an individual pocket of melt. In contrast, essentially the same source hypocenter and deformation pattern have been observed for different, but larger events and time intervals. Examples are the 1924 subsidence [Ryan et al., 1983; Mogi, 1958], the November 1975 deflation [Lipman et al., 1985, Figure 17C] and two periods of gradual deflation during Janaury 1976 to April 1979 and January 1984 to July 1986 (HVO, unpublished data, 1986). During these time intervals the effective source volume may coincide with the entire plastic region and extensions reaching into both the southwest and east rift zones. The location and geometry of this source volume remains fixed and governs the repeat pattern of surface displacements. Collapse during these periods is greatest at the south margin of Kilauea caldera. Some subsidence is found in the upper reaches of the rift zones and well to the south of the deflation center. This pattern is unlikely to be due to a simple point source of deformation; the complex distribution of change suggests an extended source. Subsidence over the upper rift zone areas may correspond to migration of the boundary between plastic and elastic behavior all the way into the aseismic rift zone cores [Ryan et al., 1983], principal conduits for magma transfer out off the summit reservoir. In other words, the effective source volume for these time intervals includes the rift zones.

Migration of the subsidence center is commonly observed during the course of rapid deflation at Kilauea [Fiske and Kinoshita, 1969; Jackson et al., 1975; Swanson et al., 1976; Dvorak and Okamura, 1987]. The usual pattern is for the northern part of the caldera to subside first followed quickly by the bulk of subsidence at the south end [Decker, 1987; Dvorak and Okamura, 1987]. This pattern would be expected if the geometric center of the reservoir complex was to the south of the locus of magmatic activity. Spreading of the plastic zone and hence expansion of the effective source would be accompanied by a southward shift of the subsidence focus because of the position difference between the small initial source and the bulk of the reservoir.

Estimates of CO2 Content and Source Volume

Solution for the source CO2 concentration from [delta]M/[delta]Ve is by equation (10) (K=11.5 GPa, [rho]=2600 kg/m^3, T=1470deg.K, [omega]=0.044 kg/mol, R=8.314 m^3 Pa/mol deg.K, [nu]=0.25). Davis [1976] gives an upper bound for [mu] of 3 GPa. This limiting value is constrained by the absence of a piezomagnetic anomaly associated with deformation. Reservoir pressure P is approximately equal to lithostatic pressure (crustal density of 2300 kg/m^3). Therefore P=56 MPa for the source depth of the Pu'u O'o deflations (an estimated 2.5 km). This and the [delta]M/[delta]Ve ratio of 7165 kg/m^3 corresponds to a source CO2 content of 0.0030 weight fraction. The deeper (3.5 and 4.0 km) 1981 and 1983 events have lower [delta]M/[delta]Ve ratios (3050 and 2625 kg/m^3) and much lower CO2 values of 0.0009 and 0.0005 weight fraction. The CO2 values for Pu'u O'o phases are compatible with previous estimates for Kilauea magma of 0.0065 [Gerlach and Graeber, 1985] and 0.0032 [Greenland et al., 1985] by weight determined from geochemical data. The difference in gas content between shallow and deep sources suggests that upward migrating gas may collect within pockets of magma at the upper portion of the magma reservoir.

The source volume may be estimated from [delta]P/[delta]Ve and equation (2) ([nu]=0.25, [mu]=3 GPa). For the small Pu'u O'o inflation cycles a maximum source volume of 6 km^3 is implied by the [delta]P/[delta]Ve value of at least 0.43 Pa/m^3. A source volume of only 1.6 km^3 is associated with the May 1973 Mauna Ulu lava lake filling event ([delta]P/[delta]Ve=1.66 Pa/m^3). In contrast, the larger January 1960 deflation ([delta]P/[delta]Ve no more than 0.20 Pa/m^3) had a source volume greater than 13 km^3.

