Gravity Changes on Mauna Loa Volcano

Johnson, D.J., Gravity changes on Mauna Loa Volcano, in Mauna Loa Revealed: Structure, composition, History and Hazards, Geophysical Monograph 92, edited by J.M. Rhodes and John P. Lockwood, pp. 127-143, AGU, Washington, D.C., 1995.

Copyright 1995 American Geophysical Union. Further electronic distribution is not allowed.

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Abstract. Gravity observations made on Mauna Loa Volcano Hawaii, before and after the March 25-April 14, 1984 eruption indicate that a magma reservoir, centered 3630+/-200 m below the summit area, lost 136(+/-50)x10^9 kg of magma mass during the event. Comparison of the reservoir mass loss figure ([Delta]M) with the volume change by surface subsidence of the edifice ([Delta]Ve) gives [Delta]M/ [Delta]Ve=2033 kg/m^3, consistent with the ratio predicted for magma withdrawal from a reservoir containing degassed, CO2-poor magma. The net reservoir mass loss is insufficient to entirely account for the mass of erupted lava and dike intrusion. A proposed explanation is that a pulse of magma flow from depth, concurrent with the eruption, may have replaced reservoir magma lost to eruption. With this model, magma resupply to the shallow Mauna Loa reservoir is episodic and is associated with eruption; during repose, extensive CO2 degassing and a low rate of magma resupply minimizes the CO2 content of stored reservoir magma.

INTRODUCTION

Accelerating rates of seismicity and ground surface displacement observed at Mauna Loa Volcano led to a published statement in September 1983 of an increased probability of eruption within the following 2 years [Decker et al., 1983]. Baseline gravity observations on Mauna Loa were made February 13-14, 1984 in anticipation of the eruption. Fortuitously an eruption began on March 25 at 01:25 HST [Lockwood et al., 1985] within just 6 weeks of the initial gravity observations. Additional measurements were begun 8 hours after the first sighting of lava, and continued at intervals of 1-6 days for the duration of the 3 week eruption. Analysis of these data give a unique perspective on how Mauna Loa works.

A classic view of the eruptive behavior of Hawaiian volcanoes is that they contain a shallow magma reservoir, located below the summit, that gradually fills with mantle-derived magma during repose. Then, on eruption, previously stored magma is rapidly expelled from the reservoir to the surface or into rift zone intrusions [Dzurisin, et al., 1984; Decker et al., 1983]. This view is reinforced by observation of surface uplift during periods of repose and subsidence of the edifice during eruption, indicating filling and draining of a subsurface magma storage zone.

An unresolved issue of the 1984 eruption is a disparity between the volume of edifice contraction and the volume of erupted lava [Dvorak et al, 1985]. Previous estimates of the volume of edifice collapse are 110x10^6 m^3 [Okamura et al., 1984], 100(+/-30)x10^6 m^3 [Lockwood et al., 1985], and 55(+/-15)x10^6 m^3 [Dvorak et al., 1985]. Approximately 220x10^6 m^3 of lava, which has an estimated density of 2000 kg/m^3, reached the surface during the eruption [Lipman and Banks, 1987]. This is equivalent to 170x10^6 m^3 of magma with density 2600 kg/m^3 - still more than the volume of collapse. Consider also that a significant volume of magma was delivered to the inferred 22 km-long intrusive dike that bisected the summit and rift zones. Perhaps 75x10^6 m^3 of magma (dike roughly estimated 0.75 m wide, 5000 m high, and 20 km long) ended up stored within the rift zone dike. The total of dike and lava flow volumes gives 245x10^6 m^3, far in excess of the subsidence volumes given above.

Okamura et al. [1984], states that the volume discrepancy between subsidence and erupted lava might be due to: (1) eruption of magma stored within the rift zone since the previous eruption in 1975, (2) subsidence restricted by crustal rigidity, and (3) vesiculation of stored reservoir magma. The first process may be minor, as geochemical analyses of 1984 lava samples presented by Rhodes [1988] do not indicate a significant proportion of rift zone-derived lavas. The remaining two processes are shown by Johnson [1992] to be important at neighboring Kilauea Volcano during a recent phase of frequent, low-volume eruptions. The idea is that the shear strength of the edifice limits the amount of downward sagging of the crust overlying the draining magma reservoir, while the space left by the expelled magma is claimed by decompressional expansion of magma and CO2, as well as CO2 exsolution.

Dvorak et al. [1985] proposed that additional magma reservoirs may also have contributed to the eruption, explaining limited subsidence with respect to the volume of lava observed at the surface. Such reservoirs may have been beyond the perimeter of the geodetic network, or possibly located deep enough that surface displacement was not detectable.

Johnson [1992] presented theoretical arguments and a suite of gravity and geodetic observations from Kilauea Volcano that show that it is not strictly necessary for the collapse volume to equal the volume of magma removed. This is because the volume change observed at the surface is the sum of the volume change due to removal of mass (i.e. magma), bulk compression of the magma resident in the reservoir, volatile (mainly CO2) compression, exsolution, and migration, and lastly volume change due to density redistribution of the crust. For example, while magma is being removed from the reservoir during eruption, decreasing internal pressure causes exsolution of CO2 plus volumetric decompression of exsolved gas and magma. All of these factors mitigate reservoir contraction [Johnson, 1992, equation 8]. Concurrently, the volume change of the edifice is 1.5 times the change in size of the reservoir cavity as a consequence of the crustal density change associated with deformation [Johnson, 1992, equation 9, with a Poisson's ratio of 0.25 typical of crustal material]. While the processes internal and external to the reservoir have opposite influence on the ratio of edifice volume change to internal reservoir mass change, Johnson [1992] shows that at Kilauea the internal processes may at times dominate. Comparison with observations from Kilauea are useful in the analysis of Mauna Loa.

The purpose of this paper is to use the gravity data collected before and after the 1984 eruption to examine the observed volume disparity between edifice contraction and lava flow at Mauna Loa. The utility of the gravity method with respect to monitoring a subsurface magma reservoir is that it is sensitive to mass change, whereas geodetic methods (such as leveling, tilt, trilateration, GPS) detect surface displacement only. An apparent volume change detected by geodetic methods may reflect expansion/contraction of existing crust and reservoir material as well as addition/ subtraction of magma from the system. Analysis of gravity data may thus help sort out these kinds of volume ambiguities. The first goal is to determine the actual mass of magma removed from the known summit magma reservoir and determine if this amount is sufficient to explain the mass of the eruptive products. Secondly, the relationship between mass removed and the resulting summit collapse will be analyzed to learn more about the shear strength of the edifice and the compressibility of the magma reservoir itself.

