On the rotation of teleseismic seismograms based on the receiver function technique
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The receiver function (RF) technique is a well-established method to investigate the crustal and upper mantle structures based on three-component seismograms of teleseismic events. In the present study, we propose a modified automatic procedure to determine the back azimuth and polarization angles of a teleseismic event based on the RF technique. The method is tested for the recording of 3 permanent and 3 temporary broadband seismic stations located in the vicinity of Poland. Additionally, the analysis of Rayleigh wave polarization is conducted to show that the new procedure is not sensitive to incorrect seismometer orientation. The synthetic modelling of RF by a modified ray-tracing method for 2.5D models beneath each seismic station down to a depth of 60 km is performed to show the effectiveness of the proposed method in the calculation of RF for a complex structure with dipping layers.
KeywordsSeismic structure Wave polarization Sensor orientation Automatic procedure
The receiver function (RF) technique is a well-established method to investigate the crustal and upper mantle structures based on three-component seismograms of teleseismic events (Langston 1977a; Vinnik 1977). Locally, RF provides the signature of sharp seismic discontinuities and information about the shear-wave (S-wave) velocity distribution beneath the seismic station. The initial data are broadband seismograms of teleseismic waves rotated into vertical, radial and tangential (Z, R, T) components or into a ray-parameter coordinate system (L, Q, T). After the deconvolution of the vertical component (Z or L) of the seismogram from the horizontal components (R, T or Q, T), the source, instrument and ray-path effects are removed from the seismogram. In the case of a stack of homogeneous horizontal layers, the RF is a simple scaled version of the radial component of the seismogram with the P multiples removed (Ammon 1991). Until now, researchers have focused on deconvolution methods and further interpretation and modelling of RF. Because many authors use the radial (RFR or RFQ) and tangential receiver function (RFT) for mapping dipping discontinuities and seismic anisotropy (Cassidy 1992; Zhu et al. 1995; Frederiksen and Bostock 2000; Bianchi et al. 2010), a proper rotation of seismograms is very important, especially in areas of complex structure. A modified automatic procedure for the determination of the back azimuth and polarization angles of teleseismic events based on the RF technique is proposed and tested for broadband permanent and temporary seismic stations. Additionally, three confidence testing is performed. First, the proposed procedure is tested for two simple models, one-layered and two-layered (with thin sediments), for which synthetic RFs are calculated by the reflectivity method (e.g. Kennett 1983). Second, an analysis of Rayleigh wave polarization is done following the method of Stachnik et al. (2012) to show that the new procedure is not sensitive to incorrect seismometer orientation. Third, synthetic modelling of RF by a modified ray-tracing method for 2.5D models beneath each seismic station down to a depth of 60 km is performed and compared with the observed back azimuth sections of RF of the presented stations.
2 Tectonic settings and data
Location of seismic stations and time range of the used data set for receiver function analysis, along with the calculated orientation of the sensors
Data for analysis
Number of stacked events
Orientation of station [o]
August 2006–July 2008
39 ± 2
45 ± 4
August 2006–July 2008
3 ± 1
11 ± 4
August 2006–October 2007
−3 ± 3
0 ± 5
August 2006–July 2008
−21 ± 1
−16 ± 4
August 2006–June 2008
−1 ± 2
5 ± 5
August 2006–January 2008
9 ± 1
10 ± 3
3 Rotation of seismograms
Some researchers, e.g. Owens et al. (1984), calculate RF from seismograms rotated into vertical (Z), radial (R), and tangential (T) components; while others, e.g. Kind et al. (1995), use a ray-coordinates system (L, Q, T). The first approach is a one-step procedure; a back azimuth angle has to be defined to rotate the N and E components of the seismograms into R and T components. The second approach is a two-step procedure: first, a back azimuth angle is defined to rotate the N and E components into R and T; next, a polarization angle is defined to rotate the Z and R components into L and Q.
