29/11.06 - (2006)c TITLE PAGE An above small earthquakes Ping Hao a, Yuan Gao a,b * and Stuart Crampin a,b,c a Institute of Earthquake Science, China Earthquake Administration, 63 Fuxing Road, 100036 Beijing, China; hp@seis.ac.cn; gaoyuan@seis.ac.cn. b Shear-Wave Analysis Group, School of GeoSciences, University of Edinburgh, Grant Institute, West Mains Road, Edinburgh EH9 3JW, Scotland UK; ygao@staffmail.ed.ac.uk; scrampin@ed.ac.uk; http://www.geos.ed.ac.uk/homes/scrampin/opinion/. c also at Edinburgh Anisotropy Project, British Geological Survey, Murchison House, West Mains Road, Edinburgh EH9 3LA, Scotland UK. Intended to be published: Computers & Geosciences Manuscript received: February, 2006 Page heading: ES for measuring shear-wave splitting Address for correspondence: Yuan Gao Institute of Earthquake Science China Earthquake Administration 63 Fuxing Road Tel: +86 10 88015660 100036 Beijing Fax: +86 10 88015627 China Email: gaoyuan@seis.ac.cn, ygao@staffmail.ed.ac.uk
An above small earthquakes Ping Hao a, Yuan Gao a,b * and Stuart Crampin a,b,c a Institute of Earthquake Science, China Earthquake Administration, 63 Fuxing Road, 100036 Beijing, China; hp@seis.ac.cn; gaoyuan@seis.ac.cn. b Shear-Wave Analysis Group, School of GeoSciences, University of Edinburgh, West Mains Road, Edinburgh EH9 3JW, Scotland UK; ygao@staffmail.ed.ac.uk; scrampin@ed.ac.uk; www.geos.ed.ac.uk/homes/scrampin/opinion/. c also at Edinburgh Anisotropy Project, British Geological Survey, Murchison House, West Mains Road, Edinburgh EH9 3LA, Scotland UK. Abstract As part of the development of a system for routinely measuring shear-wave splitting, this paper introduces an Expert System, ES, to measure the polarisations and time-delays of seismic shear-wave splitting in three-component seismograms above small earthquakes. Expert Systems are rule-based computer techniques designed to provide expertise in particular topics, where the rules are algorithms developed from previous knowledge and experience. The technique is tested on data recorded by the seismic network in Iceland. The statistics suggests that the ES is reasonably successful and provides appropriate initial input parameters for a more precise analysis, which leads to the success of the comprehensive Shear-Wave Analysis System, SWAS, for semi-automatic measurement of shear-wave splitting. Keywords: Expert System, measurement of shear-wave splitting, fast shear-wave, slow shear-wave, polarisations, time-delay. 1. Introduction Phase identification and phase picking of seismic-wave arrivals are key elements in earthquake location, earthquake analysis, and seismological research. Seismic shear-waves split into two approximately orthogonal polarisations (seismic birefringence) when travelling through the anisotropic crust. Consequently, shear-wave splitting is playing an increasingly important part in earthquake and exploration seismology (Crampin & Chastin, 2004). Due to the complexity and temporal and spatial variations of shear-wave splitting waveforms (Crampin et al., 2004), no existing technique is wholly successful at automatically identifying and measuring shear-wave splitting. For example, artificial neural networks (Dai & MacBeth, 1995) and correlation functions (Gao & Zheng, 1995; Gao et al., 1998) have been used to measure shear-wave splitting, but the complicated waveforms of shear-waves mean that these techniques are only partially successful. Murat & Rudman (1992) introduced a successful automatic technique, but only for first arrival picking. The estimation by orthogonal transformations (Shieh, 1997) is possibly subject to restriction the 2
restrictions of cross-correlation techniques (Crampin & Gao, 2006). Teanby et al. (2004) used an automatic identification with cluster analysis and optimum window in hydrocarbon-reservoir induced events, but at the expense of rejecting much of the data. The various techniques for identifying and measuring shear-wave splitting have been reviewed by Crampin and Gao (2006). Many methods use various cross-correlation techniques. Crampin and Gao (2006) showed that these methods are only effective for classic examples of orthogonally-polarised shear-wave splitting. This means that they typically reject 50% to 70% of recorded events. This severe rejection heavily biases any results and should not be used for scientific conclusions. This heave rejection is avoided by the semi-automatic technique of Gao et al. (2006), whose first estimation is by the Expert System outlined below. This paper presents an Expert System, ES, for picking polarisations and fast and slow split shear-wave arrivals. ES analyses are computer techniques using rule-based algorithms for providing expertise in particular topics (Jackson, 1990). ES have been used for earthquake hazard assessment (Zhu et al., 1996), and for identifying seismic phase arrivals (Tong and Kennett, 1996). However, ES and other artificial intelligence, AI, techniques, although intended to solve problems in particularly complicated phenomena, are not always wholly successful, and are probably only appropriate when