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Table 1 Best-fit parameters of time functions

From: Quantitative relationship between plume emission and multiple deflations after the 2014 phreatic eruption at Ontake volcano, Japan

 acτ (days)AICa
ΔVS
 Path 126
  f1(t)(7.4 ± 0.2) × 105 (m3)379 ± 31119.8
  f2(t)b(6.1 ± 2.1) × 105 (m3)106 ± 183 (m3/day)313 ± 118121.2
 Path 20
  f1(t)(9.2 ± 1.2) × 105 (m3)641 ± 150191.5
  f2(t)b(9.0 ± 25.3) × 105 (m3)10 ± 1437 (m3/day)632 ± 1300193.5
Qout
 f1(t)(1.1 ± 0.03) × 1010 (kg)209 ± 16447.1
 f2(t)(5.0 ± 0.1) × 109 (kg)(8.6 ± 0.1) × 106 (kg/day)47 ± 2274.2
ΔLd
 Path 126
  f1(t)− 1.90 ± 0.16 (cm)905 ± 115− 2350.7
  f2(t)(− 2.63 ± 0.22) × 10−1 (cm)(− 1.04 ± 0.04) × 10−3 (cm/day)20 ± 11− 2445.1
 Path 20
  f1(t)− 1.34 ± 0.04 (cm)378 ± 26− 2345.2
  f2(t)(− 4.62 ± 0.26) × 10−1 (cm)(− 0.88 ± 0.04) × 10−3 (cm/day)41 ± 10− 2465.9
  1. a\({\text{AIC}} = n\log \left( {\frac{1}{n}\mathop \sum \limits_{i = 1}^{n} \left( {O_{i} - C_{i} } \right)^{2} } \right) + 2k\), where n is number of data, i is index, O is an observed value, C is a calculated value, k is number of model parameters (Akaike 1974)
  2. bParameters included in f2(t) of ΔVS were not determined uniquely, which indicates that linear terms are completely unnecessary to characterize the time series of ΔVS