If the 1981 and 1983 events also had large source volumes, then the CO2 value given above for them would be about the averaged gas content of the reservoir. Indeed the average CO2 abundances in a suite of glasses from Kilauea submarine lavas, which may best represent preeruption concentrations of volcanic gases, is 0.00092 by weight [Garcia et al., 1989]. The apparently exceptionally gas-rich pocket of melt at shallow depth, source of the Mauna Ulu and Pu'u O'o deformation events, is therefore anomalous.

Long-Term Changes

Decker [1987] suggested that long-term deformation may not correlate with reservoir pressure change. This may be seen from analysis of Kilauea's eruptive history. Eruptions within the summit caldera took place in November 1967, August 1971, July and September 1974, November 1975, and April and September 1982 [Dzurisin et al., 1984]. These eruptions took place at a wide range of inflation levels, indicated by changes in summit tilt [Dzurisin et al., 1984]. Analysis of leveling surveys (HVO, unpublished data, 1989) suggests that collapse in the 8-year period between 1974 and 1982 amounts to roughly 300 x 10^6 m^3. However, eruption of lava to the elevation of the caldera floor in 1982 shows that reservoir pressure was just as high then as it was in 1974 despite the net collapse. It is not possible for an elastic deflation mechanism to explain long-term subsidence because reservoir pressure would decrease in proportion to subsidence.

The process of rifting (and widening) of Kilauea's edifice is a ubiqituous feature of Kilauea trilateration data. Long-term summit subsidence is therefore explained by loss of horizontal support of the fluid reservoir [Johnson, 1987]. This mechanism is consistent with the observation that the gravity to height-change ratio for long-term intervals is sometimes near the free-air rate; such a ratio cannot be obtained from simple deflation relating to magma extraction. The further attraction of the rifting model is that it explains long-term collapse by change in the reservoir shape rather than pressure.

Contraction of magma as it cools and gas escape may produce subsidence. After a major collapse, additional gradual subsidence may occur because of continued escape of gas bubbles that first formed during the initial event. These processes produce a source volume contraction with little mass loss and would produce surface subsidence with no [delta]g*. In fact, this is the pattern of change observed between January 1983 and July 1986 as well as between December 1975 and October 1977 [Dzurisin et al., 1980]. Both periods follow major summit collapses.

Unfortunately, no data exist on the emission rate of CO2 at Kilauea's summit before 1983. SO2 emission measurements however have been made since 1979 [Casadevall et al., 1987]. Emissions of SO2 from the summit area of Kilauea show that reservoir degassing is favored when internal pressure is low such as after a major deflation. Shortly after both the August 1981 and January 1983 deflations SO2 degassing increased by a factor of 1.6 [Casadevall et al., 1987; Greenland et al., 1985]. The August 1981 event was followed by reinflation while the SO2 release rate returned to previous levels. Ever since the rapid January 1983 deflation, however, Kilauea has remained in a slowly deflating trend and SO2 degassing has continued at a high rate [Casadevall et al., 1987; HVO, unpublished data, 1989]. This is consistent with a pressure recovery after the August 1981 event which limited degassing, and a sustained low pressure regime after the January 1983 event which has facilitated gas release.


Three distinct modes of deflation are observed at Kilauea volcano. Small, brief deflations associated with Mauna Ulu and Pu'u O'o eruptive activity have a shallow source confined to a gas-rich region at the uppermost portion of the magma reservoir. Low pressure and abundant CO2 at this level mean that volume changes of a CO2 gas phase play an enhanced role relative to edifice deformation in accommodating volume changes of stored magma. Large, rapid deflations, with relatively deep sources, have pressure change distributed over a larger portion of the reservoir. A larger effective source volume, produced by spreading of the plastic zone, results in less pressure decrease relative to the volume of subsidence. Higher lithostatic pressure associated with deeper sources for these events and lower average CO2 concentration for the reservoir as a whole result in a diminished role of CO2 gas volume change. Thus volume change of magma for these events is accommodated to a larger degree by edifice deformation. Gradual, long-term subsidences of Kilauea volcano, not associated with specific eruption, are caused by a combination of gas escape, cooling contraction, and rifting of the summit area. Such long-term subsidence is not accompanied by a change in reservoir pressure.


