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Strain rotation coupling and its implications on the measurement of rotational ground motions

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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

    Google Scholar 

  • Bernauer F, Wassermann J, Igel H (2012) Rotational sensors—a comparison of different sensor types. J Seismol. doi:10.1007/s10950-012-9286-7

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Chapter  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Graizer V (2009) Tutorial on measuring rotations using multipendulum systems. Bull Seismol Soc Amer 99(2B):1064–1072. doi:10.1785/0120080145

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Chapter  Google Scholar 

  • Harrison JC (1976) Cavity and topographic effects in tilt and strain measurement. J Geophys Res 81(2):319–328

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Langston CA (2007a) Spatial gradient analysis for linear seismic arrays. Bull Seismol Soc Amer 97(1B):265–280. doi:10.1785/0120060100

    Article  Google Scholar 

  • Langston CA (2007b) Wave gradiometry in the time domain. Bull Seismol Soc Amer 97(3):926–933. doi:10.1785/0120060152

    Article  Google Scholar 

  • Langston CA (2007c) Wave gradiometry in two dimensions. Bull Seismol Soc Amer 97(2):401–416. doi:10.1785/0120060138

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Masters G, Barmine M, Kientz S (2007) Mineos: user manual. Calif Inst Techbol, Pasadena

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Nolet G (2008) A breviary of seismic tomography: imaging the interior of the earth and sun. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Wielandt E, Forbriger T (1999) Near-field seismic displacement and tilt associated with the explosive activity of Stromboli. Ann Geofisc 42(3):407–416

    Google Scholar 

  • 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

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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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Correspondence to Martin van Driel.

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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

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