THE 1984 ERUPTION

Mauna Loa, like neighboring Kilauea Volcano, contains a central subcaldera magma reservoir which is recharged by magma during repose [Decker et al., 1983; Rhodes, 1988]. With time, this filling produces a measurable distention of the edifice. Analysis of surface displacement patterns prior to the 1984 eruption by Decker et al. [1983] placed the region of filling roughly 3 km below the southeast rim of the summit caldera Mokuaweoweo.

The events of the March 1984 eruption have been described by Lockwood et al. [1985]. The first phase of eruption saw the propagation of an eruptive fissure to the floor of Mokuaweoweo at 01:25 HST on March 25. Over the next several hours the eruptive fissures migrated out of the caldera, into both the southwest and the northeast rift zones. By 07:00 HST fountaining was restricted to a portion of the upper northeast rift zone at an elevation of 3700 m. The eruption migrated down the northeast rift zone through the first day in a series of jumps; as new fountains appeared downrift, activity farther uprift waned. At 16:41 HST venting began near 2900 m elevation and continued in that vicinity for the remainder of the 3-week eruption.

Observations

As the eruption progressed, subsidence of the ground surface above the reservoir was monitored by frequent geodetic surveys [Lockwood et al., 1985; Dvorak and Okamura, 1987]. Subsidence is attributed to magma removal from the reservoir; some of this magma was intruded as dikes into both of Mauna Loa's rift zones while a large volume was erupted to the surface [Lockwood et al., 1985]. Locations of geodetic and gravity observation sites on Mauna Loa are shown in Figure 1, and measured tilt and leveling changes are illustrated in Figure 2. The area of maximum subsidence, as indicated by the orientation of ground tilting and the vertical movement of leveling benchmarks, was located southeast of Mokuaweoweo Caldera (Figure 2), at a location similar to the area of previous uplift [Decker et al., 1983].

Leveling surveys to third-order standards were done on June 27, 1983 and May 7-8, 1984 [Okamura et al., 1984; Dvorak, et al., 1985] on a route that traverses the summit area of Mauna Loa. A maximum subsidence of 574 mm relative to site ML7 was measured along the southeast rim of Mokuaweoweo caldera. Most likely neither end of the leveling traverse was distant enough from the apex of subsidence to escape subsidence. An estimate of the amount of subsidence of the reference benchmark, or "float" of the level line, will thus be made in the following section.

Occupation of the entire inventory of spirit-level tilt sites located around the rim of Mokuaweoweo caldera and the upper slopes of Mauna Loa was done between July 12-August 24, 1983 and April 23-27, 1984. These data are considered to have a precision of +/-12 urad [Dvorak and Okamura, 1987]. The changes (Figure 2) define an inward tilt, towards a common focus at the southeast rim of Mokuaweoweo.

A complete survey of gravity sites C1, ML1, ML3, and ML8 was done on February 13-14 and May 2, 1984. Gravity readings are corrected for tidal effects [Longman, 1959]. Calibration functions with linear and periodicterms were determined from calibration ranges and applied to the data. Gravity data were reduced using JOSH v. 3 [unpublished, 1994] which inputs data from an unlimited number of individual runs and calculates a least squares solution of second-order 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. A run comprises a sequence of gravity readings made using a particular gravimeter. Separate runs, which may be made during the same day or on multiple days, are combined to make a survey. In this study, gravity surveys were done using two gravimeters run over closed loops between the base station SAS and monitoring sites using helicopter transport. The February survey comprised two loops over both days and reduced values have standard errors of from +/-8 to +/-12 [Micro]Gal. The May survey comprised three loops on the same day and values have std. errors of about +/-7 [Micro]Gal. Observed gravity changes between the complete surveys, bracketing the 1984 eruption, are given in Table 1 along with corresponding elevation changes.

During the course of the 1984 eruption gravity measurements were occasionally made at station ML1 to record the chronology of gravity change. These surveys were accomplished by closing two loops between SAS and ML1 with two gravimeters. The exception was the March 26 survey, when only one loop could be completed because helicopter support was unavailable. A time plot of ML1 gravity is given in Figure 3. First impressions of the ML1 data are that the pattern of change closely follows the exponentially diminishing rates of tilt change and horizontal strain [Lockwood, et al., 1985]. Also, the positive sign of the change is consistent with a strong contribution of an increase due to the decreased height of the observation point (the free-air change), which is both greater and of opposite sign to the component due to the subsurface magma mass loss.

As a part of the gravimeter calibration procedure, a gravity tie was made between base station SAS and GC7, located 16 km north of SAS on the lower slope of neighboring Mauna Kea Volcano. Measured gravity change at SAS between pre- and post-eruption surveys on February 21 and May 15, 1984 is +1.6+/-11.2 [Micro]Gal relative to GC7. The absence of a significant gravity change at SAS diminishes the probability that this station moved up or down.

REVIEW OF MODEL EQUATIONS

Model for Deformation from Reservoir Volume Change

The principles of deformation and gravity analysis presented here are a foundation for the analysis that follows. These generalized equations enable inferences to be made about the nature of mass and volume changes at depth associated with the gravity and surface displacement anomalies. However, because of the dramatic topography of Mauna Loa which is not anticipated in the derivation of the principles, they should be used with some caution.

Deformation resulting from the inflation and deflation of the summit reservoir of Mauna Loa is simulated using a model first applied to volcanology by Mogi [1958]. This model gives deformation of an elastic body having one free surface as a function of pressure change within a spherical cavity inside the body. Surface uplift is given as

                                         (1)

where Z is the source depth, X is the radial distance of the point from the source epicenter, [Delta]P is the pressure change, Vr is the volume of the source and [Nu] and u are the Poisson's ratio and shear modulus of the body [modified from Hagiwara, 1977]. The change in radius, [Delta]a, of the source of radius a is given by Hagiwara [1977] as:

                                         (2)

As long as a is large relative to [Delta]a, the volume change [Delta]Vr of the spherical source may be estimated as the surface area of the sphere (4[Pi]a2) times the change in radius (equation 2), or

                                         (3)

[Johnson, 1987, with volume relation 3Vr/4=[Pi]a3 substituted]. Integration of equation (1) over the surface of the body gives

                                         (4)

which is the volume change of the body due to displacement, [Delta]h, of the free surface. Division of equation (4) by (3) gives

                                         (5)

which is the volume change of the body as a function of volume change of the imbedded spherical source. Notice that for a Poisson's ratio of 0.25, typical of crustal rock, equation (5) predicts dilation, or expansion, of the crust equal to 50% of the volume change of the source. The volume of surface uplift would equal the volume change of the source only if the Poisson's ratio were 0.5; media with such a Poisson's ratio include rubber and fluids.

