9:00 AM - 10:30 AM
[MTT37-P02] Study of Automatic Detection of Atmospheric Lamb Waves by Inverse Problem
Keywords:atmospheric Lamb waves, inverse problems, early warning of tsunamis, automatic detection
1. Background
Lamb waves, a type of atmospheric wave, are trapped by the earth's surface and propagate horizontally at nearly the speed of sound. Their phase velocity (about 310 m/s) is faster than that of tsunamis (typically about 200 m/s), so that they are expected to arrive before tsunamis while keeping the shape of tsunamis because of their almost non-dispersive nature. In fact, the atmospheric Lamb wave excited by the tsunami generated by the Tohoku-Pacific Ocean Earthquake was like the tsunami shape (Arai et al. 2011). Therefore, it is considered that the detection of atmospheric Lamb waves by establishing an extensive network of micro-pressure measurements will be useful for early warning of tsunamis. To realize early warning, automatically detect Lamb waves from observed atmospheric pressure fluctuations is highly desirable. Here we study a method to detect atmospheric lamb waves as an inverse problem.
2. Methods
An inverse problem is generally the problem of finding the input v given a known system M and output w. In the present problem, the output w corresponds to a time series of atmospheric pressure observations, and the input v corresponds to the spatial distribution of the pressure and wind fields at the desired time. We hypothesize a possibility that atmospheric Lamb waves can be selectively extracted from the atmospheric pressure observation time series when the system M is constructed using the governing equations for atmospheric Lamb waves (equations of momentum and continuity supporting the waves of c = 310 m/s). In this study, we consider a spatial one-dimensional inverse problem to examine the above possibility. In constructing the system M, the d'Alembert's solution is used subsidiarily to avoid numerical errors.
3. Experiments and Discussion
The following two experiments were conducted with the detection of Lamb waves in mind.
3.1 Study of detectability based on reproducibility of initial values
First, we examined whether the initial values of the spatial distribution of the pressure and wind fields can be estimated using time series of atmospheric pressure observations of waves traveling in both directions at 310m/s, 280m/s, and 200m/s with initial values of Gaussian functions and waves traveling in one direction at 50m/s with initial values of sine functions, respectively. If the initial value can be correctly estimated only for waves traveling at 310 m/s, we can say that atmospheric Lamb waves can be detected. As a result, the initial values for waves traveling at 310 m/s were correctly reproduced, but not for waves traveling at 200 m/s and 50 m/s. The estimated initial values for waves traveling at 280 m/s were split into two peaks. This indicates that if the initial value is known, it may be possible to determine whether atmospheric Lamb waves are present based on the reproducibility of the initial value.
3.2 Study of detectability based on reproducibility of observed time series
In the real world, initial values cannot be known a priori. Therefore, a method to detect atmospheric Lamb waves from observed time series must be considered. Next, we compared the observed time series given in the inverse problem with the one estimated from the estimated initial values. The two time series are expected to agree well only for atmospheric Lamb waves. The correlation coefficient for waves traveling at 310 m/s is close to 1, but the correlation is also high (>0.6) for waves traveling at 280 m/s, 200 m/s, and 50 m/s. This is because the inverse problem finds the spatial distribution of the pressure and wind fields that best reproduces the observed time series. Therefore, we should examine not only the correlation coefficient but also the equation of the regression line. In the future, we are also considering a method to estimate the current state of the pressure and wind fields from the observed time series and compare it with the current pressure observations.
Acknowledgements
This research was supported by a grant from JSPS Scientific Research Grants JP22K18872.
Lamb waves, a type of atmospheric wave, are trapped by the earth's surface and propagate horizontally at nearly the speed of sound. Their phase velocity (about 310 m/s) is faster than that of tsunamis (typically about 200 m/s), so that they are expected to arrive before tsunamis while keeping the shape of tsunamis because of their almost non-dispersive nature. In fact, the atmospheric Lamb wave excited by the tsunami generated by the Tohoku-Pacific Ocean Earthquake was like the tsunami shape (Arai et al. 2011). Therefore, it is considered that the detection of atmospheric Lamb waves by establishing an extensive network of micro-pressure measurements will be useful for early warning of tsunamis. To realize early warning, automatically detect Lamb waves from observed atmospheric pressure fluctuations is highly desirable. Here we study a method to detect atmospheric lamb waves as an inverse problem.
2. Methods
An inverse problem is generally the problem of finding the input v given a known system M and output w. In the present problem, the output w corresponds to a time series of atmospheric pressure observations, and the input v corresponds to the spatial distribution of the pressure and wind fields at the desired time. We hypothesize a possibility that atmospheric Lamb waves can be selectively extracted from the atmospheric pressure observation time series when the system M is constructed using the governing equations for atmospheric Lamb waves (equations of momentum and continuity supporting the waves of c = 310 m/s). In this study, we consider a spatial one-dimensional inverse problem to examine the above possibility. In constructing the system M, the d'Alembert's solution is used subsidiarily to avoid numerical errors.
3. Experiments and Discussion
The following two experiments were conducted with the detection of Lamb waves in mind.
3.1 Study of detectability based on reproducibility of initial values
First, we examined whether the initial values of the spatial distribution of the pressure and wind fields can be estimated using time series of atmospheric pressure observations of waves traveling in both directions at 310m/s, 280m/s, and 200m/s with initial values of Gaussian functions and waves traveling in one direction at 50m/s with initial values of sine functions, respectively. If the initial value can be correctly estimated only for waves traveling at 310 m/s, we can say that atmospheric Lamb waves can be detected. As a result, the initial values for waves traveling at 310 m/s were correctly reproduced, but not for waves traveling at 200 m/s and 50 m/s. The estimated initial values for waves traveling at 280 m/s were split into two peaks. This indicates that if the initial value is known, it may be possible to determine whether atmospheric Lamb waves are present based on the reproducibility of the initial value.
3.2 Study of detectability based on reproducibility of observed time series
In the real world, initial values cannot be known a priori. Therefore, a method to detect atmospheric Lamb waves from observed time series must be considered. Next, we compared the observed time series given in the inverse problem with the one estimated from the estimated initial values. The two time series are expected to agree well only for atmospheric Lamb waves. The correlation coefficient for waves traveling at 310 m/s is close to 1, but the correlation is also high (>0.6) for waves traveling at 280 m/s, 200 m/s, and 50 m/s. This is because the inverse problem finds the spatial distribution of the pressure and wind fields that best reproduces the observed time series. Therefore, we should examine not only the correlation coefficient but also the equation of the regression line. In the future, we are also considering a method to estimate the current state of the pressure and wind fields from the observed time series and compare it with the current pressure observations.
Acknowledgements
This research was supported by a grant from JSPS Scientific Research Grants JP22K18872.