[gamma] universal gravitational constant, 6.67 x 10-11 N m2 kg-2.

[mu] crustal shear modulus, GPa.

[nu] edifice Poisson's ratio, dimensionless.

[rho] magma density, 2600 kg/m^3 [Fujii and Kushiro, 1977].

[delta][tau] tilt change, [mu]rad.

[omega] mass of 1 mol of CO2, 0.044 kg/mol.

b CO2 solubility constant, 5.9 x 10-12 Pa-1.

[delta]g gravity change, [mu]Gal.

[delta]g* free-air corrected gravity change, [mu]Gal.

[delta]h height change, mm.

K magma bulk modulus, 11.5 GPa [Murase et al., 1977].

[delta]M reservoir magma mass change, kg.

[delta]M* lava flow or dike injection mass, kg.

m exsolved CO2 in magma, weight fraction.

N total CO2 in magma, weight fraction.

n limit of disolved CO2 in magma, weight fraction.

P pressure, Pa.

[delta]P pressure change, Pa.

R gas constant, 8.314 m^3 Pa/mol deg.K.

T reservoir magma temperature, 1420deg.-1470deg.K.

Vr volume of source, m^3.

[delta]Vr source volume change, m^3.

[delta]Ve edifice volume change, m^3.

Vg exsolved CO2 in reservoir, m^3.

X horizontal distance to source, m.

Z depth to source, m.

Acknowledgments. The staff of the Hawaiian Volcano Observatory of the U.S. Geological Survey made essential contributions to this study. Logistical assistance was arranged on behalf of HVO by Reggie Okamura. I thank Thomas Wright, who maintained the gravity vigilance at Kilauea during times that I was away. John Dvorak, Ron Hanatani, Arnold Okamura, Maurice Sako, and Ken Yamashita made the geodetic measurements and answered my countless questions about Hawaiian geodetic data. Jurgen Kienle (Univ. Alaska) did the June 1981 gravity survey and kindly sent his gravimeter to Hawaii in 1985 for calibration. John Dvorak carried out the gravity surveys between August 1981 and February 1983. Discussions with Eduard Berg, Daniel Dzurisin, and Roger Denlinger helped guide me in this research. Suggestions and editorial assistance by Eduard Berg, Mike Garcia, and Twyla Thomas significantly improved this paper. I thank Charles Helsley for providing partial financial support. This paper is part of a doctoral dissertation submitted to the Department of Geology and Geophysics of the University of Hawaii. School of Ocean and Earth Science and Technology contribution 2713.


Brown, R. J. S., and J. Korringa, On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid, Geophysics, 40, 608-616, 1975.

Casadevall, T. J., J. B. Stokes, L. P. Greenland, L. L. Malinconico, J. R. Casadevall, and B. T. Furukawa, SO2 and CO2 emission rates at Kilauea Volcano, 1979-1984, U.S. Geol. Surv. Prof. Pap., 1350, 771-780, 1987.

Crosson, R. S., and R. Y. Koyanagi, Seismic velocity structure below the Island of Hawaii from local earthquake data, J. Geophys. Res., 84, 2331-2342, 1979.

Davis, P. M., The computed piezomagnetic anomaly field for Kilauea volcano, Hawaii, J. Geomagn. and Geoelectr., 28, 113-122, 1976.

Davis, P. M., Surface deformation due to inflation of an arbitrarily oriented triaxial ellipsoidal cavity in an elastic half-space, with reference to Kilauea Volcano, Hawaii, J. Geophys. Res., 91, 7429-7438, 1986.

Davis, P. M., D. B. Jackson, J. Field, and F. D. Stacey, Kilauea Volcano, Hawaii: A search for the volcanomagnetic effect, Science, 180, 73-74, 1973.

Davis, P. M., L. M. Hastie, and F. D. Stacey, Stresses within an active volcano-with particular reference to Kilauea, Tectonophysics, 22, 355-362, 1974.