other techniques are ineffective. (((((AI techniques are currently effective in measuring shear-wave splitting for records from small earthquake events. SUGGEST OMITTING THIS, IT DOES NOT SEEM TO FIT IN WITH PREVIOUS SENTENCE))))) Here we develop a more widely applicable ES analysis for identifying and measuring shear-wave splitting. [FIGURE 1 HERE] The two-stage iterative process is illustrated in the flow chart in Figure 1. A three-component record of an earthquake is first processed by the Expert Rules, given below, developed from specific knowledge of shear-wave splitting. Preliminary determination of the two principal parameters, the polarisation of fast split shear-wave, and the time-delay between the fast and slow split shear-waves, are obtained from the initial calculation. The results are again processed by Expert Rules until the output stabilises. Finally the results are evaluated to decide whether the ES estimations are acceptable. 2. Initial identification of shear-wave splitting 2.1 Initial Expert Rules: approximate polarisation of fast shear-wave To operate the ES analysis scheme, we require both the (approximate) time of the shear-wave phase and the earthquake hypocentral position. The ES has been developed in order to operate on the SIL Seismic Network in Iceland (Stefánsson et al., 1993), and shear-wave arrival times and earthquake locations are available from the online (Internet) earthquake catalogue. In order to identify the initial shear-wave polarisation, we consider two-dimensional motion of a shear-wave arrival in the horizontal plane. For the vector amplitudes of each earthquake, we define two basic quantities, n max, the maximum value of amplitude of the noise for a time window (BTW) before the shear wave arrival, and s max, the maximum value of shear wave amplitude in a time window after the initial shear-wave arrival (ATW). For each earthquake, we define a threshold parameter, V eq : 3
V eq = max(c bef n max, s max /c aft ) (1) where c bef and c aft are two coefficients, c bef > 1 and c aft > 1, chosen by experience for each particular seismic station. The coefficients c bef and c aft, are usually different for different seismic stations, because of the particular geology and geophysical structure surrounding each station. The shear-wave has arrived when the amplitude becomes greater than V eq. We take B as the three-component seismogram data point immediately after the signal has exceeded V eq. We define data point A as the point in BTW before B which is nearest to the average value of data in BTW. The approximate value of the shear-wave polarisation, 0, of fast shear-wave is the direction A B. 2.2 Initial Expert System Rules: approximate arrivals of fast and slow shear-waves The horizontal-components of seismogram are rotated parallel and orthogonal to 0, to separate the waveforms of the fast and slow split shear-waves. The fast component within BTW contains a number of cycles of motion where each half-cycle we number sequential j = 1 to k bef, say, for each peak-to-trough each with amplitude a. Similarly the cycles of motion in ATW are numbered j = 1 to k aft. The value of a before the shear-wave arrival is defined as a bef and the value of a after shear-wave arrival as a aft. The maximum of a bef within time window BTW and the maximum of a aft within time window ATW can be written as: A w = max(a w1, a w2,, a wj, a wk ), (w = bef and aft, j = 1, k w ); (2) where k bef, and k aft, are the number of peaks and troughs the windows BTW and ATW, respectively. 2.2.1 ES Rules for approximate arrivals of fast and slow shear-waves. The fast shear-wave arrives only when a is larger than the appropriate threshold, H. The initial threshold is defined as H 0, where: H 0 = c i A aft, (0 < c i <1; i = 1 or i = 2 ); (3) where c i, chosen by experience, are coefficients for i = 1 or i = 2, for fast and slow split shear-wave, respectively. The coefficients c 1 and c 2 may be different for different seismic station records. For instance, c 1 0.2, c 2 0.2, at most stations in Iceland for this ES. For the initial calculation or evaluation, let H = H 0. 2.2.2 ES Rules for evaluation of fast and slow shear-wave arrivals. In order to improve arrival times we up-date the threshold values for the fast and slow shear-waves by the next three rules. We define two constant coefficients, 1 and 2, (0 < 1.< 2 ) in Rule 1, two further constant coefficients, m and t in Rules 2 and 3, and: = H t / A bef ; (4) where H t is the current H value; and H t+1 is the next calculated of H. The three rules are: 1) If < 1, let 4
