Multiscale analysis of GPS velocity fields in the oblique collision zone of Arabia-Eurasia tectonic plates using spherical wavelet

Document Type : Research Article

Author

Department of Surveying, Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran.

Abstract

GPS velocity fields consist of a set of geodetic observations of displacement with an irregular spatial distribution on the sphere. In this study, multiscale analysis based on spherical wavelet is used to estimate the GPS velocity field in the oblique collision zone of Arabia-Eurasia tectonic plates. Multiscale velocity field estimation is well suited for dense geodetic networks and is straightforward to implement.
We show that for DOG wavelet a scale of 3 to 8 is suitable for GPS velocity field analysis in the study area. Estimation output can be used as a data layer in GIS analysis. Regularization is required to obtain a smooth estimated velocity field from the discrete observations. This is achieved through two possible actions. First, one can cull the set of possible spherical wavelets based on the coverage of observations. If each spherical wavelet has a sufficient number of observations constraining its coefficient, then no regularization is needed (λ = 0). Second, if all spherical wavelets are used for the inverse problem, then extensive regularization will be needed, since most wavelets will have zero observations for constraining their corresponding coefficients. In this research, we have chosen something in between these two extreme cases, where we at the outset eliminate many candidate spherical wavelets based on data coverage, but we still require a moderate amount of explicit regularization in the inversion.
As the adopted spherical wavelets are analytically differentiable, spatial gradient tensor quantities such as strain rate, dilatation rate and rotation rate can be directly computed using the same coefficients. The gradient quantities are then calculated directly from the estimated field to identify potential deformation signals. The first factor controlling the estimation is the distance between the network stations. Wherever stations are dense, short-scale spherical wavelets participate in the estimation; and where stations are sparse, only long-scale spherical wavelets is used to do the estimation. As we allow shorter length-scale frame functions to be used in estimating the velocity field, the residual field vectors decrease in magnitude. The smallest residuals occur at observation points that are dense enough to fall within the support of the smallest length-scale frame functions which also have the smallest estimated uncertainties in the data. The largest residuals overall are associated with the largest uncertainties in the data.
From the perspective of monitoring a GPS network, the residual map may be helpful in detecting spurious behaviour of singles at stations. If unusual strain, dilation, or rotation are observed around a station, such an observation would warrant additional analysis of the GPS time-series and error estimate. We remove a rotational field from the observation set to obtain the velocity field. We then estimate the horizontal velocity field. Once we have estimated the multiscale velocity field, we can readily compute other scalar quantities, such as dilatation, strain and rotation. The high density of stations near the fault system could capture the spatial gradient in the velocity field, and give rise to estimate strain-rates with a maximum of 1.410×10-7, an average of 1.786×10-8 and a standard deviation of 1.626×10-8 per year. The dilation rate is obtained with a maximum of -8.684×10-8, an average of -3.487×10-9 and a standard deviation of 1.144×10-8 per year and the rotation rate is obtained with a maximum of 7.771×10-8, an average of 7.720×10-9 and a standard deviation of 7.040×10-9 radians per year in the study area.
Due to the shorter distance of observation stations in the southern part of central Alborz and northwestern Iran, the values of strain, dilatation and rotation rate can be observed in these areas on large scales.
In multiscale estimation, the residual field between the original field and estimated field may reveal two key features. First, if there are systematic residuals in a particular region, then it is probable that one needs to include shorter-scale wavelets in the estimation. Second, if there is a strong residual at a single station, then the station is anomalous and is either malfunctioning or is capturing a signal that is not spatially resolved. The advantages of the multiscale approach are its ability to localize the deformation field in space and scale, as well as its ability to identify outliers in the set of observations. This approach can also locally match the smallest process obtained with the local density of observations, thus maximizing both the amount of information extracted and the possibility of comparing the resulting quantities in different regions of a scale. Multiscale estimation of the three-dimensional GPS velocity field is also possible using spherical wavelet frame functions. The vertical component, if any, should be used to estimate the velocity field, as deformation may not be predominant in horizontal directions. This formulation may be easily applied either regionally or globally and is ideally suited as the spatial parametrization used in any automatic time-dependent geodetic transient detector.