Decker, R. W., Dynamics of Hawaiian volcanoes: An overview, U.S. Geol. Surv. Prof. Pap., 1350, 997-1018, 1987.

Decker, R. W., A. T. Okamura, and J. J. Dvorak, Pressure changes in themagma reservoir beneath Kilauea Volcano, Hawaii, Eos Trans. AGU, 64, 901, 1983.

Dobrin, M., Introduction to Geophysical Prospecting, McGraw-Hill, New York, 446pp, 1960.

Dvorak, J. J., and A. T. Okamura, Variations in tilt rate and harmonic tremor amplitude during the January-August 1983 east rift eruptions of Kilauea Volcano, Hawaii, J. Volcanol. Geotherm. Res., 25, 249-258, 1985.

Dvorak, J. J., and A. T. Okamura, A hydraulic model to explain variations in summit tilt rate at Kilauea and Mauna Loa volcanoes, U.S. Geol. Surv. Prof. Pap., 1350, 1281-1296, 1987.

Dvorak, J., A. Okamura, and J. H. Dieterich, Analysis of Surface deformation data, Kilauea volcano, Hawaii, October 1966 to September 1970, J. Geophys. Res., 88, 9295-9304, 1983.

Dvorak, J. J., A. T. Okamura, T. T. English, R. Y. Koyanagi, J. S. Nakata, M. K. Sako, W. T. Tanigawa, and K. M. Yamashita, Mechanical response of the south flank of Kilauea Volcano, Hawaii, to intrusive events along the rift systems, Tectonophysics, 124, 193-209, 1986.

Dzurisin, D., L. A. Anderson, G. P. Eaton, R. Y. Koyanagi, P. W. Lipman, J. P. Lockwood, R. T. Okamura, G. S. Puniwai, M. K. Sako, and K. E. Yamashita, Geophysical observations of Kilauea volcano, Hawaii, 2, Constraints on the magma supply during November 1975-September 1977, J.Volcanol. Geotherm. Res., 7, 241-269, 1980.

Dzurisin, D., R. Y. Koyanagi, and T. T. English, Magma supply and storage at Kilauea volcano, Hawaii, 1956-1983, J. Volcanol. Geotherm. Res., 21, 177-206, 1984.

Eaton, J. P., Crustal structure and volcanism in Hawaii, in The Crust of the Pacific Basin, Geophys. Monogr. Ser., vol. 6, edited by G. A. Macdonald and H. Kuno, pp. 13-29, AGU, Washington , D. C., 1962.

Eaton, J. P., and K. J. Murata, How volcanoes grow, Science, 132, 925-938, 1960.

Eggers, A. A., Temporal gravity and elevation changes at Pacaya volcano, Guatemala, J. Volcanol. Geotherm. Res., 19, 223-237, 1983.

Epp, D., R. W. Decker, and A. T. Okamura, Relation of summit deformation to east rift zone eruptions on Kilauea Volcano, Hawaii, Geophys. Res. Lett., 10, 493-496, 1983.

Fiske, R. S., and W. T. Kinoshita, Inflation of Kilauea volcano prior to its 1967-1968 eruption, Science, 165, 341-349, 1969.

Fujii, T., and I. Kushiro, Density, viscosity, and compressibility of basaltic liquid at high pressures, in Annual Report of the Director 1976-1977, pp. 419-424, Geophysical Laboratory, Carnegie Institution, Washington, D. C., 1977.

Garcia, M. O., D. W. Muenow, and K. E. Aggrey, Major element, volatile, and stable isotope geochemistry of Hawaiian submarine tholeiitic glasses, J. Geophys. Res., 94, 10,525-10,538, 1989.

Gerlach, T. M., and E. J. Graeber, Volatile budget of Kilauea Volcano, Nature, 313, 273-277, 1985.

Greenland, L. P., W. I. Rose, and J. B. Stokes, An estimate of gas emissions and magmatic gas content from Kilauea volcano, Geochim. Cosmochim. Acta, 49, 125-129, 1985.