H t+1 = 1 A bef, (5) and if > 2, let: H t+1 = 2 (A bef.+ H t ); (6) where the constant coefficient, chosen by experience, that meets the condition, 0 < <<1. 2) If H t > A aft, let: H t = m A aft, (0 < m <1). (7) 3) If a wj > H t, (w = bef or w = aft; j = 1,2, k), and a w(j-1) > t H t, (0 < t < 1); (8) and the threshold has been up-dated. The initial arrival of the fast shear-wave is within the half-cycle j-1. A similar rule also applies for the slow shear-wave. Generally, the parameters m and t are larger than 1.0. With these rules related to amplitudes, it is easy to find the preliminary arrival for fast shear-wave or slow shear-wave. The next two rules chose the best estimates for the shear-wave arrivals relative to these new thresholds. 4) In order to up-date arrivals of the fast and slow shear-waves, we define the absolute value of a data point, i, within the j th half-cycle as x j,i. If a wi > H t, and: x j,1 > c spe n max, (c spe >1); (9) where c spe is a coefficient which may be different at different seismic stations, then the arrival of the fast shear-wave is within the last vibration, that is the vibration (j 1). A similar rule applies to the slow split shear-wave. 5) If x j,1 n max, move the sample point forward sequentially to the point i where x j,i n max, but x j,i+1 > n max. We define this point i as point C, and use a new time window NBTW, with the same length as BTW but ending at C. We analyse the polarisation directions of every point from the start of the window NBTW to point C and decide which point is the arrival of the fast shear-wave. In order to objectively obtain the fast split shear-wave arrival, we define a new parameter p: end p = Z amp (i) { abs[(i) 0 ]}; (10) i=start where start advances sequentially until reaching the point before C and end is point C; Z amp (i) is the absolute value of the amplitude difference between point, i, and point i - 1; is an acceptable range of angle errors, such as 22.5º, (((((((SURELY 22.5 SEEMS A LITTLE LARGE))))))) (i) is the vibration direction of every point, and 0 is the initial value of the polarisation of the fast shear-wave. The point with the largest value of p, named D, is taken as the arrival of the fast split shear-wave. The parameter 5
p is related to the polarisation characteristics. Equation (10) is also suitable for the slow split shear-wave, where 0 in the equation (10) is now the initial value of the polarisation of slow shear-wave. In equation (10), start is the first data point in time window NBTW, the value of end advances sequentially from the second data point in NBTW to the end point C. With same rule as equation (10), the largest value of p is immediately before the arrival of the slow shear-wave at point D. Following these five measurement rules, we obtain preliminary approximate arrivals of fast and slow shear-waves. 3. Accurate identification of shear-wave splitting Having obtained approximate arrivals of the fast and slow split shear-waves, the ES evaluation scheme in Figure 1 enters the second stage of evaluation and repeats the Expert Rules improving the estimations of the polarisation of fast shear-wave, and the arrival times of the fast and slow split shear-waves. The ES scheme repeats this process until the values stabilise. These values usually lead to a good automatic evaluation of the polarisation of the fast split shear-wave and the time-delay between the split shear-wave arrivals. Some additional rules are applied in this second application of ES rules. 1) If the arrival of slow shear-wave is later than that of fast shear-wave, the result is acceptable, and ES then continues with the Rule 2, below. However, application of the ES rules in Section 2, above, may disturb the order of fast and slow shear-waves. If the arrival of the selected slow shear-wave is earlier than the fast shear-wave, the program rotates the two horizontal components by 90º. Using the new polarisation, the arrivals of fast and slow shear-waves are re-calculated. If the new rotated arrival of the slow shear-wave is still earlier than new arrival of the fast shear-wave, the data is considered to be unacceptable and will be rejected for further analysis. 2) If the ratio of signal-to-noise r sn is smaller, at any evaluation step, than some specific reference value c rsn2 = 3.0, say, chosen by experience, the data is considered to be unacceptable and will be rejected for further analysis. 3) If the arrival of the slow shear-wave is earlier than the fast shear-wave at the conclusion of the second application of ES rules, the data is considered to be unacceptable and will be rejected for further analysis. [FIGURE 2 HERE] Sometimes, more complicated waveforms will result in incorrect identification. After using the rules in Section 2, ES may obtain, say, a shear-wave arrival at the point m in Figure 2a. However, the preferred true shear-wave arrival should be at point k as in Figure 2b. A further rule is given here. 4) Define a new coefficient, c k, as below: k 1 (i) = [x(i) x(m + 1)]/(i - m - 1); k 2 (i) = [x(n 1) x(i)]/(n 1 - i); and c k (i) = abs[k 1 (i) / k 2 (i)]; for (i = m + 2, m = 3,,n - 3, n - 2); (11) 6