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References

راست‌بود، ا. (1402الف). تغییرشکل‌های معاصر پوسته ای در منطقه البرز بر اساس میدان سرعت GPS و توابع اسپلاین. مجله ژئوفیزیک ایران، 17(1)، 1-19.
راست‌بود، ا. (1402ب). تحلیل تغییر شکل قارهای زمان حاضر در محدوده فلات ایران با استفاده از تانسور کرنش مستخرج از مشاهدات دائم و دورهای GPS. مجله فیزیک زمین و فضا، 49(1)، 97-117.
راست­بود، ا.، و وثوقی، ب. (1389). بررسی تغییرشکل بین­لرزه­ای در ناحیه برخورد صفحه­های زمین­ساختی عربستان و اوراسیا در منطقه خاورمیانه با استفاده از یک مدل تحلیلی. مجله ژئوفیزیک ایران، 4(2)، 89-102.
Antoine, J.P., & Vandergheynst, P. (1999). Wavelets on the 2-sphere: a group-theoretical approach, Appl. Comput. Harmonic Anal., 7(3), 262–291.
Argus, D.F., Heflin, M.B., Peltzer, G., Crampe, F., & Webb, F.H. (2005). Interseismic strain accumulation and anthropogenic motion in metropolitan Los Angeles. J. geophys. Res., 110, B04401, doi:10.1029/2003JB002934.
Bayer, M., Freeden, W., & Maier, T. (2001). A vector wavelet approach to iono- and magnetospheric geomagnetic satellite data. J. Atmos. Solar-Terr. Phys., 63, 581–597.
Beavan, J., & Haines, J. (2001). Contemporary horizontal velocity and strain rate fields of the Pacific-Australian plate boundary zone through New Zealand. J. geophys. Res., 106(B1), 741– 770.
Becker, T.W., Hardebeck, J.L., & Anderson, G. (2005). Constraints on fault slip rates of the southern California plate boundary from GPS velocity and stress inversions. Geophys. J. Int., 160, 634–650.
Bogdanova, I., Vandergheynst, P., Antoine, J.R., Jacques, L., & Morvidone, M. (2005). Stereographic wavelet frames on the sphere. Appl. Comput. Harmonic Anal., 19(2), 223–252.
Bos, A.G., Spakman, W., & Nyst, M.C.J. (2003). Surface deformation and tectonic setting of Taiwan inferred from a GPS velocity field. J. geophys. Res., 108(B10), 2458, doi:10.1029/2002JB002336.
Chambodut, A., Panet, I., Mandea, M., Diament, M., Holschneider, M., & Jamet, O. (2005). Wavelet frames: an alternative to spherical harmonic representation of potential fields. Geophys. J. Int., 163(3), 875–899.
Dahlke, S., & Maass, P. (1996). Continuous wavelet transforms with applications to analyzing functions on spheres. J. Fourier Anal. Appl., 2(4), 379–396.
Dragert, H., Wang, K., & James, T.S. (2001). A silent slip event on the deeper Cascadia subduction interface. Science, 292, 1525–1528.
Feigl, K.L., King, R.W., & Jordan, T.H. (1990). Geodetic measurement of tectonic deformation in the Santa Maria fold and thrust belt, California. J. geophys. Res., 95(B3), 2679–2699.
Freeden, W., & Windheuser, U. (1996). Spherical wavelet transform and its discretization. Adv. Comput. Math., 5(1), 51–94.
Freeden, W., & Windheuser, U. (1997). Combined spherical harmonic and wavelet expansion—a future concept in earth’s gravitational potential determination. Appl. Comput. Harmonic Anal., 4, 1–37.
Frohling, E., & Szeliga, W. (2016). GPS constraints on interpolate locking within Makran subduction zone. Geophys. J. Int., 205, 67–76.
Ghods A., Shabanian E., Bergman E., Faridi M., Donner S., Mortezanejad G., & Aziz-Zanjani A. (2015). The Varzaghan–Ahar, Iran, Earthquake Doublet (Mw 6.4, 6.2): implications for the geodynamics of northwest Iran. Geophys. J. Int., 203, 522–540.
Guilloux, F., Fay, G., & Cardoso, J.-F. (2009). Practical wavelet design on the sphere, Appl. Comput. Harmonic Anal., 26(2), 143–160.
Haines, A.J., & Holt, W.E. (1993). A procedure for obtaining the complete horizontal motions within zones of distributed deformation from the inversion of strain rate data. J. geophys. Res., 98(B7), 12 057–12 082.
Hastie, T., & Loader, C. (1993). Local regression: automatic kernel carpentry. Stat. Sci., 8(2), 120–143.
Heki, K. (1997). Silent fault slip following an interplate thrust earthquake at the Japan Trench. Nature, 386, 595–598.
Hessami, K., Jamali, F., & Tabassi, H. (2003). Major Active Faults of Iran (map), Ministry of Science, Research and Technology, International Institute of Earthquake Engineering and Seismology.
