Abstract
Spatial derivatives of the seismic wave field are known to be sensitive to various site effects (e.g., cavity effects, topography, and geological inhomogeneities). In this study, the focus is on strain rotation coupling that can cause significant differences between point measurements compared to array-derived rotational motions. The strain rotation coupling constants are estimated based on finite element simulations for inhomogeneous media as well as for the 3D topography around Wettzell, Germany (the location of the G ring laser). Using collocated array and ring laser data, the coupling constants of the ring laser itself are shown to be small. Several examples are shown to illustrate the order of magnitude that strain-induced rotation might have on the seismograms in the near field of volcanoes as well as in the far field and in the low-frequency spectrum (free oscillations).
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References
Berger J, Beaumont C (1976) An analysis of tidal strain observations from the united states of america II. The inhomogeneous tide. Bull Seismol Soc Amer 66(6):1821
Bernauer F, Wassermann J, Igel H (2012) Rotational sensors—a comparison of different sensor types. J Seismol. doi:10.1007/s10950-012-9286-7
Beyreuther M, Barsch R, Krischer L, Megies T, Behr Y, Wassermann J (2010) ObsPy: a python toolbox for seismology. Seismol Res Lett 81(3):530–533. doi:10.1785/gssrl.81.3.530
Cochard A, Igel H, Schuberth B, Suryanto W, Velikoseltsev A, Schreiber U, Wassermann J, Scherbaum F, Vollmer D (2006) Rotational motions in seismology: theory, observation, simulation. In: Teisseyre R, Takeo M, Majewski E (eds) Earthquake source asymmetry, structural media and rotation effects. Springer, New York, pp 391–411
Dunn RW, Mahdi HH, Al-Shukri HJ (2009) Design of a relatively inexpensive ring laser seismic detector. Bull Seismol Soc Amer 99(2B):1437–1442. doi:10.1785/0120080092
Evans JR, Hutt CR, Nigbor RN, de la Torre T (2010) Performance of the new R2 Sensor—presentation at the 2nd IWGoRS meeting in Prague
Gerstenecker C, Läufer G, Snitil B, Wrobel B (1999) Digital elevation models for Merapi. DGG Special Issue
Gomberg J, Agnew D (1996) The accuracy of seismic estimates of dynamic strains: an evaluation using strainmeter and seismometer data from Pifion Flat Observatory, California. Bull Seismol Soc Amer 86(1):212–220
Graizer V (2009) Tutorial on measuring rotations using multipendulum systems. Bull Seismol Soc Amer 99(2B):1064–1072. doi:10.1785/0120080145
Graizer V (2010) Strong motion recordings and residual displacements: what are we actually recording in strong motion seismology? Seismol Res Lett 81(4):635–639. do10.1785/gssrl.81.4.635
Gross L, Bourgouin L, Hale A, Muhlhaus H (2007a) Interface modeling in incompressible media using level sets in Escript. Phys Earth Planet In 163(1-4):23–34. doi:10.1016/j.pepi.2007.04.004
Gross L, Cumming B, Steube K, Weatherley D (2007b) A Python module for PDE-based numerical modelling example: seismic wave propagation. In: Applied parallel computing. State of the Art in Scientific Computing, Springer, New York, pp 270–279. doi:10.1007/978-3-540-75755-9_33
Harrison JC (1976) Cavity and topographic effects in tilt and strain measurement. J Geophys Res 81(2):319–328
Igel H, Cochard A, Wassermann J, Flaws A, Schreiber U, Velikoseltsev A, Pham ND (2007) Broad-band observations of earthquake-induced rotational ground motions. Geophys J Int 168(1):182–196. doi:10.1111/j.1365-246X.2006.03146.x
Kohl ML, Levine J (1995) Measurement and interpretation of tidal tilts in a small array. J Geophys Res 100(B3):3929–3941. doi:10.1007/s11605-011-1421-1
Komatitsch D, Tromp J (2002a) Spectral-element simulations of global seismic wave propagation-I. Validation. Geophys J Int 149(2):390–412. doi:10.1046/j.1365-246X.2002.01653.x
Komatitsch D, Tromp J (2002b) Spectral-element simulations of global seismic wave propagation-II. Three-dimensional models, oceans, rotation and self-gravitation. Geophys J Int 150(1):303–318. doi:10.1046/j.1365-246X.2002.01716.x
Kurrle D, Igel H, Ferreira AMG, Wassermann J, Schreiber U (2010) Can we estimate local Love wave dispersion properties from collocated amplitude measurements of translations and rotations? Geophys Res Lett 37(4):1–5. doi:10.1029/2009GL042215
Lambotte S, Rivera L, Hinderer J (2006) Vertical and horizontal seismometric observations of tides. J Geodyn 41(1–3):39–58. doi:10.1016/j.jog.2005.08.021
Langston CA (2007a) Spatial gradient analysis for linear seismic arrays. Bull Seismol Soc Amer 97(1B):265–280. doi:10.1785/0120060100
Langston CA (2007b) Wave gradiometry in the time domain. Bull Seismol Soc Amer 97(3):926–933. doi:10.1785/0120060152
Langston CA (2007c) Wave gradiometry in two dimensions. Bull Seismol Soc Amer 97(2):401–416. doi:10.1785/0120060138
Lin CJ, Huang HP, Liu CC, Chiu HC (2010) Application of rotational sensors to correcting rotation-induced effects on accelerometers. Bull Seismol Soc Amer 100(2):585–597. doi:10.1785/0120090123
