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Songlin Li, Xiaoling Lai, Yi Sun, Qi Miao. Calculation of Ground Rotational Motions Using Seismic Array Data. Journal of Earth Science, 2012, 23(2): 173-179. doi: 10.1007/s12583-012-0242-9
Citation: Songlin Li, Xiaoling Lai, Yi Sun, Qi Miao. Calculation of Ground Rotational Motions Using Seismic Array Data. Journal of Earth Science, 2012, 23(2): 173-179. doi: 10.1007/s12583-012-0242-9

Calculation of Ground Rotational Motions Using Seismic Array Data

doi: 10.1007/s12583-012-0242-9
Funds:

the National Natural Science Foundation of China 90814001

the National Natural Science Foundation of China 40974053

the National Natural Science Foundation of China 41074069

More Information
  • Corresponding author: Songlin Li, slli-cea@163.com
  • Received Date: 30 May 2011
  • Accepted Date: 29 Sep 2011
  • Publish Date: 01 Apr 2012
  • This article gives a description of our first study on ground rotational motion and its preliminary results. The ground rotational motions around vertical axis were obtained using near-field translational records of a temporal seismic array with observational distances of 1.8 to 2.7 km. The sources used are explosions with explosive of 500 kg for each. Ground rotational velocities were calculated using the space derivatives of the horizontal components of translational velocities from the array. The peak ground rotational velocities (PGRV) are approximately 30 to 57 μrad/s. Our results are very close to those from Wassermann et al. (2009), who used both a seismic array and a rotational sensor to record an explosion in Germany and obtained PGRV values of about 50 μrad/s. Their explosives are 150 kg, only one third of ours, but their observational distance is 250 m, much less than ours.

     

  • To describe the motion of a point on the ground completely, besides three translational components, three rotational components are also required. Furthermore, six strain components should be also added if deformations of the earth media are taken into consideration. However, for quite a long time, observations of traditional seismology are mainly limited to three translational motions. One reason is the limitation of observational technique, because it is more difficult to observe rotational motions than to observe translational ones. Another important reason is the widespread belief that rotational motions are very weak. However, a lot of examples show that rotational motions generated by strong earthquakes play important roles in destructions of buildings. Rotations of chimneys, monuments, and gravestones with respect to their bases were found at many strong earthquake sites (Kozák, 2009). Thus, to understand the destructive mechanism of earthquakes, it is necessary to study the rotational motions. Furthermore, rotational motions are closely related to the fractured process of earthquake sources and thus carry valuable information related to the dynamic parameters and characters of seismic sources (Knopoff and Chen, 2009).

    In recent years, scientists gradually recognize the importance of rotational motions generated by earthquakes and pay attention to their observations and studies. A special branch in seismology was set up by the name of Rotational Seismology. In 2006, with suggestions of Evans and Lee, the International Working Group on Rotational Seismology (IWGoRS) was organized to promote investigations of rotational motions and their implications and to share experience, data, software, and results (Todorovska et al., 2008). Then, in 2007, the first International Workshop on Rotational Seismology and Engineering Applications was held in Menlo Park, California (Lee et al., 2009a).

    Rotational motions can be observed directly using rotational sensors or be inferred by indirect method, which usually uses records from an array of translational sensors (Lee et al., 2009a). Using both direct and indirect methods, seismologists of Taiwan have done a lot of studies on rotational seismology and obtained many significant results (Lee et al., 2009b; Lin et al., 2009; Liu et al., 2009). By comparison, studies on this field in mainland China are just at the beginning and need to be enhanced. Cai and Fu (2009) did some experiments in the manufacture of rotational seismograph. As an initial experiment, we used the indirect method to study rotational motions generated by explosive sources. The advantage of explosive sources is that near-field seismic records can be obtained easily by temporal seismic arrays. This article gives a brief description of our work and preliminary results.