Holschneider, M. (1996). Continuous wavelet transforms on the sphere. J. Math. Phys., 37(8), 4156–4165.
Holschneider, M., Chambodut, A., & Mandea, M. (2003). From global to regional analysis of the magnetic field on the sphere using wavelet frames. Phys. Earth planet. Inter., 135, 107–124.
Hsu, Y.-J., Yu, S.-B., Simons, M., Kuo, L.-C., & Chen, H.-Y. (2009). Interseismic crustal deformation in the Taiwan plate boundary zone revealed by GPS observations, seismicity, and earthquake focal mechanisms, Tectonophysics, in press.
Khorrami F., Vernant P., Masson F., Nilfouroushan F., Mousavi Z., Nankali H., Saadat S. A., Walpersdorf A., Hosseini S., Tavakoli P., Aghamohammadi A., & Alijanzade M. (2019). An up-to-date crustal deformation map of Iran using integrated campaign-mode and permanent GPS velocities. Geophys. J. Int., 217, 832–843.
Kovacevic, J., & Chebira, A. (2007a). Life beyond bases: the advent of frames (Part I). IEEE Signal Process. Mag., 24(4), 86–104.
Kovacevic, J., & Chebira, A. (2007b). Life beyond bases: the advent of frames (Part II). IEEE Signal Process. Mag., 24(5), 115–125.
Malvern, L.E., (1969). Introduction to the mechanics of a continuous medium, Prentice-Hall, Upper Saddle River, NJ, USA, ISBN: 0134876032.
Masson, F., Lehujeur, M., Ziegler Y., & Doubre, C. (2014). Strain rate tensor in Iran from a new GPS velocity field. Geophys. J. Int., 197(1), 10-21, doi:10.1093/gji/ggt509.
Matheron, G. (1963). Principles of geostatistics, Econ. Geol., 58, 146–1266. McCaffrey, R. et al., 2007. Fault locking, block rotation and crustal deformation in the Pacific Northwest. Geophys. J. Int., 169, 1315–1340.
McCaffrey, R., Qamar, A. I., King, R. W., Wells, R., Khazaradze, G., Williams, C. A., Stevens, C. W., Vollick, J. J., & Zwick, P. C. (2007). Fault locking, block rotation and crustal deformation in the Pacific Northwest. Geophys. J. Int., 169, 1315–1340.
McGuire, J.J., & Segall, P. (2003). Imaging of aseismic fault slip transients recorded by dense geodetic networks. Geophys. J. Int., 155, 778–788.
Meade, B.J., & Hager, B.H. (2005). Block models of crustal motion in southern California constrained by GPS measurements. J. geophys. Res., 110, B03403, doi:10.1029/2004JB003209.
Meade, B.J., Hager, B.H., McClusky, S.C., Reilinger, R.E., Ergintav, S., Lenk, O., Barka, A., & Ozener, H. (2002). Estimates of seismic potential in the Marmara Sea region from block models of secular deformation constrained by Global Positioning System measurements. Bull. seism. Soc. Am., 92, 208–215.
Melbourne, T.I., Webb, F.H., Stock, J.M., & Reigber, C. (2002). Rapid postseismic transients in subduction zones from continuous GPS. J. geophys. Res., 107(B10), 2241, doi:10.1029/2001JB000555.
Menke, W. (1989). Geophysical Data Analysis: Discrete Inverse Theory. Academic Press, San Diego, CA, USA, ISBN: 0124909213,9780124909212,0124909205,9780124909205,9780080507323.
Miyazaki, S., McGuire, J.J., & Segall, P. (2003). A transient subduction zone slip episode in southwest Japan observed by the nationwide GPS array. J. geophys. Res., 108(B2), 2087, doi:10.1029/2001JB000456.
Miyazaki, S., Segall, P., Fukuda, J., & Kato, T. (2004). Space time distribution of afterslip following the 2003 Tokachi-oki earthquake: Implications for variations in fault zone frictional properties. Geophys. Res. Lett., 31, L06623, doi:10.1029/2003GL019410.
Oh, H.-S., & Li, T.-H. (2004). Estimation of global temperature fields from scattered observations by a spherical-wavelet-based spatially adaptive method. J. R. Statist. Soc. B, 66, 221–238.
Ozawa, S., Murakami, M., Kaidzu, M., Tada, T., Sagiya, T., Hatanaka, Y., Yarai, H., & Nishimura, T. (2002). Detection and monitoring of the ongoing aseismic slip in the Tokai region, Central Japan. Science, 298, 1009– 1012.
Pritchard, M.E., & Simons, M. (2006). An aseismic slip pulse in northern Chile and along-strike variations in seismogenic behavior. J. geophys. Res., 111, B08405, doi:10.1029/2006JB0042580.
