5:15 PM - 6:30 PM
[SSS11-P05] Assessment of applicability of a proposed method to estimate phase velocity using arbitrary 5-site arrays
Keywords:Arbitrary-shape array, phase velocity, Complex Coherence Function (CCF), Centerless Circular Array (CCA) method, Spatial Auto-correlation (SPAC) method, Artificial Bee Colony (ABC) algorithm
To estimate earthquake ground motion, it’s necessary to model the ground structure. Then the use of array method was proposed by using microtremors because it’s an inexpensive and mobile means of estimating the phase velocity of surface waves. Based on the analytical solution of Lamb's problem for vertical components of Rayleigh wave, the relationship between two observation points, p and q for example, is given in a discrete representation with the Bessel function of the first kind and higher-order Bessel functions, which is called Complex Coherence Function (CCF) [4]. Zhang and Morikawa [5] extended the CCF to apply it to linear array situation. By adding an extra observation point s, the relationship between p and s can be expressed [6]. At last, the CCF equations have only 5 unknowns left, including the phase velocity. Therefore, we proposed a method [7] to estimate the phase velocity using Artificial Bee Colony (ABC) algorithm [8] under a constraint of kr belongs to [0, 5]. The selection of the constraint condition will affect the results and will be discussed.
The numerical simulations and the site observations’ results confirmed the availability of the proposed algorithm for array shapes with more free arrangement of sensors. When it comes to selecting the constraint condition, constraint condition is a better choice for most 3-site arrays if we expect a wider effective range. For 4-site arrays, we think acceptable results can be obtained with no constraint condition. After comparing with 4-site arrays without constraint condition and related 3-site arrays under rave constraint condition, we can see that the 4-site arrays' results are influenced by all of the 3-site arrays it contains, meaning that it might not be better than all of the 3-site arrays' results, especially the small regular 3-site array. However, they are better than most of other 3-site arrays which have irregular shapes.
Based on this method, we think the application to more-sites arrays, 5-site arrays for example, can further improve the results. If 5-site arrays were chosen, the 5 unknowns will remain the same but there will be 10 CCFs. On the other hand, since there will be 10 CCFs, we can extend the CCF’s application range and thus there will be 2 more unknowns, for example. In that case, the unknowns are still less than the CCFs and the constraint range, kr belongs to [0, 5], can be wider, too. However, similarly as 4-site arrays, adding more sites will inevitably extend the optimization time. And optimizing one phase velocity result to satisfy all of the CCF equations together will leave the result influenced by all of the CCFs. Still, numerical simulations and the application to ZRS field data using more-sites arrays, 5-site arrays for example, will be conducted to testify the validity of the proposed assumption. And comparisons with conventional methods will be conducted at the same time.
[1] Capon, J. (1969). Proceedings of the IEEE, 57(8), 1408-1418.
[2] Aki, K. (1957). Bull. Earthq. Res. Inst., 35, 415-456.
[3] Cho, I., Tada, T., & Shinozaki, Y. (2006). Journal of Geophysical Research: Solid Earth, 111(B9).
[4] Shiraishi, H. & Matsuoka, T. (2005). BUTSURI-TANSA, 58(2), 137-146.
[5] Zhang, X. & Morikawa, H. (2014). British Journal of Applied Science & Technology, 6(4), 350–363.
[6] Morikawa, H. & Iiyama, K. (2015). Program and Abstracts, The Seismological Society of Japan, Fall Meeting.
[7] Zhang, H., Iiyama, K. & Morikawa, H. (2020). 17th World Conference on Earthquake Engineering.
[8] Karaboga, D. & Basturk, B. (2007). Journal of global optimization, 39(3), 459-471.
The numerical simulations and the site observations’ results confirmed the availability of the proposed algorithm for array shapes with more free arrangement of sensors. When it comes to selecting the constraint condition, constraint condition is a better choice for most 3-site arrays if we expect a wider effective range. For 4-site arrays, we think acceptable results can be obtained with no constraint condition. After comparing with 4-site arrays without constraint condition and related 3-site arrays under rave constraint condition, we can see that the 4-site arrays' results are influenced by all of the 3-site arrays it contains, meaning that it might not be better than all of the 3-site arrays' results, especially the small regular 3-site array. However, they are better than most of other 3-site arrays which have irregular shapes.
Based on this method, we think the application to more-sites arrays, 5-site arrays for example, can further improve the results. If 5-site arrays were chosen, the 5 unknowns will remain the same but there will be 10 CCFs. On the other hand, since there will be 10 CCFs, we can extend the CCF’s application range and thus there will be 2 more unknowns, for example. In that case, the unknowns are still less than the CCFs and the constraint range, kr belongs to [0, 5], can be wider, too. However, similarly as 4-site arrays, adding more sites will inevitably extend the optimization time. And optimizing one phase velocity result to satisfy all of the CCF equations together will leave the result influenced by all of the CCFs. Still, numerical simulations and the application to ZRS field data using more-sites arrays, 5-site arrays for example, will be conducted to testify the validity of the proposed assumption. And comparisons with conventional methods will be conducted at the same time.
[1] Capon, J. (1969). Proceedings of the IEEE, 57(8), 1408-1418.
[2] Aki, K. (1957). Bull. Earthq. Res. Inst., 35, 415-456.
[3] Cho, I., Tada, T., & Shinozaki, Y. (2006). Journal of Geophysical Research: Solid Earth, 111(B9).
[4] Shiraishi, H. & Matsuoka, T. (2005). BUTSURI-TANSA, 58(2), 137-146.
[5] Zhang, X. & Morikawa, H. (2014). British Journal of Applied Science & Technology, 6(4), 350–363.
[6] Morikawa, H. & Iiyama, K. (2015). Program and Abstracts, The Seismological Society of Japan, Fall Meeting.
[7] Zhang, H., Iiyama, K. & Morikawa, H. (2020). 17th World Conference on Earthquake Engineering.
[8] Karaboga, D. & Basturk, B. (2007). Journal of global optimization, 39(3), 459-471.