Maeda Y, Takeo M, Ohminato T (2011) A waveform inversion including tilt: method and simple tests. Geophys J Int 184(2):907–918. doi:10.1111/j.1365-246X.2010.04892.x
Masters G, Barmine M, Kientz S (2007) Mineos: user manual. Calif Inst Techbol, Pasadena
Megies T, Beyreuther M, Barsch R, Krischer L, Wassermann J (2011) ObsPy—what can it do for data centers and observatories? Ann Geophys 54(1). doi:10.4401/ag-4838
Mogi K (1958) Relations between the eruptions of various volcanoes and the deformations of the ground surface around them. Bull Earth Res Inst 36:99–134
Nader MF, Igel H, Ferreira AMG, Kurrle D, Wassermann J, Schreiber KU (2012) Toroidal free oscillations of the Earth observed by a ring laser system: a comparative study. J Seismol, this issue
Nigbor RL (1994) Six-degree-of-freedom ground-motion measurement. Bull Seismol Soc Amer 84(5):1665–1669
Nigbor RL, Evans JR, Hutt CR (2009) Laboratory and field testing of commercial rotational seismometers. Bull Seismol Soc Amer 99(2B):1215–1227. doi:10.1785/0120080247
Nolet G (2008) A breviary of seismic tomography: imaging the interior of the earth and sun. Cambridge University Press, Cambridge
Peter D, Komatitsch D, Luo Y, Martin R, Le Goff N, Casarotti E, Le Loher P, Magnoni F, Liu Q, Blitz C, Nissen-Meyer T, Basini P, Tromp J (2011) Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes. Geophys J Int 186(2):721–739. doi:10.1111/j.1365-246X.2011.05044.x
Pham ND, Igel H, Wassermann J, Käser M, de la Puente J, Schreiber U (2009) Observations and modeling of rotational signals in the P coda: constraints on crustal scattering. Bull Seismol Soc Amer 99(2B):1315–1332. doi:10.1785/0120080101
Schreiber U, Hautmann JN, Velikoseltsev A, Wassermann J, Igel H, Otero J, Vernon F, Wells JPR (2009) Ring laser measurements of ground rotations for seismology. Bull Seismol Soc Amer 99(2B):1190–1198. doi:10.1785/0120080171
Schreiber U, Velikoseltsev A, Igel H, Cochard A, Flaws A, Drewitz W, Müller F (2003) The GEOsensor: a new instrument for seismology. GEO-TECHNOLOGIEN Science Report 3, pp 12–13
Schreiber U, Stedman GE, Igel H, Flaws A (2006) Ring laser gyroscopes as rotation sensors for seismic wave studies. In: Teisseyre R, Takeo M, Majewski E (eds) Earthquake source asymmetry, structural media and rotation effects. Springer, New York
Spudich P, Fletcher JB (2008) Observation and prediction of dynamic ground strains, tilts, and torsions caused by the Mw 6.0 2004 Parkfield, California, earthquake and aftershocks, derived from UPSAR Array observations. Bull Seismol Soc Amer 98(4):1898–1914. doi:10.1785/0120070157
Spudich P, Fletcher JB (2009) Software for inference of dynamic ground strains and rotations and their errors from short baseline array observations of ground motions. Bull Seismol Soc Amer 99(2B):1480–1482. doi:10.1785/0120080230
Spudich P, Steck LK, Hellweg M, Fletcher JB, Baker LM (1995) Transient stresses at Parkfield, California, produced by the M 7.4 Landers earthquake of June 28, 1992: observations from the UPSAR dense seismograph array. J Geophys Res 100:675–675
Suryanto W, Igel H, Wassermann J, Cochard A, Schuberth B, Vollmer D, Scherbaum F, Schreiber U, Velikoseltsev A (2006) First comparison of array-derived rotational ground motions with direct ring laser measurements. Bull Seismol Soc Amer 96(6):2059–2071. doi:10.1785/0120060004
Wassermann J, Ohrnberger M (2001) Automatic hypocenter determination of volcano induced seismic transients based on wavefield coherence—an application to the 1998 eruption of Mt. Merapi, Indonesia. J Volcanol Geoth Res 110(1–2):57–77. doi:10.1016/S0377-0273(01)00200-1
Wassermann J, Lehndorfer S, Igel H, Schreiber U (2009) Performance test of a commercial rotational motions sensor. Bull Seismol Soc Amer 99(2B):1449–1456. doi:10.1785/0120080157
Wielandt E, Forbriger T (1999) Near-field seismic displacement and tilt associated with the explosive activity of Stromboli. Ann Geofisc 42(3):407–416
Yoon M (2005) Deep seismic imaging in the presence of a heterogeneous overburden—numerical modelling and case studies from the Central Andes and Southern Andes. Ph.D., Freie Universität Berlin. doi:10.1016/0926-9851(93)90007-L
Acknowledgements
This study was supported by the QUEST Initial Training Network (Marie Curie Actions, www.quest-itn.org) and DFG project Ig16-8. BSAS was supported by a Marie Curie Intra European Fellowship within the 7th European Community Framework Programme (FP7/2007-2013) under grant agreement nr. 235861. We thank the Leibniz Supercomputing Centre for access to computing resources. The manuscript benefited from the constructive comments of two anonymous reviewers.
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van Driel, M., Wassermann, J., Nader, M.F. et al. Strain rotation coupling and its implications on the measurement of rotational ground motions. J Seismol 16, 657–668 (2012). https://doi.org/10.1007/s10950-012-9296-5
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DOI: https://doi.org/10.1007/s10950-012-9296-5