To the gravity modeler, the significance of crustal dilation predicted by equation (5) is the implied density change, which has a direct effect on the measured gravity field. The variation in density [Delta][Rho] at a point located within the body at depth D below the surface is

                                         (6)

where Z is the depth of burial of the spherical source, and X is the horizontal distance between source and observation point [modified from Hagiwara, 1977]. Notice, again, that equation (6) predicts a changing density distribution within the body, except in the special case that [Nu]=0.5.

To the volcanologist seeking to estimate the magma budget of a volcano by monitoring surface uplift, the significance of equations (5) and (6) is that a portion of the volume of expansion or contraction of a volcanic edifice is the consequence of crustal density change, not magma accumulation. Analyses that have assumed that one unit volume of uplift is equivalent to one unit volume of reservoir magma accumulation (of which there are many) are thus in error.

Model for Gravity Change from Reservoir Volume Change

The problem of modeling gravity change associated with an altered density distribution of the crust has been treated by Hagiwara [1977], Rundle [1978], Walsh and Rice [1979], and Savage [1984] for the case of a spherical source. The consensus is that deformation of the crust caused solely by the volume change of a spherical source does not produce a net gravity change. Previous gravity studies of Kilauea Volcano [Jachens and Eaton, 1980; Dzurisin et al., 1980; Johnson, 1987; Johnson, 1992] have made the explicit assumption that crustal deformation yields no gravity change. (Some gravity change, however, is expected due to related vertical movement of the observation site with respect to the mass of the Earth plus any change in the mass of magma contained within the source.)

It is useful to review some details of the Hagiwara [1977] study of deformation-induced gravity change for a spherical source model. Hagiwara [1977] separated the deformation into three components and solved the gravity change for each separately: (1) the volume change of the spherical source cavity, (2) the surface uplift, and (3) the crustal density change. I have modified the original equations to reduce the number of elastic constants to only the Poisson's ratio [Nu] and to use a source volume change term [Delta]Ve rather than a pressure change.

The component of gravity change due to the volume change [Delta]Vr of the source is

                                        (7)

where [Rho]c is the crustal density. The value of [Gamma] is 6.67x10-11 Nm2kg-2. Included is an allowance for mass, such as magma, of density [Rho]0 which replaces displaced crustal material. If no matter moves into or out of the source to balance [Delta]Vr, then [Rho]0=0. The magnitude of (7) is essentially the gravitational attraction of a spherical shell that represents the mass gained or lost by a change in diameter of the source. For example, expansion of an empty reservoir would result in a spherical shell where empty space of density [Rho]0=0 has displaced crustal rock of density [Rho]c. This would give a negative gravity change component.

The component of gravity change due to surface uplift is

                                         (8)

To illustrate this component, consider a gravimeter fixed in space above the Earth's surface. An increase in Vr results in surface uplift - uplift moves mass upward and displace air with a thin layer of crustal material. This layer has an area equal to the uplift anomaly, and a variable thickness depending on the local uplift. The gravimeter located above the uplifted area would record a gravity increase due to this component of deformation.

Finally, an outcome of deformation is variation in the density of the crust within the deformed region. The gravity change component due to density variation is

                                         (9)

Notice that only in the unrealistic case of a Poisson's ratio of 0.5 does the density change term vanish. Otherwise, for a typical Poisson's ratio of 0.25, the effect of this term for inflation, as an example, is a gravity decrease corresponding to the net density decrease of the deformed crust.

Considering only the deformation-induced components of the gravity change (by setting [Rho]0=0 to reflect no inflow or outflow of matter from the source sphere), the uplift component ([del]1) is exactly offset by the sum of the source volume change and crustal density change components ([del]0+[del]2). In other words, the net gravity change due to deformation caused by a point source is nil as stated by Hagiwara [1977], Rundle [1978], Walsh and Rice [1979], and Savage [1984].

The residual gravity change, [Delta]g' using the notation of Johnson [1992], is defined as the sum of the above components, including the mass of material flowing into or out of the source, but not including the free-air change. Summing (7), (8), and (9) above gives

                                        (10)

Division of (10) by (1) and substitution of (3) gives

                                        (11)

Equation (11) is of greater use if we modify [Rho]0 to incorporate the concept of "effective density" which is used in previous work on Kilauea Volcano by Jachens and Eaton [1980]. To do this, recall that [Rho]0 is, in effect, the mass change within the spherical source divided by the volume change of the source, or [Delta]M/[Delta]Vr. Equation (11) is further generalized if all mass change within the source volume is included in [Delta]M, regardless of whether the mass is accommodated specifically within [Delta]Vr or, as more likely the case, distributed within the entirety of the reservoir cavity Vr. Equation (11) is then rewritten as

                                        (12)
Equation (12) is made directly equivalent to the Jachens and Eaton [1980] effective density concept as well as previous equations given by Johnson [1987, equation 5; 1992, equation 3] by substitution of equation (5) giving

                                        (13)

The difference is use of the edifice volume change [Delta]Ve rather than the source volume change [Delta]Vr.

Gravity benchmarks ride on the Earth's surface, and so deformation also changes the height of the benchmarks with respect to the Earth's center of mass. Gravity changes observed at the surface include the free-air term which accounts for vertical reposition of the gravity site with respect to the Earth's gravity field. The Earth's gravity field decreases with height at a gradient of -0.3086 [Micro]Gal/mm on average and at sea level. The complete expression for the gravity change ([Delta]g) observed by a gravimeter resting on the surface is

                                        (14)

using units of [Micro]Gal and mm.