    To describe the motion of a rigid body, three-component translational (Tx, Ty, and Tz) and three-component rotational motions (θx, θy, and θz), as shown in Fig. 1, are required. For a deformed body, six-component strains are also required. According to Cochard et al. (2006), displacement u of a point x is related to its neighboring point x+δx by the equation

    (1)
    Figure  1.  Definition of motions with six degrees of freedom.

    where ϵ is the strain tensor and

    (2)

    is a pseudovector representing the angle of rigid rotation due to the disturbance. Considering that the z component of stress tensor is zero at the free surface, the three components of rotation about the x axis, y axis, and z axis are

    (3)

    (4)

    Using equations (3) and (4), rotational ground motions can be obtained by spatial gradients of translational ground motions from an array (Huang, 2003; Spudich et al., 1995). These translational motions can be acceleration, velocity, and displacement. The calrotation ØZ, i.e., rotational motion in horizontal plane, which is easily observed in strong earthquake site.

    To study ground rotational motions, records of active seismic sources would be an ideal choice. By scheduled explosions and a temporary array, near-field records can be obtained very quickly and easily. The data used are from our project, Experiment on Active Fault Exploration in Urban Area. In that project, three shots with charge of 500 kg explosives for each were fired at the southern part of North China plain in 2006, and their signals were received by temporary arrays with digital translational seismographs (Fig. 2). The seismographs used are our DAS-3 3-component velocity instruments with sampling rate of 200/s.

    Figure  2.  Position map of shot points and arrays.

    By comparison, the distances from Array A to shots SP1 and SP2 are smaller and the corresponding near-field records are suitable to our study on rotational motions. The distances from the array center to SP1 and SP2 are 2.7 and 1.8 km, respectively. Besides receiving distance, station spacing is an important factor we need to consider. As seismic waves from explosions have more high-frequency contents than those from typical earthquakes, the station spacing should be small enough and thus allows us to study the variations of ground translation motions in tens of meters scale rather than the traditional kilometer scale. Thus, we selected four stations (S51–S54) for calculation. As shown in Fig. 3, stations S51 and S52 are in NS direction and stations S52 to S54 are in EW direction, with station spaces of 60 and 30 m, respectively. The surface of the region is quite flat, and all the shot points and stations can be regarded as in a same horizontal plane.

    Figure  3.  Stations used for this experiment. (a) Stations of array A; (b) stations in the small rectangular.

    According to Spudich and Fletcher (2008), the station spacing h and wavelength λ should satisfy relation

    (5)

    Thus, for S wave velocity c=2.4 km/s and h=60 m, fmax should be 10 Hz. Therefore, we band-pass filtered our records from 0.3 to 10 Hz.

    As a preliminary study, we only calculated the vertical component of rotation using equation (4). The simplest method to approximate the derivatives of the horizontal components of motion is to subtract two recordings of ground displacement (velocities and acceleration) and divide by their distance. This can be done especially when the points are distributed regularly (Huang, 2003).

    As shown in Fig. 3, data from four stations were used for calculations. In order to compare and check the results directly and easily, we combined these stations into two groups so that we could get two results for each shot. Group one (G1) includes S51, S52, and S53, and Group two (G2) includes S51, S52, and S54. As our instruments are velocity seismography, what we obtained using (4) were angular velocities around Z axis. Then, angular displacements were obtained by integral operations. Figures 4 and 5 show the results of angular velocities for SP1 and SP2, respectively. Figure 6 gives the corresponding results of angular displacements by integrals. From Figs. 4 and 5, we can see that two results from a same shot are similar in waveforms, and their cross-correlation coefficients are all near 0.7.

    Figure  4.  Seismic records and rotational velocities obtained from SP1. (a) Translational records of Group 1; (b) translational records of Group 2; (c) rotational velocity of Group 1 (10-5 rad/s); (d) rotational velocity of Group 2 (10-5 rad/s).
    Figure  5.  Seismic records and rotational velocities obtained from SP2. The meanings of four parts are same as Fig. 4.
    Figure  6.  Rotational displacements obtained by integrations of rotational velocities. (a) Result of Group 1 from SP1 (10-6 rad); (b) result of Group 1 from SP2 (10-6 rad); (c) result of Group 2 from SP1 (10-7 rad); (d) result of Group 2 from SP2 (10-6 rad).

    The peak ground rotational velocity (PGRV) values and the peak ground rotational displacement (PGRD) values for these two shots are given in Tables 1 and 2, respectively. The PGRVs of these two shots are very close with approximate values of 30 to 57 μrad/s.

