9:15 AM - 9:30 AM
[SCG39-20] Extraction of fine space-time structures in deep low-frequency tremor using the Hough transform
Keywords:Deep low-frequency tremor,, Hough transform, Migration, Kii Peninsula
Tremor migration is one of the important features of deep low-frequency tremors. The characteristics of the tremor migration are classified into the following three types: (1) Long-term migration (Obara, 2010) for which tremor propagates along the strike of a subducting plate at approximately 10 km/day in synchronization with a slow slip event (SSE); (2) Rapid tremor reversal (RTR) for which tremor propagates along the strike into the reverse direction to the long-term migration with a speed of approximately 200 km/day (Houston et al., 2011); (3) Tremor streak which is a migration of tremor along the dip at approximately 1000 km/day (Ghosh et al., 2010). We usually investigate the temporal evolution of tremors by projecting tremor locations into an axis (Obara, 2010; Sagae et al., 2021, GJI). Therefore, it is necessary to study the three-dimensional behavior of tremors from the epicentral distribution and the time of occurrence. In the field of astronomy, Morii (2019) performed a detection of straight lines using the 3-D Hough transform (2D in space and 1D in time) to investigate movements of celestial bodies in the observed images. We called the method as “space-time Hough transform” to distinguish it from the conventional 3-D Hough transform in 3D spatial dimensions. As a previous study which applied Hough transform in seismology, Uchide and Imanishi (2017, SSJ) detected fault planes using hypocenter locations and focal mechanism information based on the conventional Hough transform. In this study, by slightly modifying the space-time Hough transform, we extract fine space-time structures in tremor migrations.
In this study, straight lines (tremor migrations) are detected in the three-dimensional space of the epicentral distribution and time. We set the positive x-axis, y-axis, and z-axis in the east, north, and time direction, respectively. Any straight line in the three-dimensional space is represented as ρ=x(-sinφsinψ+cosθcosφcosψ)+y(sinφcosψ+cosθcosφsinψ)-z(sinθcosφ), where ρ is the distance from the origin to the straight line, θ is the zenith angle, φ is the azimuth, and ψ is the rotation angle, respectively. In particular, tanθ represents the migration speed, and the vector (cosψ, sinψ) represents the direction vector in the x-y plane. In this study, the direction vector of a straight line is taken in the radial direction, whereas in Morii (2019), that is taken in a direction perpendicular to the radial direction. We set a “bin” for each parameter of (ρ, θ, φ, ψ). Then, we calculate ρ while changing (θ, φ, ψ) for each event, and perform a “vote” to the corresponding “bin”. Finally, the “bin” (ρ, θ, φ, ψ) with the largest number of votes is the best straight line that represents event data best. Furthermore, even if there are multiple straight lines in the space, these straight lines can be detected separately using the Hough transform because votes for different lines are cast on different “bins”. This enables to relax a constraint of one migration in one time-window used in previous studies (Obara et al., 2012; Maeda et al., 2020 SSJ). Our method has a potential to detect multiple migrations within a time window.
We analyzed a tremor catalog in which tremor epicenters were determined using a dense seismic array beneath the Kii Peninsula (Sagae et al., 2021, GJI). This catalog is suitable for investigating details of tremor migrations because it determined approximately 2.2 times more tremors than a catalog determined by the envelope correlation method (Obara, 2002). The analyzed period is from July 2012 to July 2014. We used every one hour time-window to detect migrations. The parameters “bins” were set in increments of 10 degrees for φ and ψ, in the range of 1–40 km/hr for θ, and in an increment of 5 km for ρ in consideration of uncertainties in the tremor locations. The Hough transform was applied when the time-window contained more than 10 events, and a straight line with the largest number of votes was detected. Then, after removing events composing the straight lines already detected, other straight lines were detected iteratively until the number of unvoted events was less than 10 events.
As a result, we found that predominant directions of migrations differ depending on locations. In the place where along-strike migrations were predominant, we found a feature that tremor migrated into the opposite direction to the long-term migration. Moreover, locations of RTR and Tremor streak reported in Sagae et al. (2021, GJI) were similar to locations where migrations were predominant in the strike and dip directions, respectively. This result suggests that RTR and Tremor streak may occur repeatedly in the same locations.
In this study, straight lines (tremor migrations) are detected in the three-dimensional space of the epicentral distribution and time. We set the positive x-axis, y-axis, and z-axis in the east, north, and time direction, respectively. Any straight line in the three-dimensional space is represented as ρ=x(-sinφsinψ+cosθcosφcosψ)+y(sinφcosψ+cosθcosφsinψ)-z(sinθcosφ), where ρ is the distance from the origin to the straight line, θ is the zenith angle, φ is the azimuth, and ψ is the rotation angle, respectively. In particular, tanθ represents the migration speed, and the vector (cosψ, sinψ) represents the direction vector in the x-y plane. In this study, the direction vector of a straight line is taken in the radial direction, whereas in Morii (2019), that is taken in a direction perpendicular to the radial direction. We set a “bin” for each parameter of (ρ, θ, φ, ψ). Then, we calculate ρ while changing (θ, φ, ψ) for each event, and perform a “vote” to the corresponding “bin”. Finally, the “bin” (ρ, θ, φ, ψ) with the largest number of votes is the best straight line that represents event data best. Furthermore, even if there are multiple straight lines in the space, these straight lines can be detected separately using the Hough transform because votes for different lines are cast on different “bins”. This enables to relax a constraint of one migration in one time-window used in previous studies (Obara et al., 2012; Maeda et al., 2020 SSJ). Our method has a potential to detect multiple migrations within a time window.
We analyzed a tremor catalog in which tremor epicenters were determined using a dense seismic array beneath the Kii Peninsula (Sagae et al., 2021, GJI). This catalog is suitable for investigating details of tremor migrations because it determined approximately 2.2 times more tremors than a catalog determined by the envelope correlation method (Obara, 2002). The analyzed period is from July 2012 to July 2014. We used every one hour time-window to detect migrations. The parameters “bins” were set in increments of 10 degrees for φ and ψ, in the range of 1–40 km/hr for θ, and in an increment of 5 km for ρ in consideration of uncertainties in the tremor locations. The Hough transform was applied when the time-window contained more than 10 events, and a straight line with the largest number of votes was detected. Then, after removing events composing the straight lines already detected, other straight lines were detected iteratively until the number of unvoted events was less than 10 events.
As a result, we found that predominant directions of migrations differ depending on locations. In the place where along-strike migrations were predominant, we found a feature that tremor migrated into the opposite direction to the long-term migration. Moreover, locations of RTR and Tremor streak reported in Sagae et al. (2021, GJI) were similar to locations where migrations were predominant in the strike and dip directions, respectively. This result suggests that RTR and Tremor streak may occur repeatedly in the same locations.