Resonance frequency of an orthotropic layer to non-principal vertically incident SH body and surface waves
Tóm tắt
In this study, non-principal waves propagating in an isotropic elastic half-space covered by an orthotropic layer are examined. The main objective is to establish a formula for the SH transfer function induced by an vertically incident SH wave and a formula for the H/V ratio of surface waves. The peak frequencies of both the SH transfer function and the H/V ratio curve are examined for models with low to high impedance contrasts to verify the applicability of the quarter wave-length rule for both SH body waves and surface waves. It is numerically shown that the quarter wave-length rule applies well for non-principal SH body wave. Non principal surface waves are shown to be a composition of Love and Rayleigh waves, and their peaks follow the quarter wave-length rule only in the case of high impedance contrast. For medium or low impedance contrasts, the peak frequencies of surface waves could differ from the peak frequencies of SH body wave with relative differences up to
$$50\%$$
.
Tài liệu tham khảo
Arai H, Tokimatsu K (2005) S-wave velocity profiling by joint inversion of microtremor dispersion curve and horizontal-to-vertical (H/V) spectrum. Bull Seis Soc Am 95(5):1766–1778
Borcherdt RD (2009) Viscoelastic waves in layered media. Cambridge University Press, Cambridge
Bonnefoy-Claudet S, Köhler A, Cornou C, Wathelet M, Bard PY (2008) Effects of Love waves on microtremor H/V ratio. Bull Seismol Soc Am 98(1):288–300
Cerv J, Plesek J (2013) Implicit and explicit secular equations for Rayleigh waves in two-dimentional anisotropic media. Wave Motion 50:1105–1117
Chenevert ME, Gatlin C (1965) Mechanical anisotropies of laminated sedimentary rocks. Soc Pet Eng J 5(01):67–77
Dung TTT, Tuan TT, Vinh PC, Trung GK (2020) An approximate formula of first peak frequency of ellipticity of Rayleigh surface waves in an orthotropic layered half-space model. J Mech Mater Struct 15(1):61–74
Ekström G, Dziewonski AM (1998) The unique anisotropy of the Pacific upper mantle. Nature 394(6689):168–172
Field E, Jacob K (1993) The theoretical response of sedimentary layers to ambient seismic noise. Geophys Res Lett 20(24):2925–2928
Forsyth DW (1975) The early structural evolution and anisotropy of the oceanic upper mantle. Geophys J Int 43(1):103–162
Franquet JA, Rodriguez EF (2012, June) Orthotropic horizontal stress characterization from logging and core derived acoustic anisotropies. In 46th US Rock Mechanics/Geomechanics Symposium. OnePetro
Frazer RA, Duncan WJ, Collar AR (1938) Elementary matrices and some applications to dynamics and differential equations. Cambridge University Press
Gupta S, Majhi DK, Kundu S, Vishwakarma SK (2013) Propagation of Love waves in non-homogeneous substratum over initially stressed heterogeneous half-space. Appl Math Mech 34(2):249–258
Gupta S, Ahmed M (2017) Shear waves in an inhomogeneous viscoelastic layer resting over a prestressed orthotropic substrate. Int J Geomech 6:04016145
Gupta S, Ahmed M (2017) On Propagation of Love waves in dry sandy medium sandwiched between fiber-reinforced layer and prestressed porous half-space. Earthq Struct 12(6):619–628
Lekhnitskii SG (1981) Theory of elasticity of an anisotropic body. Mir publishers, Moscow
Lermo J, Chávez-García FJ (1994) Are microtremors useful in site response evaluation? Bull Seis Soc Am 84(5):1350–1364
Lermo J, Chávez-García FJ (1994) Site effect evaluation at Mexico City: dominant period and relative amplification from strong motion and microtremor records. Soil Dyn Earthq Eng 13(6):413–423
