GEOPHYSICAL RESEARCH LETTERS, VOL. 38, L03302, doi:10.1029/2010GL045977, 2011
Determining the seismic source mechanism and location for an explosive eruption with limited observational data: Augustine Volcano, Alaska Phillip B. Dawson,1 Bernard A. Chouet,1 and John Power2 Received 25 October 2010; revised 9 December 2010; accepted 28 December 2010; published 4 February 2011.
[ 1 ] Waveform inversions of the very‐long‐period components of the seismic wavefield produced by an explosive eruption that occurred on 11 January, 2006 at Augustine Volcano, Alaska constrain the seismic source location to near sea level beneath the summit of the volcano. The calculated moment tensors indicate the presence of a volumetric source mechanism. Systematic reconstruction of the source mechanism shows the source consists of a sill intersected by either a sub‐vertical east‐ west trending dike or a sub‐vertical pipe and a weak single force. The trend of the dike may be controlled by the east‐ west trending Augustine‐Seldovia arch. The data from the network of broadband sensors is limited to fourteen seismic traces, and synthetic modeling confirms the ability of the network to recover the source mechanism. The synthetic modeling also provides a guide to the expected capability of a broadband network to resolve very‐long‐period source mechanisms, particularly when confronted with limited observational data. Citation: Dawson, P. B., B. A. Chouet, and J. Power (2011), Determining the seismic source mechanism and location for an explosive eruption with limited observational data: Augustine Volcano, Alaska, Geophys. Res. Lett., 38, L03302, doi:10.1029/2010GL045977.
1. Introduction [2] Augustine Volcano is a frequently active 1.2‐km‐high stratovolcano located 280 km southwest of Anchorage, Alaska. Between 11 and 28 January, 2006 a series of 13 explosive eruptions produced ash plumes reaching altitudes of 9–14 km above sea level. Five broadband sensors with flat ground‐velocity response between 0.01 and 30 s were deployed on Augustine in December, 2005 in response to increasing unrest of the volcano [Power et al., 2006]. The stations were positioned at distances of 1.7 to 4 km from the summit and elevations ranging from 120 to 480 m (Figure 1a). We invert the waveforms of the very‐long‐ period components of the seismic wavefield using a deconvolved and bandpassed (0.033–0.10 Hz) window of data for the initial 13:44 UTC January 11, 2006 eruption to determine the seismic source mechanism and location. Fourteen components of data are used in the inversions as the east component of station AU12 was inoperative. Forward modeling and synthetic tests are conducted to evaluate the robustness 1
U.S. Geological Survey, Menlo Park, California, USA. Alaska Volcano Observatory, U.S. Geological Survey, Anchorage, Alaska, USA. 2
This paper is not subject to U.S. copyright. Published in 2011 by the American Geophysical Union.
of the resulting source mechanism and location given the limited observational data.