Model for Deformation and Gravity Change from Dike Intrusion

Yang and Davis [1986] give analytic expressions for displacements and strain for an elastic half-space subject to opening of a rectangular crack. This model, published as FORTRAN subroutine DEFOR is adopted here to simulate the March 25 Mauna Loa dike-forming intrusion and the resulting deformation. The eight parameters of the dike are latitude and longitude of the dike center, dike length, azimuth and dip, depth to dike top and bottom, and dike thickness. Surface displacements are output directly, and density changes throughout the body are calculated from the output strains.

Savage [1984], Sasai [1986], and Okubo [1992] give expressions for the gravity changes caused by deformation associated with the widening of a vertical crack. In contrast to the spherical source example, the ratio of gravity change to uplift is not simply linear for the vertical crack.

Application of Models to Mauna Loa

A critical drawback of using (14) to analyze gravity changes on Mauna Loa is that the derivation of the equation is based on a model having a free surface which is flat. Mauna Loa, in reality, like all volcanoes has a free surface which is irregular and sloped. The topography of Mauna Loa affects the modeled gravity and deformation changes. In terms of gravity, the changes predicted by the density change component of the model involve parts of the crust that do not in reality exist and they involve a surface uplift component which is based on a model with a mislocated surface. As an example, station ML1 is located at a topographically high spot on the rim of Mokuaweoweo caldera; the surface of Mauna Loa adjacent to ML1 is generally lower in altitude. The model is based on surface uplift at a similar horizon as ML1, however, in reality the uplifted areas are significantly below the level of ML1. In terms of deformation, the unique geometry of Mauna Loa will make actual deformation differ from the model predictions.

Procedures used in the following analysis section take into consideration the effect of topography on the gravity change. To allow for the vertical relief of Mauna Loa in the gravity change calculations, a numerical model is used that has a grid of surface elevations at 100 meter spacings to correctly position the mass elements of Mauna Loa's edifice with respect to the observation points in three-dimensional space. Testing of the model using a flat surface grid gives identical results to (13) above. A correction for the effect of topography on deformation is not implemented in this analysis. Here deformation is calculated using a model which has a flat free surface at an elevation of 3970 meters, representative of the general elevation of the summit area of Mauna Loa.

ANALYSIS

Determining Subsidence of ML8

A problem that has to be dealt with first is that the leveling survey conducted prior to the eruption did not include ML8. I made pre-eruption gravity measurements at ML8 because, as I understood at the time, it was at the southeast terminus of the level line. Unfortunately, it was only after the eruption that I learned that, while ML8 was considered to be a "leveling benchmark", actual leveling surveys had never reached ML8 - previous leveling had extended only as far as ML7.

The height change of ML8 was reconstructed by fitting a least-squares "Mogi" solution to the leveling data, plotting measured height changes as a function of radial distance from the source, and extrapolating the model height change curve to predict the height change of ML8. Figure 4 shows the results of this procedure; ML8 is estimated to have moved up 27 mm relative to the zero datum at ML7. Note that the latitude and longitude of the source are among the estimated parameters, so the X position of the data on the plot are not fixed in the inversion.

The zero change at ML7, of course, is not absolute: increasing values of the model curve at radial distances further out than ML8 suggest that the entire leveling line subsided relative to land beyond the periphery of the surveyed area. Simply extrapolating the model curve shown in Figure 4 to where it flattens out gives a total of 90 mm absolute subsidence of the reference site ML7.

Determining Height Change of "Floating" Level Line

It is apparent from the subsidence curve plotted in Figure 4 that the distant stations ML7 and ML8 experienced subsidence relative to points further out. How much the level network "floated" relative to stable ground surrounding the subsidence region is important to the analysis that follows. There are no geodetic measurements that tie subsidence measurements to a stable datum. However, an estimate of the subsidence can be made from the gravity data since gravity change and uplift are related by the free-air gradient.

A positive gravity change of +13.5+/-13.3 [Micro]Gal measured at ML8 (Table 1, relative to SAS) is evidence of slight subsidence. The classic interpretation of this change would apply a [Delta]g'/[Delta]h ratio of around -0.2 [Micro]Gal/mm (simply the Bouguer adjusted free-air gradient) to predict an elevation change of minus 67 mm. The problem with this approach is that actual [Delta]g'/[Delta]h ratios are difficult to predict and vary greatly from volcano to volcano and over time at the same volcano [Rymer, 1994]. In fact, rather than applying a generic ratio to gravity data as another way to measure uplift, current volcano research using gravity methods is now focused on modeling the details that make observed ratios differ from the previously expected ones [e.g. Johnson, 1992].

So, given that there is really no universal conversion factor for gravity and height changes on volcanoes, we should use only one that is locally determined for the specific time period. Here a representative factor was picked using relative changes between ML1, ML3, and ML8 (site C1 was excluded because of it's proximity to the eruptive fissure). A linear fit to these data, shown in Figure 5 gives a ratio of -0.3096 [Micro]Gal/mm. Thus, the 13.5 [Micro]Gal increase at ML8 relative to SAS corresponds to 43 mm of subsidence at this site, assuming that the observed correlation is constant over the region of subsidence.

We now have an estimate of the subsidence at the reference benchmark ML7; this offset may be applied to all the level data to correct for the vertical "float" of the level line. The ML7 subsidence value of -70 mm is a sum of - 27 mm change relative to ML8, estimated from point-source model, plus -43 mm change of ML8 relative to SAS, estimated by extrapolating the correlation between height and gravity change. Height change values corrected for this network float are listed in Table 2. These values are presumed here to be absolute with respect to initial positions.

The network float estimate of -90 mm obtained earlier from a least-squares fit of a point-source model to the leveling data is similar, giving us some confidence that the values are accurate. The method used to obtain this value, while useful for extrapolating height changes over the short 1-km distance between ML7 and ML8, probably should not be extended as a predictor of network float because the model does not include the effect of the dike and topography.

Inversion of Geodetic Data for Dike and Reservoir Parameters

Displacement of Mauna Loa's surface resulted from a composite of the injection of magma into a vertical dike, feeding the surface effusion of lava, and contraction of the summit reservoir as some previously stored magma exited into the dike and to the surface. Since the dike and reservoir superimposed displacements on each other, the inversion used here attempts to model both sources together. The goal here is to estimate the position and volume change of the dike and summit reservoir.