Malischewsky PG, Scherbaum F, Lomnitz C, Tuan TT, Wuttke F, Shamir G (2008) The domain of existence of prograde Rayleigh-wave particle motion for simple models. Wave Motion 45(4):556–564
Molnar S, Sirohey A, Assaf J, Bard PY et al (2022) A review of the microtremor horizontal-to-vertical spectral ratio (MHVSR) method. J Seismol:1-33
Nakamura Y (1989) A method for dynamic characteristics estimation of subsurface using microtremor on the ground surface. Quarterly Report of RTRI, Railway Technical Research Institute(RTRI) 30(1):25-33
Nakamura Y (2000) Clear identification of fundamental idea of Nakamuras technique and its applications. 12WCEE Vol. 2656
Nishimura CE, Forsyth DW (1989) The anisotropic structure of the upper mantle in the Pacific. Geophys J Int 96(2):203–229
Ohyoshi T (2000) The propagation of Rayleigh waves along an obliquely cut surface in a directional fibre-reinforced composite. Compos Sci Technol 60:2191–2196
Sayers CM, Van Munster JG (1991) Microcrack-induced seismic anisotropy of sedimentary rocks. J Geophys Res Solid 96(B10):16529–16533
Singh B, Kumar A, Singh J (2006) Reflection of generalized thermoelastic waves from a solid half-space under hydrostatic initial stress. Appl Math Comput 177(1):170–177
Stroh AN (1962) Steady state problems in anisotropic elasticity. Stud Appl Math 41(1–4):77–103
Tanuma K (2007) Stroh formalism and Rayleigh waves. In Stroh Formalism and Rayleigh Waves (pp. 5-154). Springer, Dordrecht
Togashi Y, Kikumoto M, Tani K, Hosoda K, Ogawa K (2021) Determination of 12 orthotropic elastic constants for rocks. Int J Rock Mech Min Sci 147:104889
Tuan TT, Scherbaum F, Malischewsky PG (2011) On the relationship of peaks and troughs of the ellipticity (H/V) of Rayleigh waves and the transmission response of single layer over half-space models. Geophys J Int 184(2):793–800
Tuan TT, Vinh PC, Ohrnberger M, Malischewsky P, Aoudia A (2016) An improved formula of fundamental resonance frequency of a layered half-space model used in H/V ratio technique. Pure Appl Geophys 173(8):2803–2812
Tuan TT, Vinh PC, Malischewsky P, Aoudia A (2016) Approximate formula of peak frequency of H/V ratio curve in multilayered model and its use in H/V ratio technique. Pure Appl Geophys 173(2):487–498
Tuan TT, Vinh PC, Aoudia A, Dung TTT, Manu-Marfo D (2019) Approximate analytical expressions of the fundamental peak frequency and the amplification factor of S-wave transfer function in a viscoelastic layered model. Pure Appl Geophys 176(4):1433–1443
Vinh PC, Linh NTK (2012) Explicit secular equations and formulas for the velocity of Rayleigh waves in a directional fiber-reinforced composite. ECCM15 - 15th European conference on composite materials, Venice, Italy, 24-28 June 2012
Vinh PC, Tuan TT, Capistran MA (2015) Explicit formulas for the reflection and transmission coefficients of one-component waves through a stack of an arbitrary number of layers. Wave Motion 54:134-144
Vinh PC, Anh VTN, Linh NTK (2016) On a technique for deriving the explicit secular equation of Rayleigh waves in an orthotropic half-space coated by an orthotropic layer. Waves Random Complex Media 26:176–188
Vinh PC, Tuan TT, Hue LT, Anh VTN, Dung TTT, Linh NTK, Malischewsky P (2019) Exact formula for the horizontal-to-vertical displacement ratio of Rayleigh waves in layered orthotropic half-spaces. J. Acoust Soc Am 146(2):1279–1289
Zheng T, Dravinski M (1998) Amplification of SH waves by an orthotropic basin. Earthq Eng Struct Dyn 27(3):243-257
Zheng T, Dravinski M (1999) Amplification of waves by an orthotropic basin: sagittal plane motion. Earthq Eng Struct Dyn 28(6):565–584