2. Waveform Inversion [3] We consider full‐waveform inversion of very‐long‐ period signals assuming a point source embedded in a homogeneous elastic medium that takes topography into account. The assumption of a homogeneous medium and approximation of the source as a point source are justified for the wavelengths considered in the present analysis (see below). To determine the source centroid location and source mechanism, we minimize the residual error between the data and synthetics calculated by the finite difference method of Ohminato and Chouet [1997] for a representative model of Augustine Volcano (see Chouet et al. [2010] for details of the methodology used in the present study). [4] The computational domain is centered on the summit of the volcano and consists of 361 × 361 × 201 nodes with 40 m grid spacing, extending 14.4 km × 14.4 km horizontally and 8 km vertically. The topography and surrounding bathymetry of Augustine were obtained from the National Elevation Dataset with a spatial resolution of 10 m. Based on the structural model of Kienle et al. [1979], we assume a compressional wave velocity Vp = 3.5 km s−1, shear wave velocity Vs = 2 km s−1, and density r = 2650 kg m−3. Wavelengths corresponding to the period range 10–30 s considered in this study span 20–100 km, hence the use of a homogeneous velocity domain is justified. The Green’s functions are convolved with a full cosine smoothing function with a period of 2.0 s to insure the stability of the inversion. [5] Because the source mechanism of the eruption is not known a priori, our initial approach is to consider three possible source mechanisms: (1) six moment tensor components and three single‐force components, (2) six moment tensor components only, and (3) three single‐force components only. The selection of an optimum solution is based on the residual error, the relevance of the free parameters used in the model measured by the Akaike Information Criterion (AIC) [Akaike, 1974], and physical significance of the resulting source mechanism. A spatial search through the computational domain for the node providing the minimum residual error and AIC value for the three types of inversions (residual errors: 6.2%, 12.3%, 83.2%; AIC: −106887, −83872, 2742, respectively) indicates that the source mechanism is best represented by either six moment tensor and three single‐force components, or six moment tensor components only. The possible spatial location of the source centroid (Figure 1b) is represented as the volume bound by the isosurface representing a residual error increment of
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Figure 1. (a) Map of Augustine, with broadband station locations indicated by black dots. The shaded square marks the region depicted in Figures 1b–1f. Contour interval is 200 m. (b) A portion of the computational domain encompassing the summit region of Augustine, viewed from the southeast. Contours (200 m interval) of the topography are projected to the bottom of the figure. Volumes representing errors of up to 2.5% above the minimum residual error obtained from inversion with moment components only, and moment and force components are indicated by the red and blue isosurfaces, respectively. Red and blue dots indicate the positions of the minimum residual errors, and their projection to the edges of the domain. Projections of the corresponding error volumes to the left and bottom sides are shown in gray and outlined in red and blue. (c) Open circles indicate the 532 investigated nodes. Nodes where models consisting of two intersecting cracks that match the statistical properties of the inversion using moments only at that point are indicated as green dots. Red dots indicate nodes with a dike that intersects the surface near the vent region. (d) An idealized depiction of the source mechanism consisting of two cracks. (e) Green dots indicate nodes for matching models consisting of a pipe intersecting a crack. Red dots indicate nodes where a pipe segment intersects the surface near the vent. (f) Idealized depiction of the source mechanism consisting of a pipe intersecting a crack. The dominant source mechanism is colored red in Figures 1d and 1f.
2.5% above the minimum misfit. The blue surface shows the shape of the misfit distribution around the minimum error for the mechanism consisting of moments and forces. The error minimum yields a source centroid located 40 m above sea level and the misfit volume has horizontal dimensions of ±400 m and spans the range −260 to 490 m in elevation. The red surface is the shape of the misfit distribution for the mechanism composed of moments only. It has horizontal dimensions of ±300 m and spans −90 to 490 m in elevation. The error minimum yields a source centroid at an elevation of 280 m. The difference in size between the misfit volumes is a reflection of the number of free parameters and limited observations, as well as the choice of a fixed value (2.5%) used to represent the volumes. The vertical elongation of both distributions is primarily due to the distribution of stations and their relatively similar elevation with respect to the source location. [6] Figures 2a and 2c illustrate the source‐time histories obtained for the fit with minimum residual error for the source mechanism featuring moments and force (blue lines). Offset below the blue traces in Figure 2a and plotted in red are the moment tensor components obtained for the best fit with a mechanism composed of moments only. Traces shown in
black are the source‐time histories for a reconstructed model (see section 4). The moment tensor components are dominated by in‐phase dipole components with little energy in the shear components, indicating the presence of a volumetric source. The average amplitude ratios Fx/Mxx, Fy/Myy, and Fz/Mzz are about 4 × 10−5 m−1, suggesting only a few percent of the observed waveforms may be attributed to the single force [Ohminato et al., 1998].