Raeesi, M., Zarifi, Z., Nilfouroushan, F., Boroujeni S., & Tiampo, K. (2017). Quantitative Analysis of Seismicity in Iran. Pure Appl. Geophys., 174, 793-833.
Reguzzoni, M., Sanso, F., & Venuti, G. (2005). The theory of general kriging, with applications to the determination of a local geoid. Geophys. J. Int., 162, 303–314.
Reilinger, R., McClusky, S., Vernant, P., Lawrence, S., Ergintav, S., Cakmak, R., Ozener, H., Kadirov, F., Guliev, I., Stepanyan, R., Nadariya, M., Hahubia, G., Mahmoud, S., Sakr, K., Arajehi, A., Paradissis, D., Al-Aydrus, A., Prilepin, M., Guseva, T., Evren, E., Dmitrotsa, A., Filikov, S. V., Gomez, F., Al-Ghazzi, R., & Karam, G. (2006). GPS constraints on continental deformation in the Africa–Arabia–Eurasia continental collision zone and implications for the dynamics of plate interactions. J. geophys. Res., 111, doi:10.1029/2005JB004051.
Rogers, G., & Dragert, H. (2003). Episodic tremor and slip on the Cascadia subduction zone: The chatter of silent slip. Science, 300, 1942– 1943.
Savage, J.C., & Prescott, W.H. (1976). Strain accumulation on the San Jacinto fault near Riverside, California. Bull. seism. Soc. Am., 66(5), 1749– 1754.
Shen, Z.-K., Jackson, D.D., & Ge, B.X. (1996). Crustal deformation across and beyond the Los Angeles basin from geodetic measurements. J. geophys. Res., 101(B12), 27 957–27 980.
Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis, Vol. 26 of Monographs on Statistics and Applied Probability, Chapman and Hall, New York.
Simons, F.J., Dahlen, F.A., & Wieczorek, M.A. (2006). Spatiospectral concentration on a sphere. SIAM Rev., 48(3), 504–536.
Simons, M., & Hager, B.H. (1997). Localization of the gravity field and the signature of glacial rebound. Nature, 390, 500–504.
Simons, M., Solomon, S.C., & Hager, B.H. (1997). Localization of gravity and topography: constraints on the tectonics and mantle dynamics of Venus. Geophys. J. Int., 131, 24–44.
Spakman, W., & Nyst, M.C.J. (2002). Inversion of relative motion data for estimates of the velocity gradient field and fault slip. Earth planet. Sci. Lett., 203, 577–591.
Talebian, M., Ghorashi, M., & Nazari, H. (2013). Seismotectonic map of the Central Alborz, Research Institute for Earth Sciences, Geological Survey of Iran.
Tape, C., Muse, P., Simons, M., Dong, D., & Webb F. (2009). Multiscale estimation of GPS velocity fields. Geophys. J. Int. (2009) 179, 945–971.
Tarantola, A. (2005). Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM, Philadelphia, PA, USA, ISBN: 9780898715729,0898715725.
Teza, G., Pesci, A., & Galgaro, A. (2008). Grid strain and grid strain3: software packages for strain field computation in 2D and 3D environments. Comput. Geosci., 34(9), 1142–1153.
Unser, M. (2014). Wavelets: on the virtues and applications of the mathematical microscope. Journal of Microscopy, 255(3), 123-127.
Vernant, P., & Chéry, J. (2006). Low Fault Friction in Iran Implies Localized Deformation for the Arabia-Eurasia Collision Zone. Earth and Planetary Science Letters, 246(3-4): 197-206.
Wahba, G. (1981). Spline interpolation and smoothing on the sphere. SIAM J. Sci. Stat. Comp., 2(1), 5–16.
Walcott, R.I. (1973). Structure of the earth from glacio-isostatic rebound. Annu. Rev. Earth planet. Sci., 1, 15–37.
Wang, Z., & Dahlen, F.A. (1995). Spherical-spline parameterization of three-dimensional Earth. Geophys. Res. Lett., 22, 3099–3102.
Ward, S.N. (1998a). On the consistency of earthquake moment release and space geodetic strain rates: Europe. Geophys. J. Int., 135, 1011–1018.
Ward, S.N. (1998b). On the consistency of earthquake moment rates, geological fault data, and space geodetic strain: the United States. Geophys. J. Int., 134, 172–186.
Wiaux, Y., Jacques, L., & Vandergheynst, P. (2005). Correspondence principle between spherical and Euclidean wavelets. Astrophys. J., 632(1), 15–28.
Journal of the Earth and Space Physics
Volume 49, Issue 3
online publication date: 15 Nov 2023
November 2023
Pages 541-565

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