    Table  1.  Values of PGRV (μrad/s)
     | Show Table
    DownLoad: CSV
    Table  2.  Values of PGRD (μrad)
     | Show Table
    DownLoad: CSV

    For these two shots, explosives are same and the receiving distances are slightly different. For G2, the PGRV and PGRD values from SP1 are slightly smaller than those from SP2. That is natural because the receiving distances from SP1 are larger than those from SP2. However, for G1, the results are just opposite. The PGRV and PGRD values from SP1 are even larger than those from SP2, although just slightly larger. It seems that the difference in receiving distances does not produce strong influences on the results.

    To some extent, the results are influenced by station group used. The results from G1 are about 1.2 to 1.9 times of those from G2. Two groups all consist of three stations, and all include S51 and S52. The only difference between two groups is that S53 is used for G1 and S54 is used for G2. Therefore, these two groups represent two triangles with different shapes and different areas. Their results reflect the average rotational effects of the corresponding triangles. Some local factors, such as lateral heterogeneities in small scale, anisotropic structures near subsurface may affect the seismic records and thus produce different results for two groups. Therefore, we need to choose the array site carefully in future observation to avoid these unfavorable factors.

    To calculate rotation using equation 4, we need at least three stations. In general, the more stations are used, and the more reliable results will be obtained (Spudich and Fletcher, 2008; Spudich et al., 1995). Usually, 5 to 11 stations are involved and the symmetric distribution pattern is used. Of course, the station spacing should satisfy equation 5. One typical example is the experiment by Lin et al. (2009). Due to limitation of our observational system, in this experiment, we could only use three stations for each group.

    The accuracy of array-derived rotation rate is also strongly dependent on the quality of the recorded translational seismograms. Errors in individual station observations play a very important role, particularly when calculating spatial derivatives. Besides background noise, uncertainties in the seismometer response may produce strong effects on the values of spatial derivatives. Another important factor is the number of stations involved in the calculation of velocity gradient. Reliability will increase with the station number.

    Our results are very close to those from Wassermann et al. (2009), who used both a seismic array and a rotational sensor to record an explosion in Germany and obtain a PGRV value of about 50 μrad/s. Their explosives were 150 kg, only one third of ours, and were fired sequentially, but their observational distance is 250 m, much less than ours. In TIGER experiment, for a shot with explosives of 750 kg and receiving distance of 500 m, the PGRV values calculated by Lin et al. (2009) are 300 to 420 μrad/s. These values are about 10 times of ours. In comparison with our experiment, their observational distance is also much smaller and their explosion is slightly larger. For large explosions, we should mention Nigbor's experiment in Nevada test site (Nigbor, 1994). He observed a PGRV of 38 m rad/s at distance of 1 km from a very large chemical explosion (1 000 t). His explosive scale and resultant PGRV are all about 1 000 times of ours.

    Rotational motions may be caused by various factors, such as non-linear elastic deformation of the medium and asymmetrical property of the seismic source. Even for explosions, the sources are not symmetrical.

    For a long time, classic seismology has been limited to measuring only the three components of translational motion. It is of great importance to measure and study the rotational components. As a preliminary experiment, we used near-field translational records of a temporal seismic array in North China to study the ground rotational motions around vertical axis. The sources used are explosions with explosive of 500 kg for each. It is the first time in mainland China to perform this kind of calculation. Ground rotational velocities were calculated using the space derivatives of the horizontal components of translational velocities from the array. The PGRVs are approximately 30 to 57 μrad/s.

    ACKNOWLEDGMENTS: This study was supported by the National Natural Science Foundation of China (Nos. 90814001, 40974053, 41074069). Prof. P Spudich gave us useful advices and suggestions for data processing. The authors are grateful to the two anonymous reviewers for their useful suggestions.
  • Cai, N. C., Fu, Z. Z., 2009. Manufacture of Rotation Seismograph. Acta Seismologica Sinica, 31(3): 347–352 (in Chinese) http://www.researchgate.net/publication/291987489_Manufacture_of_rotation_seismograph
    Cochard, A., Igel, H., Schuberth, B., et al., 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-Verlag, Heidelberg. 391–411
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    Knopoff, L., Chen, Y. T., 2009. Single-Couple Component of Farfield Radiation from Dynamical Fractures. Bull. Seismol. Soc. Am. , 99(2B): 1091–1102, doi: 10.1785/0120008288
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