3. Source Geometry [7] Information about the source geometry can be obtained from an eigenvalue decomposition of the amplitudes of the moment tensor components [e.g., Chouet, 1996]. For a subset of nodes in the computational domain that encompass the overlapping portion of the blue and red error volumes in Figure 1b (a total of 532 nodes with average spacing of 80 m, shown as open circles in Figure 1c) the eigenvectors estimated for the model with moments and forces or moments only are obtained for samples taken every 0.05 s in the moment time histories. An amplitude threshold of 30% of the absolute maximum value of the largest moment component is set to exclude the large variance observed at the
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Figure 2. (a) Moment tensor components for the best fitting solution for moment and force (blue), moments only solution (red), and reconstructed geometry featuring a sill and dike (black lines), (b) volumetric components for the sill and dike, and (c) single force components for the moment and force (blue) and reconstructed (black) solutions. The traces are offset for clarity. zero crossing of the source‐time functions. The orientations of the eigenvectors are described by the angles (measured from vertical) and (measured counterclockwise from the positive x (east) axis). Mean eigenvalues describe the dipole ratios. The mean dominant dipole orientation and angular standard deviation d, and mean dipole ratio and standard deviation for all solutions featuring moments and forces are = 14.4°, = 84.9°, d = 11°, [0.49 ± 0.22 : 0.75 ± 0.14 : 2] and for all solutions featuring moments only are = 15.4°, = 33.7°, d = 9.5°, and [0.42 ± 0.12 : 0.68 ± 0.1 : 2]. The dipole ratios are normalized here to a value of 2 (see the auxiliary material for a detailed explanation).1 Figures S1a and S1c of the auxiliary material show the dipole projections onto a unit sphere and Figures S1b and S1d show histograms of the dipole ratios for the two source mechanisms. [8] The results obtained for mechanisms composed of moments only have smaller standard angular deviations in their dipole orientations and ratios compared to the mechanisms featuring moments and forces. This suggests that using nine free parameters with our limited number of observations may result in a coupling of amplitude and phase between the force and moment source‐time functions, producing lower residual error and AIC values at the expense of a realistic representation of the source mechanism. In both source models the orientations of the dominant dipoles are nearly vertical, while the observed dipole ratios suggest the presence of a composite volumetric source mechanism.
4. Source Reconstruction [9] To estimate the source geometry we carry out systematic reconstructions of the very‐long‐period source mechanism for models consisting of a single pipe, a single crack, two intersecting pipes, two intersecting cracks, and a 1 Auxiliary materials are available in the HTML. doi:10.1029/ 2010GL045977.
pipe intersecting a crack. Keeping in mind that a single force may be part of the source mechanism we include three single‐ force components in the models. To determine the best fit point source we conduct a grid search over the 532 nodes. A search for the best fitting model at each node is carried out by systematically varying the angles and defining the orientation of each source component (2.4 × 107 models overall). For each model we determine the residual error and statistical estimates of the dipole orientations and ratios calculated from a point‐by‐point eigenvalue decomposition of the reconstructed source mechanism. [10] Five separate criteria are used to select models that best match the inversion using moments only at each node. First, the residual error of the model must be within 2.5% of the minimum error found for the same type of volumetric mechanism. Second, the mean dipole orientations of the reconstructed moment tensor must be within one angular standard deviation of the mean dipole orientations from the moments only inversion. Third, the dipole ratios of the reconstructed moment tensor must be within one standard deviation of the mean dipole ratios from the moments only inversion. Fourth, the averaged cross‐correlation of the volumetric components of the reconstructed moment tensor and moments only inversion must be 0.85 or higher. Finally, the model must have geological plausibility. [11] The dipole ratios for models representing a single crack, a single pipe, and two intersecting pipes do not match those of the original inversions and are dropped from further consideration. Models featuring intersecting cracks or a pipe intersecting a crack are possible representations of the source mechanism. Of the 532 nodes investigated, and without consideration of the geologically plausible constraint, models consisting of two cracks that match the respective statistics for inversions with moments only are found at 31 nodes, and models consisting of a pipe‐crack combination are found at 112 nodes (green dots in Figures 1c and 1e).