Equations used to describe deformation due to a dike are from Yang and Davis [1986]. Eight parameters of the dike are latitude and longitude of the dike center, dike length, azimuth and dip, depth to dike top and bottom, and dike thickness. In this case, visual observations of the eruptive fissure at the surface can be used to fill in some of the parameters and, thus, reduce the number of unknown parameters in the inversion. Figure 2 shows a plan view of the model dike which corresponds to the surface trace of the curtain of fire. It is centered at 19.4753 degrees N, 155.5940 degrees W, strikes 38.6 degrees and is 10 km in length. In reality the fissure extended further to the northeast and southwest, but increasing the model dike length was found to not affect the results of the inversion. This is because the ends of the model dike are well outside the survey area and contribute little to the total change observed at each site. The depth to the dike top is set to zero and the dike is assumed to be vertical. This leaves two remaining unknowns: depth to the dike bottom and dike width.

Equations used in modeling deformation due to volume changes of a spherical source are given by Hagiwara [1977]. Unknowns are latitude, longitude, and depth of the source, and the volume change of the source. The magma reservoir is situated a few kilometers below the surface so there are no visual clues to the model parameters as there are for the dike - all reservoir parameters will come from the inversion.

Data used in the inversion consisted of all tilt and height changes shown in Figure 2. Based on the determination described above, height changes were adjusted by -70 mm to account for the network "float" and a change of -43 mm was assigned to ML8. The routine used to find the best-fit dike and summit reservoir parameters consisted of 3000 sets of forward dike model calculations and point-source model inversions. The 3000 sets cover all combinations of dike width between 400 and 1000 mm in 10 mm steps and depth to dike bottom between 2000 and 7000 meters in 100 meter steps. For each set, first a forward model was run which corrected the tilt and level observations for the effect of the dike intrusion. Then the adjusted data were inverted using a least-squares technique [Dvorak et al., 1983] to determine the parameters for a best-fit elastic point source model. Finally, the list of 3000 resultant sum of squared residuals was searched for the minimum value. The parameters that corresponded with the best least-squares fit are listed in Table 2. The horizontal location of the reservoir source is mapped on Figure 2.

Results of the inversion are sensitive to the estimate of level line "float", or subsidence of the reference benchmark. If the level line as a whole is assumed to have subsided more than that predicted here, then the inversion yields a larger subsidence volume and a deeper Mogi source depth. An attempt was made to run the geodetic inversion with the network float as an additional unknown parameter. This endeavor did not yield a stable solution, however, probably because of the lack of far-field geodetic data. Without far-field data, the parameters of the Mogi source depth and the dike bottom depth tend to couple with, and also drift with, the level line float parameter. This problem is attacked here by using the far-field gravity tie to assess the vertical movement of the leveling reference benchmark; hence the accuracy of the gravity tie and assumptions used in the assessment have some bearing on the realiablity of the inversion results.

Determining the error bounds for the model solution is problematic because of the mixture of forward and inverse modeling techniques used. Adjustment of the dike parameters by up to +/-0.1 meters in width and +/-1000 meters depth of dike bottom can be made with only slight degradation of the model fit. The model fit is substantially poorer with parameters beyond the bounds given above, so we may be fairly confident that the true values lie within the interval. Error bounds for the three dimensional position of the spherical source is estimated at +/-200 meters, and for the volume change +/-5x10^6m^3. The error bounds given here indicate only the uncertainty of the model parameters as determined from the available data. Additional data would have helped to better resolve the parameters and, more importantly, to constrain the selection of appropriate models.

Adjustments to Gravity Data

The observed gravity changes are a composite of the changes due to mass movement and density change throughout Mauna Loa's edifice, plus the change due to variation of the vertical position of the gravity stations with respect to the Earth's mass. In this section, we adjust the gravity measurements for known changes resulting from the dike intrusion, contraction of the reservoir, and height change of the gravity sites. The gravity effect of the mass of the magma that flowed out of the reservoir during the deflation is left as the single remaining unknown. This will be estimated later from the residual gravity changes.

Rather than use the theoretical relations of [Delta]g'/[Delta]h in this study (e.g. equations 13 and 15), I have chosen to make specific calculations of [Delta]g' and [Delta]h using the basic equations for deformation and explicit source parameters. The main improvement results from the ability to specify in three-dimensions the location of mass components that are being displaced and dilated. The gravity change at a specified position (corresponding to a gravity station location) is calculated individually for all components and the values are summed to give the composite change.

I use a digital elevation model (DEM) for the Mauna Loa vicinity (modified by NOAA from USGS 7.5' quadrangle data to give 100 meter grid spacing) to insure that only mass components that actually exist are included in the summation. The DEM grid used here covers a 40 km by 40 km area of Mauna Loa, giving elevations at 100-meter-spaced grid nodes to the nearest meter. Three-dimensional calculations are based on subdivision of vertical columns below each DEM grid node into 100-m cubes Each column of cubes has an origin at the surface and extends 20 km below the surface.

Table 3 summarizes the adjustments made to the observed gravity changes and gives the residuals.

Free-air gradient. The free-air gradients used here to correct the gravity data for height change are up to 16 percent steeper than the -0.3086 [Micro]Gal/mm value considered average for the Earth's surface. Hammer [1970] points out that the actual gradient may differ from theory in areas of local gravity anomalies due to density contrasts in the Earth's crust. At Kilauea Volcano, field measurements by Johnson [1992] gave a free-air gradient 6 percent steeper than normal; a positive Bouguer anomaly [Kinoshita et al., 1963] centered over Kilauea may contribute to the steepness of the gradient. While the summit area of Mauna Loa also has a positive Bouguer anomaly indicating a dense intrusive core, similar to Kilauea, an even greater concern is the topographic effect of Mauna Loa's high profile on the gradient. There is a huge density contrast between the rock of Mauna Loa's cone and the air which surrounds its flanks - many times the density contrast between the intrusive core and edifice. A very steep free-air gravity gradient on Mauna Loa would be expected from this.

The free-air gradients are calculated individually for each station and are listed in Table 3. These values are derived from the theoretical gradient formula given by Hammer [1970, equation 1] for specified site elevation and latitude. Then a correction was made to the gradient for terrain above sea-level. This involved use of a DEM of the Island of Hawaii with elevations at 100 meter grid spacing as input to a program that calculated the gravitational attraction of the island's mass at a specific location. A density of 2300 kg/m^3 [Kinoshita et al., 1963] was used and only mass above sea level was included in the model. Two calculations were made for each station: one at the surface elevation and location of the station and another at an elevation one meter above the surface. The difference in gravity at the two heights is then added to the per-meter theoretical gradient as a terrain correction.