Hammer, S., The anomalous vertical gradient of gravity, Geophysics, 35, 153-157, 1970.

Hardee, H. C., Heat and mass transport in the east-rift-zone magma conduit of Kilauea Volcano, U.S. Geol. Surv. Prof. Pap., 1350, 1471-1486, 1987.

Harris, D. M., The concentration of CO2 in submarine tholeiitic basalts, J. Geol., 89, 589-701, 1981.

Hill, D. P., and J. J. Zucca, Geophysical constraints on the structure of Kilauea and Mauna Loa volcanoes and some implications for seismomagmatic processes, U.S. Geol. Surv. Prof. Pap., 1350, 903-917, 1987.

Jachens, R. C., and G. P. Eaton, Geophysical observations of Kilauea volcano, Hawaii, 1, temporal gravity variations related to the 29 November 1975, M=7.2 earthquake and associated summit collapse, J. Volcanol. Geotherm. Res., 7, 225-240, 1980.

Jackson, D. B., D. A. Swanson, R. Y. Koyanagi, and T. L. Wright, The August and October 1968 East Rift eruptions of Kilauea Volcano, Hawaii, U.S. Geol. Surv. Prof. Pap., 890, 33pp, 1975.

Johnson, D. J., Elastic and inelastic magma storage at Kilauea Volcano, U.S. Geol. Surv. Prof. Pap., 1350, 1297-1306, 1987.

Kinoshita, W. T., H. L. Krivoy, D. R. Mabey, and R. R. MacDonald, Gravity survey of the Island of Hawaii, U.S. Geol. Surv. Prof. Pap., 475-C, C114-C116, 1963.

Klein, F. W., R. Y. Koyanagi, J. S. Nakata, and W. R. Tanigawa, The seismicity of Kilauea's magma system, U.S. Geol. Surv. Prof. Pap., 1350, 1019-1186, 1987.

Koyanagi, R. Y., J. D. Unger, E. T. Endo, and A. T. Okamura, Shallow earthquakes associated with inflation episodes at the summit of Kilauea volcano, Hawaii, Bull. Volcanol., 39, 621-631, 1976.

Lipman, P. W., J. P. Lockwood, R. T. Okamura, D. A. Swanson, and K. M. Yamashita, Ground deformation associated with the 1975 magnitude-7.2 earthquake and resulting changes in activity of Kilauea volcano 1975-1977, U.S. Geol. Surv. Prof. Pap., 1276, 45 pp., 1985.

Lockwood, J. P., N. G. Banks, T. T. English, L. P. Greenland, D. B. Jackson, D. J. Johnson, R. Y. Koyanagi, K. A. McGee, A. T. Okamura, and J. M. Rhodes, The 1984 eruption of Mauna Loa Volcano, Hawaii, Eos Trans. AGU, 66, 169-171, 1985.

Longman, I. M., Formulas for the tidal acceleration of gravity, J. Geophys. Res., 64, 2351-2355, 1959.

Manghnani, M. H., and G. P. Woollard, Elastic wave velocities in Hawaiian rocks at pressures to ten kilobars, in The Crust and Upper Mantle of the Pacific Area, Geophysical Monogr. Ser., vol. 12, edited by L. Knopoff, C. L. Drake, and P. J. Hart, pp. 501-516, AGU, Washington, D. C., 1968.

McTigue, D. F., Elastic stress and deformation near a finite spherical magma body: Resolution of the point source paradox, J. Geophys. Res., 92, 12,931-12,940, 1987.

Mogi, K., Relations of eruptions of various volcanoes and the deformation of the ground surfaces around them, Bull. Earthquake Res. Inst. Univ. Tokyo, 39, 99-134, 1958.

Murase, T., I. Kushiro, and T. Fujii, Compressional wave velocity in partially molten peridotite, in Annual Report of the Director 1976-1977, pp. 414-416, Geophysical Laboratory, Carnegie Institution, 414-416, Washington, D. C., 1977.

Pollard, D. D., P. T. Delaney, W. A. Duffield, E. T. Endo, and A. T. Okamura, Surface deformation in volcanic rift zones, Tectonophysics, 94, 541-584, 1983.