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[12] Our final test in selecting a model is to require that the projection of one of the geometrical components of the source onto the topographic model of Augustine intersect the free surface near the summit vent. Nine nodes with models consisting of two cracks and thirteen nodes with models consisting of a pipe‐crack combination (minimum residual error: 19.8%, 14.1%; and AIC: −62936, −80992, respectively) meet this constraint (red dots in Figure 1c and 1e). For the models that meet all of the imposed constraints the dominant source component is a sub‐horizontal crack (sill) dipping 10°–30° to the east‐northeast. Either a steeply inclined pipe or sub‐vertical EW to ESE–WNW trending crack (dike) with a maximum amplitude 1/3 to 1/2 that of the sill and opposite in sign, is consistently obtained as the sub‐dominant source component. The mean source centroid of these models is centered beneath the summit at an elevation of 80 m. Idealized representations of the two mechanisms are shown in Figures 1d and 1f (plotted at the mean location and with the mean component orientations for the best‐fitting models). The reconstructed moment tensor and single‐force components for a representative model consisting of a sill intersecting a dike is shown in Figures 2a and 2c (black traces). Figure 2b shows the volume changes in the sill and dike.
5. Network Resolution [13] An idealized network of 20 stations at distances of 1, 2.5, and 4.5 km from the summit and 5 stations located in the same position as those of the broadband network is used to test network capability (Figure S2b of the auxiliary material). Using the Earth model representing Augustine, synthetic seismograms consisting of a Ricker wavelet with a period of 3 s were computed for each station for sources at elevations of 480 m, sea level, and 1000 m below sea level and centered below the summit of Augustine (source epicenter shown by black dot in Figure S2b of the auxiliary material). The 3 s period used here is similar to the 2 s period used to generate Green’s functions in the previous sections, but is otherwise an arbitrary choice primarily controlled by computational requirements. Waveforms for nine source mechanisms consisting of a single horizontal crack, a single vertical crack, a single vertical pipe, combinations of one horizontal crack and a vertical crack or vertical pipe, and the same sources combined with either a single vertical force or three force components were calculated for each source location (Table S1 of the auxiliary material). The synthetic data for each source mechanism were scaled to reflect the amplitudes observed in the reconstructed source models (see section 3). Five levels of noise in the frequency band 0.1 < f < 1 Hz were added to each trace with network averaged signal‐to‐noise ratios of 50, 20, 10, 5, and 2. [14] Green’s functions were computed for each source position and convolved with a full cosine smoothing function with period of 0.5 s. Twenty‐two subsets of the synthetic network consisting of one to twenty stations (Table S2 of the auxiliary material) were used to assess the recovery of the known source mechanisms. For each source depth, source model, subnet of stations, and signal‐to‐noise ratio twenty‐one inversions were conducted including inversions for (1) six moment tensor and three single‐force components, (2) six moment tensor components only, (3) three single‐force components only, and (4) eighteen fixed source
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geometries (Table S3 of the auxiliary material). The residual error, AIC, and the following criteria were calculated to assess the recovery of each known source mechanism. For each inversion of type (1) the maximum peak‐to‐trough amplitude of each moment and force component, and the amplitude ratios of the dipole components normalized to the maximum dipole amplitude expected for the known source (Table S1 of the auxiliary material) were measured. For each inversion of type (2) the moment amplitudes and ratios were similarly measured. For inversions of type (4) the moment amplitudes and ratios, and, if present, the force component amplitudes of the reconstructed source mechanism were measured. The cross‐correlation between the dipole components of the reconstructed model with those of inversion of types 1 and 2, and, if present, the cross‐correlation of force components with those from the inversion of type 1 was calculated. In addition, for each model of type (4) the cross‐correlation of the individual source‐time histories with the respective source‐time function used to generate the synthetic data was calculated. [15] Of direct interest to this work is the ability of the synthetic broadband network to recover sources similar to those suggested by our original source reconstructions. Subnet R5 (Table S2 of the auxiliary material) represents the Augustine broadband network. Examples of the recovery