Field measurements of the free-air gradient were made at site MLO (Figure. 1) located on the north flank of Mauna Loa at an elevation of 3375 m. A wooden structure at MLO served as a convenient platform on which to make precise measurements of the gravity difference (to +/-2.5 [Micro]Gal) between two points separated vertically by 1.8 meters. The observed -0.3387 [Micro]Gal/mm gradient compares favorably with a gradient of -0.327 [Micro]Gal for MLO predicted by the computational procedure above. Agreement between the calculated and observed gradients at MLO gives confidence in the calculated values in Table 2 which have not been field checked.

The free-air correction is simply the calculated gradient times the height change and is subtracted from the observed gravity change.

Spherical reservoir source. The position and deflation volume of a spherical reservoir were determined in the inversion of geodetic data described above (Table 2). The modeled surface collapse volume [Delta]Ve of 66.9x10^6m^3 corresponds to a reservoir contraction [Delta]Vr of 44.6x10^6m^3 according to equation (5). Magma mass transfer from or into the reservoir is left as an unknown by setting [Rho]0=0. The gravity change due to inlay of a spherical shell of crustal material, [Rho]=2300 kg/m^3, equal in volume to the reservoir volume loss [Delta]Vr above is calculated using equation (7).

Next, the gravity change due to crustal density change associated with contraction of the reservoir is estimated numerically. To do this, Mauna Loa's edifice is represented as a three dimensional grid of 100-meter cubes with density [Rho]=2300 kg/m^3. Equations (4) and (6) are used to find the density change for each cubic cell, the gravity change resulting from the density increment is calculated for each cube [Parasnis, 1986, equation 3.25], and the values summed for all the cells in the model.

Finally, vertical displacements of the surface are calculated from equations (1) and (4) at horizontal positions defined by the DEM grid center point and vertical position defined by the elevation given in the DEM. The gravitational attraction of adding or subtracting square plates of crust (horizontal dimensions of 100 m, thickness given by [Delta]h, density [Rho]=2300 kg/m^3) positioned according to the DEM grid node location and elevation is calculated. A summation is made of calculated gravity changes for all grid nodes in the model.

Resulting gravity corrections for contraction of the spherical source are listed in Table 3. Recall that the theoretical model (equation 10) which is based on elastic crust with a flat free surface gives [Delta]g'=0, assuming, as we did in making the numerical calculation above, that magma mass within the reservoir remains constant (i.e. [Rho]0=0). Numerical results for all gravity stations are within a few [Micro]Gal of zero, with the exception of ML1 which is 20 [Micro]Gal. The large change at ML1 compared to the theoretical value is probably a consequence of the placement of ML1 on a high point of the Mauna Loa's edifice, in proximity to a sudden drop off into Mokuaweoweo caldera.

Dike intrusion source. The gravity effect of the dike which formed during the early stages of the 1984 Mauna Loa eruption is estimated using a numerical procedure similar to that used to model the reservoir source. The specific position of the dike and opening are from the inversion of geodetic data described earlier (Table 2).

The gravity effect of the dike itself is calculated for each gravity station. [Parasnis, 1986, equation 3.25]. Since the process of dike intrusion essentially creates a crack, or void, in the crust and then immediately fills the crack with magma, the appropriate density to use in the calculation is the density difference between the extracted crust ([Rho]c) and the magma ([Rho]m) that replaced it. A density contrast of ([Rho]m-[Rho]c=2600 kg/m^3-2300 kg/m^3) 300 kg/m^3 between intruded magma and displaced crust is assumed here. Crustal density change and surface uplift is determined using the Yang and Davis [1986] DEFOR program for all grid cells in the three-dimensional model of Mauna Loa; the resultant gravity changes are calculated and summed.

Gravity changes specific to the dike intrusion and related deformation are listed in Table 3. The dike-related gravity change correction is substantial - ranging up to -72 [Micro]Gal at C1 - and is strongly a function of the density change component.

Composite gravity adjustment. Residual gravity changes, after adjustment of the observed changes for free-air change and changes related to the dike injection and reservoir contraction described above, range up to a value of -57 [Micro]Gal at C1 and ML1. Residual values for all gravity sites are listed in Table 3. The negative sign of the residual changes indicates mass (magma) loss from the reservoir which, so far, has not been accounted for by the adjustments.

Estimate of Reservoir Mass Loss

An estimate of the mass of magma removed from the summit reservoir may be made from the residual gravity changes. We assume that the center of mass of the removed magma is coincident with the location and depth of the [Delta]Vr source which we solved earlier from the geodetic data. This spot, to review, is positioned at a depth of 3630 m (below a 3970 m datum) within the edifice and is below a location mapped on Figure. 2 with a circle symbol. Calculated as a point mass [Parasnis, 1986], a loss from the reservoir of 133x10^9 kg is indicated by the ML1 gravity residual and a loss of 140x10^9 kg by the ML3 data. The mass loss indicated by the residual gravity change at C1 is much greater, however values for C1 are suspect because of proximity of the eruptive fissure and greater distance from the reservoir. Taking the average of [Delta]M estimates from ML1 and ML3 data only gives a reservoir mass loss figure of 136x10^9 kg.

I estimate that this mass loss value may have an uncertainty of +/-50x10^9 kg. While the precision of the gravity change data is adequate, the lack of redundant observations is limiting. Additional gravity data at sites distributed over the Mauna Loa summit area would help considerably.

DISCUSSION

Analysis of gravity and geodetic changes recorded during the 1984 Mauna Loa eruption has determined that 136(+/-50)x10^9 kg of mass, presumably magma, was removed from a reservoir situated at a depth of 3630+/-200 m. Concurrent collapse of Mauna Loa's surface, attributed to reservoir deflation, totaled 66.9(+/-5)x10^6 m^3. The "effective density" of the deflation, calculated by dividing the mass change by the edifice volume change, is [Delta]M/[Delta]Ve=2033 kg/m^3. For comparison, two major deflations of Kilauea Volcano in August 1981 and January 1983 showed slightly higher [Delta]M/[Delta]Ve ratios of 3050 kg/m^3 and 2625 kg/m^3, respectively [Johnson, 1992]. Jachens and Eaton [1980] found a [Delta]M/[Delta]Ve ratio of 3290 kg/m^3 from analysis of gravity and elevation changes during a major summit collapse of Kilauea in November 1975; however, the effect of significant earthquake-related horizontal displacements and dike intrusion were not considered in the analysis. Larger ratios, averaging 7165 kg/m^3, accompanied brief episodes of eruption at the Pu'u O'o vent of Kilauea in 1985-1986 [Johnson, 1992]. Considering the Mauna Loa [Delta]M/[Delta]Ve ratios are at the low end of the range observed at Kilauea, it appears that some aspects of the structure and mechanical properties may be dissimilar. The reader is referred to Johnson [1992] for a discussion of the mechanical properties of Kilauea's edifice and magmatic system that govern [Delta]M/[Delta]Ve during deflation.