Generally, in receiver function techniques, a back azimuth angle between the north direction and a great path from the seismic station to the source of the recorded event are calculated from the known coordinates of the seismic station and the coordinates of the source taken from seismic bulletins. If we assume that a seismic sensor is properly installed, or the deviation of its orientation from true north is known, and a structure beneath a seismic station does not cause an azimuthal change of the propagation direction of waves, RF gives us a good approximation of the impulse response of the structure beneath the seismic station (Ammon 1991). Unfortunately, the seismic structure of the Earth is complex, and it often happens that the orientation of the seismometer is not precisely measured, or is unknown for ocean bottom seismometers. An incorrect choice of rotation angle will result in a wrong distribution of seismic energy between the components of RF. The orientation of seismometers can be verified by the analysis of Rayleigh wave polarization (Stachnik et al. 2012), which is not sensitive to local structure. A polarization of seismic waves can be found by the analysis of particle motion diagrams, the cross-correlation method, the smallest eigenvalue minimization method or minimizing/maximizing the energy of the components of the seismograms. These methods are more sensitive to the signal-to-noise ratio of the recorded signal because of the presence of source time functions in seismograms.
3.1 Back azimuth angle
3.2 Polarization angle
A polarization angle can be found by maximizing/minimizing the energy on the Q and T components of the seismograms of the direct P-wave or by measuring the amplitudes of the direct P-wave on the RFR (Saul et al. 2000). In the present study, we propose to estimate a polarization angle based on RFQ components. The Z, R and T components of seismograms are filtered with a band-pass Butterworth filter of corner periods 2 and 10 s and rotated into L, Q and T components with polarization angles from 0o to 45o; every 1o, RFQs are calculated. Then, the RFQs were cut 5 s before and 5 s after the direct P-wave, and a mean value and a linear trend were removed to emphasize the relative change of the shape of RFQ around time 0 s. Next, two values are calculated for each RFQ: (a) the root mean square for the time window between −2 and 0 s, to measure seismic energy, and (b) the sum of the negative amplitudes for the same time window. For a theoretical RFQ, the amplitude of the direct P-wave at time 0 s should be zero and no negative amplitude should be observed before time 0 s. The optimal polarization angle is determined when a difference of the value of the (b) parameters for successive polarization angles (starting from 0o) becomes negative and its absolute value increases until the (a) value reaches minimum (it is close to zero). Figure 3b shows the above-described procedure for the seismograms from Fig. 2 for the KSP and PG42 stations. For the KSP station, the difference of the (b) parameters becomes negative at an angle of 21o, so the optimal value of the polarization angle is 18o; while for PG42 it is 0o. Minimizing the (a) parameter only is not an optimal procedure because of the presence of noise in real data. Also, it does not work in the case of a seismic structure with thin sedimentary layers, as is the case for the PG42 station, because at time 0 s, part of the energy of the P-to-S-wave from shallow discontinuities is present at RFQ. The polarization angle found in this way can be used later for the standard procedure of calculation of RFQ for the station-event pair (Fig. 4 for the KSP and PG42 stations and Fig. S2 in the electronic supplement for all stations).
4 Receiver function
5 Confidence testing
Parameters of simple flat models used for testing the RF-rotation procedure
The RF-rotation method is automatic and effective and can be used to find the back azimuth and polarization angles of a teleseismic event recorded by permanent and temporary broadband seismic stations. In the present study, the stations are located in the Paleozoic platform deformed by Variscan orogeny (KSP, PG42), in the area of a thick sedimentary basin in TESZ (GKP, PQ47), and in the East European Craton with thin sedimentary cover and a strong contrast of seismic velocities between sediments and crystalline crust (SUW, PA73). The latter area particularly causes problems with RF calculation because of the existence of a strong reverberation of waves just beneath the seismic station. The recordings of the temporary stations are also usually strongly affected by the near-surface structure. The presented method of rotation of teleseismic seismograms based on the RF technique shows its ability to deal with such issues. Additionally, the method is not sensitive to misorientation of the seismic sensor, which is very valuable in the case of temporary campaigns. Based on the presented method, it is possible to find a sensor orientation of land and ocean seismometers (if vertical orientation is fixed, and if not, the three dimensional grid search of parameters is necessary). The sensor orientation found by the RF-rotation method is confirmed by the Rayleigh wave polarization and is previously found by SKS wave analysis.
Seismograms of permanent seismic stations of the Polish Seismic Network can be obtained from the GFZ Seismological Data Archive. Seismograms of the temporary seismic stations were collected as part of the PASSEQ 2006–2008 experiment and can be obtained from the GFZ Seismological Data Archive (Wilde-Piórko et al. 2006). Plots were made using the Generic Mapping Tools version 4.5.0 (Wessel and Smith 1998) and AH++ package (Saul 1997). The calculation of RF was performed by the Seismic Handler software package (Stammler 1993). National Science Centre Poland provided financial support for this work by NCN grant DEC-2011/02/A/ST10/00284.
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