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[SSS07-01] Analytical solutions of attenuation relation for the near-field term in earthquake displacement fields
Keywords:Near-field term, Attenuation relation, Earthquake displacement fields, Analytical solution
In recent years, seismic and geodetic records have been densely observed near faults, such as the 2016 Kumamoto earthquake, the 2023 Kahramanmaras, Turkey, earthquake, and the 2024 Noto Peninsula earthquake. Therefore, the contributions of the near, intermediate, and far-field terms of seismic waves in Aki and Richards (1980, 2002) are receiving renewed attention. We here conducted an analytical study on the distance attenuation of the near-field term of the seismic wave displacement field radiated from a double-couple point source.
The displacement field of seismic waves radiated from a double-couple point source is expressed by the convolution of the spatial differentials of the moment tensor and the Green's tensor. There are various previous studies on the characteristics of seismic waves in nearby areas, but except for permanent displacement and results when r→0, the dependence of displacement and velocity on epicenter distance r, that is, distance attenuation, has not been fully investigated.
In this study, we use several representative moment rate functions (delta function, box-car function, isosceles triangle function, smoother ramp function, etc.) to solve the analytical solution of the distance decay of the near term of displacement and velocity. As a result, we proved that the near-field term of displacement attenuates by r-2 with respect to the epicenter distance, regardless of the moment rate function. In addition, for the distance attenuation of the near-field term of velocity, the distance at which the attenuation rate switches is uniquely determined depending on the shape of the hypocenter time function, and from this boundary point it shifts to r-2 at short distances and to r-3 at long distances. Finally, we verified the consistency between our derived analytical result and the result of calculating the near-field term using numerical integration.
The displacement field of seismic waves radiated from a double-couple point source is expressed by the convolution of the spatial differentials of the moment tensor and the Green's tensor. There are various previous studies on the characteristics of seismic waves in nearby areas, but except for permanent displacement and results when r→0, the dependence of displacement and velocity on epicenter distance r, that is, distance attenuation, has not been fully investigated.
In this study, we use several representative moment rate functions (delta function, box-car function, isosceles triangle function, smoother ramp function, etc.) to solve the analytical solution of the distance decay of the near term of displacement and velocity. As a result, we proved that the near-field term of displacement attenuates by r-2 with respect to the epicenter distance, regardless of the moment rate function. In addition, for the distance attenuation of the near-field term of velocity, the distance at which the attenuation rate switches is uniquely determined depending on the shape of the hypocenter time function, and from this boundary point it shifts to r-2 at short distances and to r-3 at long distances. Finally, we verified the consistency between our derived analytical result and the result of calculating the near-field term using numerical integration.