Elastic Properties of Edifice and Reservoir Content

The relationship between the mass of magma withdrawn from a reservoir and resultant edifice collapse is dependent on the mechanical properties of the edifice and magma as shown by Johnson [1992, equation 10]:

                                        (15)

Edifice properties incorporated in (15) are Poisson's ratio [Nu], assumed to be 0.25, and shear modulus u. Magma property terms in (15) are enclosed by brackets and are the gas-free magma compressibility (1/K) and the CO2 gas phase compressibility; the sum of the bracketed items comprise the aggregate compressibility of the magma. The magma bulk modulus is K, and N is the CO2 content of the magma expressed as total mass fraction. The mass of 1 mol of CO2, [omega], is 0.044 kg. R is the gas constant, equal to 8.314 m^3Pa/moldeg.K. Russell [1987] estimates a temperature T of 1423K for magma contained within Mauna Loa's reservoir. Pressure P within the reservoir, approximated here by the lithostatic pressure at the 3630 m reservoir depth, is 82 MPa. A value N less than n, given by Harris [1981] as

                                        (16)

where b is the solubility constant equal to 5.9x10-12, indicates that the magma is undersaturated in CO2 and will not exsolve a separate gas phase. In this case, only the 1/K term appears within the brackets in equation (15).

The first term on the right-hand side of (15) reflects the volume reduction of the reservoir by magma withdrawal. The second term reflects additional magma mass removed from the reservoir without further decrease in the reservoir volume. Here decompressional expansion of magma and CO2, and CO2 exsolution fills reservoir space formerly occupied by the magma. If the reservoir magma has a high compressibility (i.e. low K) and high CO2 content, volumetric expansion of the reservoir contents will tend to limit reservoir contraction and surface subsidence. On the other hand, if the crustal shear modulus u value is low, suggesting a relatively weak edifice, the amount of reservoir contraction and crustal subsidence [Delta]Ve will be enhanced. The Poisson's ratio appears in (15) as part of the conversion between [Delta]Ve and [Delta]Vr, accounting for crustal dilation associated with deformation (see equation 5).

Johnson [1992] applied values of u=3 GPa [based on Davis et al., 1973, 1974; Davis, 1986; and Rubin and Pollard, 1987] and K=11.5 GPa [from Murase et al., 1977] to evaluate the Kilauea [Delta]M/[Delta]Ve data and obtained magmatic CO2 concentrations of 0.0009 (August 1981 deflation) and 0.0005 (January 1983 deflation) by weight. These CO2 concentrations are low compared to estimates of 0.0065 [Gerlach and Graeber, 1985] and 0.0032 [Greenland et al., 1985] for the initial load of CO2 contained in mantle-supplied magma at Kilauea. Apparently exsolved CO2 in Kilauea's reservoir tends to escape, keeping the retained amount low. A case may be made that CO2 gas migration and escape is so complete as to remove all exsolved CO2. This is supported by the similarity between values reported by Johnson [1992] and the predicted saturation level of roughly 0.0005 CO2 by weight as indicated by (16) for pressures equivalent to lithostatic at source depths active in the 1981 and 1983 events.

Returning to Mauna Loa, the [Delta]M/[Delta]Ve value of 2033 kg/m^3 is interpreted to indicate a low CO2 gas content for the reservoir. Parameters u=3 GPa and K=11.5 GPa, previously used in the Kilauea analysis [Johnson, 1992], are adopted here. Assuming a lithostatic 82 MPa pressure within the 3630 m-deep reservoir, the solubility relationship (16) indicates that up to a weight fraction of 0.0005 CO2 may be dissolved in the magma. Evaluation of equation (15) using the above concentration of CO2, and assuming presence of a free CO2 gas phase in the melt, gives [Delta]M/[Delta]Ve=2672 kg/m^3. If, on the other hand, the concentration of CO2 was slightly less than the saturation level and no free gas were present, then (15) is properly evaluated with the terms in brackets reduced to only 1/K, giving [Delta]M/[Delta]Ve=2336 kg/m^3. The measured [Delta]M/[Delta]Ve value is near the unsaturated estimate. The details may not be significant, given the uncertainties in chosen values for elastic parameters and the process of deriving [Delta]M/[Delta]Ve from the gravity and geodetic data. The fundamental conclusion is that the concentration of CO2 resident within the reservoir is low, and I suggest that migration and escape of exsolved gas keeps CO2 content trimmed to very near levels defined by the saturation limit.

Comparison of Mass of Lava Erupted to Reservoir Supply

Examination of the 1984 Mauna Loa eruption with the added perspective provided by the gravity change data has enabled us to estimate the mass change of the magma reservoir. This estimate is a more direct measure of magma supplied by the reservoir than previous estimates based on surface subsidence alone. The 136x10^9 kg mass loss so determined is comparable to a 52x10^6 m^3 volume of magma figured at fixed density of 2600 kg/m^3. This value is only 30 percent of the amount of erupted lava [Lipman and Banks, 1987, adjusted to 2600 kg/m^3 density equivalent]. Since additional magma filled a 22-km long dike that was intruded during the early stages of the eruption, the actual contribution of the summit reservoir to the eruption may be lower. A reservoir contribution in the 20 to 25 percent range is calculated for plausible dike dimensions of 0.75 m width, 5000 m height, and 10 km to 22 km in length.

Where then did the extra magma come from? An additional, undetected source is required to account for erupted lava and dike filling in excess of the amount estimated here to have been supplied by the monitored reservoir. The idea that additional reservoirs supplemented the eruption has been previously suggested by Dvorak et al. [1985]. I agree, and suggest that the extra magma was delivered from a source substantially deeper than the known reservoir.

