| Popis: |
During the ongoing eruption at Mount St. Helens, Washington, lava has extruded continuously at a rate that decreased from ~7-9 m 3 /s in October 2004 to 1-2 m 3 /s by December 2005. The volume loss in the magma reservoir estimated from the geodetic data, 1.6-2.7×10 7 m 3 , is only a few tens of percent of the 7.5×10 7 m 3 volume that had erupted by the end of 2005. In this paper we use geodetic models to constrain the size and depth of the magma reservoir. We also ask whether the relations between extruded volume and geodetic deflation volume are consistent with drainage of a reservoir of compressible magma within a linearly elastic host rock. Finally, we compare the time histories of extrusion and geodetic deflation with idealized models of such a reservoir. Critical parameters include erupted volume V e , dome density ρ e , reservoir volume V C , initial reservoir overpressure ρ ex 0 , pressure drop during the eruption Δp, reservoir compressibility κ C ≡(1/V C )(dV C / dp), magma density ρ M , and magma compressibility κ M ≡ (1/ρ M )(dρ M /dp). Seismic velocity and reservoir geometry suggest κ C ≈2×10 -11 Pa -1 , but mechanical considerations suggest κ C =7-15×10 -11 Pa - 1 . The geodetic data are best fit with an ellipsoidal source whose top is 5±1 km deep and whose base is ~10-20+ km deep. In the absence of recharge, the decrease in magma-reservoir volume dV C is theoretically related to the erupted volume V by V e /dV C =(ρ M /ρ e )(1+κ M /κ C ). For κ C =~7-15×10 -11 Pa -1 and ρ M ≈ρ e , estimates of V e and dV C suggest that κ M =1.4-3.0×10 -10 Pa -1 . corresponding to a magmatic gas content in the reservoir of v g =0 to 1.8 percent by volume. If we assume that effusion rate is linearly related to reservoir pressure and that the recharge rate into the reservoir is constant, the effusion rate should decrease exponentially with time to a value that equals the recharge rate. Best-fit curves of this form suggest recharge rates of 1.2-1.3 m 3 /s over the first 500 days of the eruption. The best-fit constants include the product V C p ex 0 (κ C + κ M ), making it possible to constrain reservoir volume using values of κ C and κ M constrained from ratios of erupted volume to geodetic deflation volume. If, on the other hand, we assume a logarithmic pressure-effusion rate relation and a constant recharge rate, the dome volume-time curve should follow a modified logarithmic relation, with the total erupted volume at a given time proportional to V C Δp (κ C + κ M ). Using κ C =7-15×10 -11 Pa -1 , results from log and exponential curves suggest a reservoir volume of at least several cubic kilometers if Δp or p ex 0 is less than ~30 MPa. Similar results are obtained from numerical calculations that consider temporal changes in (1) magma compressibility, (2) the weight of the lava dome suppressing effusion, and (3) recharge rate. These results are consistent with the notion that the reservoir volume is at least a few times larger than the largest Holocene eruption of Mount St. Helens (4 km 3 dense-rock-equivalent + volume for the 3.4-ka Yn eruption). Both the exponential and logarithmic models predict a history of reservoir decompression that imperfectly matches displacement data at GPS station JRO1. Neither model, for example, predicts the rapid radially inward movement at JRO during the first month of the eruption. Such movement, followed by long-term linear deflation, suggests that erupted magma has been replaced in increasing proportions by recharge, but that the recharge rate remains somewhat less than the current (early 2006) effusion rate. |
