3:45 PM - 4:00 PM
[SSS06-07] Inversion of envelope widths of volcanic earthquakes to estimate temporal variations of scattering properties
Keywords:scattering, inversion, volcano
Estimating seismic heterogeneous structures beneath volcanoes, described by the mean free path (l0) and the quality factor for medium attenuation (Qi) for S waves, is important to understand spatio-temporal variations of magma and hydrothermal systems. Kumagai & Hamamoto (JpGU Meeting, 2022) proposed a new inversion approach to estimate 3D l0 and Qi distributions from envelope widths (p) of volcano-tectonic (VT) earthquakes using sensitivity kernels or space-weighting functions, and applied it to VT earthquakes at three volcanoes including Taal volcano, Philippines. The inversion result at Taal points to the existence of two anomaly regions near the summit and beneath the eastern flank of Volcano Island.
In this study, we developed an inversion method to estimate temporal variations of l0 and Qi values in an anomaly region from p values of individual VT earthquakes. In this method, the partial derivatives of p values with respective to l0 and Qi perturbations in the anomaly region are calculated from envelope waveforms synthesized by the Monte Carlo method of Yoshimoto (JGR, 2000). We solve the damped least squares problem for the envelope width residuals between observed p values and those calculated with 3D models to estimate l0 and Qi values in the anomaly region. The inversion is performed for individual events to estimate l0 and Qi temporal variations in the region.
To evaluate the feasibility of this inversion method, we carried out numerical tests using p values of synthesized envelope waveforms for 3D models consisting of the two anomaly regions, in which l0 and Qi values in the anomaly region beneath the eastern flank changed temporarily. We used 82 source locations of observed VT earthquakes at Taal, which were selected with a criterion of 500 m away from each other and observed at 6 stations in and around Volcano Island. Our tests indicate the following features: (1) The numerical instability and estimation accuracy are improved when the combination of Qi and scattering attenuation Qs instead of l0 is used and the ratio of their initial model values is used as the ratio of their hyperparameters; (2) The appropriate perturbation ranges for the partial derivatives should be selected from initial Qs and Qi solutions obtained from the partial derivatives with narrow perturbation ranges; (3) The residual sum of squares (RSS) increases sharply when the hyperparameters are larger than certain values, and their values are slightly dependent on the source locations; (4) There is a trade-off relationship between Qs or l0 and Qi values.
Based on these features, we applied the inversion method to observed p data of 535 VT earthquakes at Taal (Hamamoto et al., AGU Meeting, 2021). Our inversion result for the anomaly near the summit shows no clear temporal variations with a very small decrease in RSS. On the other hand, our inversion for the anomaly beneath the eastern flank provided a larger decease in RSS and the estimated l0 and Qi values in the anomaly displayed large fluctuations when seismicity was high. These fluctuations were clearly larger than the trade-off between l0 and Qi found in the numerical tests. The moving averages of the l0 and Qi values over 4 weeks showed fluctuations similar to those of CO2 flux, suggesting that our estimated temporal variations were caused by heterogeneous distributions of degassed bubbles in magma. Our results indicate that the inversion method is useful to estimate temporal variations of scattering and attenuation properties, although further examinations to improve the solution accuracy are required.
In this study, we developed an inversion method to estimate temporal variations of l0 and Qi values in an anomaly region from p values of individual VT earthquakes. In this method, the partial derivatives of p values with respective to l0 and Qi perturbations in the anomaly region are calculated from envelope waveforms synthesized by the Monte Carlo method of Yoshimoto (JGR, 2000). We solve the damped least squares problem for the envelope width residuals between observed p values and those calculated with 3D models to estimate l0 and Qi values in the anomaly region. The inversion is performed for individual events to estimate l0 and Qi temporal variations in the region.
To evaluate the feasibility of this inversion method, we carried out numerical tests using p values of synthesized envelope waveforms for 3D models consisting of the two anomaly regions, in which l0 and Qi values in the anomaly region beneath the eastern flank changed temporarily. We used 82 source locations of observed VT earthquakes at Taal, which were selected with a criterion of 500 m away from each other and observed at 6 stations in and around Volcano Island. Our tests indicate the following features: (1) The numerical instability and estimation accuracy are improved when the combination of Qi and scattering attenuation Qs instead of l0 is used and the ratio of their initial model values is used as the ratio of their hyperparameters; (2) The appropriate perturbation ranges for the partial derivatives should be selected from initial Qs and Qi solutions obtained from the partial derivatives with narrow perturbation ranges; (3) The residual sum of squares (RSS) increases sharply when the hyperparameters are larger than certain values, and their values are slightly dependent on the source locations; (4) There is a trade-off relationship between Qs or l0 and Qi values.
Based on these features, we applied the inversion method to observed p data of 535 VT earthquakes at Taal (Hamamoto et al., AGU Meeting, 2021). Our inversion result for the anomaly near the summit shows no clear temporal variations with a very small decrease in RSS. On the other hand, our inversion for the anomaly beneath the eastern flank provided a larger decease in RSS and the estimated l0 and Qi values in the anomaly displayed large fluctuations when seismicity was high. These fluctuations were clearly larger than the trade-off between l0 and Qi found in the numerical tests. The moving averages of the l0 and Qi values over 4 weeks showed fluctuations similar to those of CO2 flux, suggesting that our estimated temporal variations were caused by heterogeneous distributions of degassed bubbles in magma. Our results indicate that the inversion method is useful to estimate temporal variations of scattering and attenuation properties, although further examinations to improve the solution accuracy are required.