Rubin, A. M., and D. D. Pollard, Origins of blade-like dikes in volcanic rift zones, U.S. Geol. Surv. Prof. Pap., 1350, 1149-1470, 1987.

Rundle, J. B., Gravity changes and the Palmdale uplift, Geophys. Res. Lett., 5, 41-44, 1978.

Ryan, M. P., Mechanical behavior of magma reservoir envelopes: Elasticity of the olivine tholeiite solidus, Bull. Volcanol., 43-(4), 743-772, 1980.

Ryan, M. P., Elasticity and contractancy of Hawaiian olivine tholeitte and its role in the stability and structural evolution of subcaldera magma reservoirs and rift systems, U.S. Geol. Surv. Prof. Pap., 1350, 1395-1448, 1987.

Ryan, M. P., J. Y. K. Blevins, A. T. Okamura, and R. Y. Koyanagi, Magma reservoir subsidence mechanics: Theoretical summary and application to Kilauea volcano, Hawaii, J. Geophys. Res., 88, 4147-4181, 1983.

Sanderson, T. J. O., G. Berrino, G. Corrado, and M. Grimaldi, Ground deformation and gravity changes accompanying the March 1981 eruption of Mount Etna, J. Volcanol. Geotherm. Res., 16, 299-315, 1983.

Sasai, Y., Multiple tension-crack model for dilatancy: Surface displacement, gravity and magnetic change, Bull. Earthquake Res. Inst. Univ. Tokyo, 61, 429-473, 1986.

Savage, J. C., Local gravity anomalies produced by dislocation sources, J. Geophys. Res., 89, 1945-1952, 1984.

Swanson, D. A., D. B. Jackson, R. Y. Koyanagi, and T. L. Wright, The February 1969 East Rift eruption of Kilauea Volcano, Hawaii, U.S. Geol. Surv. Prof. Pap., 891, 30pp., 1976.

Swanson, D. A., W. A. Duffield, D. B. Jackson, and D. W. Peterson, Chronological narrative of the 1969-71 Mauna Ulu eruption of Kilauea Volcano, Hawaii, U.S. Geol. Surv. Prof. Pap., 1056, 55 pp., 1979.

Thurber, C. H., Seismic detection of the summit magma complex of Kilauea Volcano, Hawaii, Science, 223, 165-167, 1984.

Thurber, C. H., Seismic structure and tectonics of Kilauea Volcano, U.S. Geol. Surv. Prof. Pap., 1350, 919-934, 1987.

Tilling, R. I., Fluctuations in surface height of active lava lakes during 1972-1974 Mauna Ulu eruption, Kilauea Volcano, Hawaii, J. Geophys. Res., 92, 13,721-13,730, 1987.

Tilling, R. I., R. Y. Koyanagi, P. W. Lipman, J. P. Lockwood, J. G. Moore, and D. A. Swanson, Earthquake and related catastropic events, Island of Hawaii, November 29, 1975: A preliminary report, U.S. Geol. Surv. Circular, 740, 33 pp., 1976.

Tilling, R. I., R. L. Christiansen, W. A. Duffield, E. T. Endo, R. T. Holcomb, R. Y. Koyanagi, D. W. Peterson, and J. D. Unger, The 1972-1974 Mauna Ulu eruption, Kilauea Volcano: An example of quasi-steady-state magma transfer, U.S. Geol. Surv. Prof. Pap., 1350, 405-470, 1987.

Walsh, J. B., and J. R. Rice, Local changes in gravity resulting from deformation, J. Geophys. Res., 84, 165-170, 1979.

Wolfe, E. W., M. O. Garcia, D. B. Jackson, R. Y. Koyanagi, C. A. Neal, and A. T. Okamura, The Pu'u O'o eruption of Kilauea Volcano, episodes 1-20, January 3, 1983, to June 8, 1984, U.S. Geol. Surv. Prof. Pap., 1350, 471-508, 1987.