If the 1984 Mauna Loa eruption were supplied by a deeper secondary source, that source is not apparent in the available data. Two factors work against us in being able to resolve a deep source. One is that the deformation and gravity change anomalies for a deep source are spread out over a very large area and have a low maximum amplitude. The other is that large changes caused by the shallow source plus dike intrusion overshadow the subtle changes that would indicate a deep source.

Although we cannot pin down a specific source depth, lack of a significant far-field gravity change increases the likelihood that the source was relatively deep. A gravity change of only +13.5+/-13.3 [Micro]Gal at ML8 relative to SAS, which is largely explained as far-field subsidence from the known shallow source, is not large enough to indicate a secondary source of volumetric contraction (of the order of 136x10^6 m^3) in the intermediate depth range between 5 and 15 km. A deep secondary source below 15 km, on the other hand, would produce a much smaller change to the ML8-SAS gravity tie which would be within the error bounds. So, while the gravity tie does not directly indicate source deeper than 15 km, the data cannot disprove the hypothesis either.

A gravity tie between the local base station SAS and a location on the lower slope of Mauna Kea, 30 km from the subsidence maximum, showed a change of only +1.6+/-11.2 [Micro]Gal between surveys spanning the eruption. Unfortunately, at the 16 km radial distance of SAS to the source, expected changes due to even a relatively large volume contraction are too small to resolve with enough certainty to model a source depth.

Model for Mauna Loa Magma Storage and Supply.

The lavas from the 1984 Mauna Loa eruption are remarkably uniform in composition, suggesting a common source [Rhodes, 1988]. Furthermore, Russell [1987] and Rhodes [1988] show that the lava geochemistry has characteristics that suggest a period of storage within a shallow magma reservoir. These observations do not support the idea of direct feeding of the eruption from a secondary, deep source.

Both geochemical and the present geophysical constraints may be satisfied with a model for the eruption that includes simultaneous magma discharge and resupply of the shallow reservoir. In other words, as previously stored magma flowed upward out of the reservoir to supply the eruption, new magma from a deep source flowed into the reservoir at the bottom. The apparent volume change of the reservoir during the eruption is simply the net difference between the inflow and outflow.

Rhodes [1988] explains that the long-term homogeneity of Mauna Loa's lavas is evidence of a steady state magmatic system where composition changes of stored magma due to crystallization are balanced by the influx of new magma of parental composition. A common view of Hawaiian volcanoes is that magma resupply to the shallow reservoir is a gradual process that accompanies periods of repose [e.g. Decker, 1987]. What I propose here is that rapid, major magmatic resupply to Mauna Loa reservoir may be a part of the eruption process. During eruption, new magma initially enters the reservoir from below, but does not mix with resident magma above rapidly enough to be incorporated into the surface eruption. With time, and before a subsequent eruption, the new and resident magmas mix.

One possible indication of magma resupply during the 1984 Mauna Loa eruption is an increase in the rate of CO2 venting from the summit observed during the later portion of the eruption [Greenland, 1987]. While some CO2 may have been released from the resident magma, following depressurization and vessiculation, the analysis here suggests that the resident magma is fairly low in CO2 concentration. A preferable source for the emission increase is newly delivered, CO2-rich magma from the deeper source.

A record of CO2 outgassing by Ryan and Chin [1992] and Ryan [this volume] shows peak rates of CO2 emission immediately following eruptions in 1950, 1975, and 1984; after each peak the rate decayed exponentially. If CO2 rich, parental magma were delivered to the reservoir at a more or less constant rate, one would expect the CO2 emission rate to remain steady as well. The exponential decay in the degassing rate, in contrast, suggests progressive degassing of a single batch of gas-rich magma.

I propose that magma supply to Mauna Loa's 3-4 km deep reservoir is episodic and that a large portion of the influx of magma from depth occurs concurrently with eruptive events. Whether the cause of, or the effect of eruption, a pulse of magma resupply would involve a drastic increase in the rate of flow between a deep (>15 km) source and the shallow reservoir. Between eruptions, a low rate of resupply of CO2-rich parental magma along with the inevitable reservoir degassing process allows reservoir CO2 levels to fall with time. A pulse of resupply during eruption satisfies the constraint from the gravity analysis that the net mass reduction of the shallow reservoir was only 20-25 percent of the mass erupted.

NOTATION

D position below surface, m.

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

[Delta]M reservoir magma mass change, kg.

N total CO2 in magma, weight fraction.

P pressure, MPa.

[Delta]P pressure change, MPa

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

T reservoir magma temperature, K, Kelvins.

Vr volume of reservoir or spherical source, m^3.

[Delta]Vr reservoir or source volume change, m^3.

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

X horizontal distance to source, m.

Z depth to source, m.

b CO2 solubility constant, 5.9x10-12Pa-1 [Harris, 1981].

[del]0 gravity change component due to source volume change, [Micro]Gal.

[del]1 gravity change component due to surface uplift, [Micro]Gal.

[del]2 gravity change component due to density variation, [Micro]Gal.

[Delta]g observed gravity change, [Micro]Gal.

[Delta]g' residual (after free-air correction) gravity change, [Micro]Gal.

[Delta]h height change, mm.

n limit of disolved CO2 in magma, weight fraction.

[Gamma] universal gravitational constant, 6.67x10-11 Nm2kg-2.

u crustal shear modulus, GPa.

[Nu] edifice Poisson's ratio, dimensionless.

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

[Rho]c crustal density, 2300 kg/m^3 [Kinoshita, et al., 1963].

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

[Rho]0 exchange density, value arbitrary.

Acknowledgments. I thank Bob Decker and the staff of the Hawaiian Volcano Observatory for their help and generosity during my stay at HVO as a student/volunteer in 1984. That they woke me early on the morning of the eruption, putting me on a helicopter at dawn to do a gravity survey, shows the kind of "let's try it" attitude that makes HVO a leader at testing ideas, in innovation. I thank John Dvorak, Ron Hanatani, Arnold Okamura, Maurice Sako, and Ken Yamashita for their skillful job of collecting geodetic data in the thin air of Mauna Loa's summit. I gratefully acknowledge the constructive comments of Mike Ryan and Hazel Rymer.

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Daniel J. Johnson, 3616 NE 97th St., Seattle, WA 98115