of a source at sea level and consisting of a horizontal crack, vertical EW striking crack, and three force components, and a horizontal crack, vertical pipe and three force components are shown in Figures S3 and S4 of the auxiliary material. The residual error and AIC are minimized for both sources using the model with moments and forces compared to the model using moments only. For both sources the residual errors and AIC values correctly identify the source if the signal‐to‐noise ratio is greater than 20, while with decreasing signal‐to‐noise ratios only the volumetric components of the source can be resolved. Requiring the cross‐correlation of the dipole components of the reconstructed model with those of the inversion using six moment components only and the reconstructed model’s dipole ratios and amplitudes to be within 15% of the known source parameters, and the force amplitudes to be within a factor of 2 of the known force amplitudes indicates the synthetic broadband network can adequately recover models similar to those observed by the broadband network. [16] Of more general interest, the synthetic modeling provides a guide to the deployment of broadband sensors on a volcano in order to extract interpretable moment tensors from the very‐long‐period components of eruptive seismicity. We find that a minimum of three stations can recover a known source mechanism if the angular separation of the stations with respect to the source is maximized, one of the stations is less than 2 km from the source, and the source is near or above the elevation of the lowest station. Using three or more stations that do not meet these criteria can lead to a misinterpretation of the source mechanism. For example, if all stations are at similar elevations and farther than 2 km from the source (R2 and R3 with eight stations each), only the moment components of the above sources can be retrieved (Figures S3 and S4 of the auxiliary material). A simple source geometry can not be distinguished from other possible simple or composite source geometries solely through the minimization of residual error and AIC. This is true regardless of source depth or number of stations (Figures S4 and S5 of the auxiliary
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material). As long as the minimum requirements of angular and vertical separation are met, increasing the number of stations allows the recovery of an interpretable moment tensor with increasing background noise. This modeling suggests that a minimum of five stations with maximized azimuthal and vertical separation with respect to the expected source location should be considered when planning a broadband experiment. These metrics are applicable where significant topography is present.
6. Discussion [17] The moment tensors at Augustine exhibit a characteristic source process consisting of inflation‐deflation‐ reinflation of the volumetric components with the second inflation displaying an amplitude larger than the initial inflation. This pattern reflects a pressurization, depressurization, and repressurization of the dominant volumetric sill over a period of about one minute. It should be noted that the duration of this process is constrained by the band‐limited response of the broadband sensors. This pattern is similar to that observed for the source of degassing bursts at Popocatépetl Volcano, Mexico although the very‐long‐period source centroid is deeper (1.5 km beneath the summit) at Popocatépetl [Chouet et al., 2005]. A model of dynamic diffusive bubble growth and pressure recovery due to a sudden pressure drop as invoked by Chouet et al. [2006] at Popocatépetl may provide a realistic explanation for the Vulcanian explosions at Augustine. In this model, the pattern of volume change in the sill (Figure 2b) is consistent with an initial pressurization of the source, followed by a sudden release of gas and subsequent repressurization of the source through bubble growth in response to the decrease in pressure. [18] Ground deformation measured by continuously recording Global Positioning System instruments prior to the initial eruption of Augustine Volcano suggests the inflation or pressurization of a source near sea level and beneath the summit [Cervelli et al., 2006]. This observation is consistent with the very‐long‐period source location where the mean source centroid determined by our modeling is near 100 m elevation with horizontal and vertical limits of ±400 and ±300 m, respectively. The general structural grain of the Cook Inlet basin strikes northeast, with the exception of the Augustine‐Seldovia arch which strikes west and intersects the northeast striking Iniskin structural zone near Augustine [Fisher et al., 2009]. The best constrained models consisting of two intersecting cracks have a vertical component that trends west as well, suggesting that the orientation of the vertical component of these constrained models may be controlled by the Augustine‐Seldovia arch.
7. Concluding Remarks [19] Waveform inversions using a limited number of broadband stations suggest the presence of a volumetric source about 1 km below the summit during the initial Vulcanian eruption of Augustine Volcano in 2006. Reconstruction of the source mechanism indicates the source consists of a sill‐like structure combined with a nearly vertical pipe or EW trending crack and a weak single force. The single force contribution to the waveforms is less than 5%, and synthetic modeling suggest that the force is not well resolved due to its
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low amplitude and the limited number of channels available for analysis. The moment tensors derived from moments and forces, moments only, and fixed geometries that best fit the data are similar in amplitude and phase, giving confidence that the source mechanism and location are adequately resolved. Synthetic tests indicate that the network is capable of imaging a source mechanism similar to that suggested by the waveform inversions. [20] The synthetic modeling pursued in this work provides a guide to the expected capability of a broadband network to resolve very‐long‐period source mechanisms. Relying solely upon residual error and estimates of the optimal number of parameters when confronted with limited observational data can lead to an incorrect interpretation of the moment tensor, while statistical measures of the shape of the moment tensor and possible orientations of the source mechanism can help constrain the interpretation of waveform inversions of eruptive seismicity. [21] Acknowledgments. Constructive comments on this work were provided by Stephanie Prejean and Matthew Haney.
References Akaike, H. (1974), A new look at the statistical model identification, IEEE Trans. Autom. Control, 19, 716–723. Cervelli, P. F., T. Fournier, J. Freymueller, and J. A. Power (2006), Ground deformation associated with the precursory unrest and early phases of the January 2006 eruption of Augustine Volcano, Alaska, Geophys. Res. Lett., 33, L18304, doi:10.1029/2006GL027219. Chouet, B. (1996), New methods and future trends in seismological volcano monitoring, in Monitoring and Mitigation of Volcano Hazards, edited by R. Scarpa and R. I. Tilling, pp. 23–97, Springer, New York. Chouet, B., P. Dawson, and A. Arciniega‐Ceballos (2005), Source mechanism of Vulcanian degassing at Popocatépetl Volcano, Mexico, determined from waveform inversions of very long period signals, J. Geophys. Res., 110, B07301, doi:10.1029/2004JB003524. Chouet, B., P. Dawson, and M. Nakano (2006), Dynamics of diffusive bubble growth and pressure recovery in a bubbly rhyolitic melt embedded in an elastic solid, J. Geophys. Res., 111, B07310, doi:10.1029/ 2005JB004174. Chouet, B. A., P. B. Dawson, M. R. James, and S. J. Lane (2010), Seismic source mechanism of degassing bursts at Kilauea Volcano, Hawaii: Results from waveform inversion in the 10–50 s band, J. Geophys. Res., 115, B09311, doi:10.1029/2009JB006661. Fisher, M. A., N. A. Ruppert, R. A. White, F. H. Wilson, D. Comer, R. W. Sliter, and F. L. Wong (2009), A distal earthquake cluster concurrent with the 2006 explosive eruption of Augustine Volcano, Alaska, Tectonophysics, 469, 25–36, doi:10.1016/j.tecto.2009.01.019. Kienle, J., D. J. Lalla, C. F. Pearson, and S. A. Barrett (1979) Search for shallow magma accumulations at Augustine Volcano, final report to Department of Energy, 157 pp., Geophys. Inst., Univ. of Alaska Fairbanks, Fairbanks. Ohminato, T., and B. A. Chouet (1997), A free‐surface boundary condition for including topography in the finite‐difference method, Bull. Seismol. Soc. Am., 87, 494–515. Ohminato, T., B. A. Chouet, P. Dawson, and S. Kedar (1998), Waveform inversion of very long period impulsive signals associated with magmatic injection beneath Kilauea Volcano, Hawaii, J. Geophys. Res., 103, 23,839–23,862, doi:10.1029/98JB01122. Power, J. A., C. J. Nye, M. L. Coombs, R. L. Wessels, P. F. Cervelli, J. Dehn, K. L. Wallace, J. T. Freymueller, and M. P. Doukas (2006), The reawakening of Alaska’s Augustine Volcano, Eos Trans. AGU, 87(37), doi:10.1029/2006EO370002. B. A. Chouet and P. B. Dawson, U.S. Geological Survey, 345 Middlefield Road, MS 910, Menlo Park, CA 94025, USA. (
[email protected];
[email protected]) J. Power, Alaska Volcano Observatory, U.S. Geological Survey, 4200 University Dr., Anchorage, AK 99508‐4667, USA. (
[email protected])
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