where x(i) is the amplitude of point i. If the maximum of c k (i) is greater than some specific value, c H, that is: max[c k (m + 2), c k (m + 3), c k (n - 2)] > c H ; (12) the sample point with the maximum c k (i) is the arrival of fast (or slow) split shear-wave. Otherwise, the arrival of fast (or slow) split shear-wave is point m (Figure 2a). After the second stage of calculation and evaluation, the ES produces the best estimates of the polarisations of the fast shear-wave and the shear-wave splitting time delays and we need to judge the quality of the estimates. 4. Identifying quality of shear-wave splitting In order to discriminate between different qualities of ES measurements of shear-wave splitting, we introduce two parameters Qp and Qt specifying the quality of the measurements of shear-wave splitting. We assume three grades of quality: Qp, Qt, = 1, 2, or 3 for good, acceptable, or unacceptable, respectively. The Qp is related to the ES identification on polarization of fast shear-wave, and Qt is related to ES identification on arrival of fast shear-wave and arrival of slow shear-wave, and hence the quality of the time-delay. We define two values specifying, c rsn1 and c rsn2, specifying, respectively, good and acceptable signal-to-noise ratios, r sn,. 1) If the ratio of signal-to-noise, r sn, is larger or equal than the reference value, c rsn1, (r sn c rsn1 ), the quality of the polarization is set equal to 1 (Qp =1). If c rsn2 r sn c rsn1, then Qp = 2. Note, we typically select c rsn2 = 3.0 and c rsn1 = 5.0 in this study of seismic records in Iceland. 2) We define two parameters d aft and d bef. The difference of the maximum and minimum values of amplitude within a time window, 10 points, say, immediately after arrival of fast shear-wave is taken as d aft, and the difference of maximum and minimum values of amplitudes within same time window immediately before arrival of fast shear-wave is d bef. If d aft /d bef r d, Qt is set to 1. If d aft /d bef < r d, Qt = 2, where r d is a ratio coefficient, set by experience (2.8 in this study). We also use the same two parameters for the slow shear-wave. If Qt=1 for both fast and slow shear-waves, the identifying quality of the time-delay is set to 1. 5. Calculation of polarisation of fast shear-wave The polarisation of the fast shear-wave,, is calculated by weighting the vibration direction of every point in the time-delay by the amplitude difference in the polarisation diagrams. We have: = Z amp (i) (i) / Z amp (i); (13) i i where Z amp (i) and (i) are defined in equation (10); and i is summed over time samples in the fast split shear-wave before the arrival of the slow wave. 7
6. Evaluation of ES identification of shear-wave splitting We developed the ES specifically for processing data recorded by the SIL Network in Iceland. To test both ES and visual analysis techniques on displayed data, we use eight-months of SIL data recorded at Station BJA in SW Iceland. [FIGURE 3 HERE] Figure 3 shows a three-component seismogram recorded at BJA together with horizontal seismograms rotated into radial and transverse directions. The magnitude 0.55 earthquake was at an epicentral distance of 1.9km, azimuth 282º, and depth 6.7km. Details are listed in the header top-left. The seismogram is filtered with a Butterworth pass-band of 3Hz - 50Hz. In Figure 4, ES has identified the fast and slow shear-waves according to the rules in equations (1) to (13), and the lower two horizontal seismograms are rotated into fast and slow directions where the fast and slow shear-waves arrivals, showing clear shear-wave splitting, are marked by vertical lines. Figure 5 shows the screen image of a polarization diagram display. The bottom line of horizontal polarisation diagrams shows the shear-wave splitting as recorded by horizontal components. The ES picks are marked by small circles on the horizontal polarisation diagrams. The large polarisation diagram at the bottom shows the horizontal polarization of the fast shear-wave bracketing the circled fast and slow picks. ES analysis has successfully selected points where the particle-motion shows abrupt approximately 90º changes in direction as the polarised shear-waves arrive. In this case there is no need for visual adjustment in the template to the right. [FIGURE 4 HERE] [FIGURE 5 HERE] The templates in the headers top-right of Figures 3 to 5 show values of fast and slow shear-wave arrivals, polarisation, and time-delays, with click-buttons and arrows indicating possible visual adjustments to optimise measurements. The rotated seismograms in Figure 4 show classic shear-wave splitting suggesting there is no need for visual adjustment, and the completely-objective automatic ES identification of shear-wave splitting gives a satisfactory result. Data recorded at Station BJA of the SIL Network from 1 st January to 31 st August 2004 are used to access the overall accuracy of automatic ES evaluations. We assume visual measurements are the best estimates, and compare the relative accuracies of the ES evaluations by their difference from the visual measurements (in degrees for polarisations and data points for phase arrival times). Only earthquake records measured both by the automatic ES technique and by visual analysis are included in the analyses. The records estimated by the ES technique as unacceptable with Qp and/or Qt = 3, in almost all cases, were small earthquakes with small signal-to-noise ratios. There were 135 earthquakes with magnitudes larger than -1.0 with Qp, Qt = 1, 2 within the shear-wave window at BJA. (The shear-wave window is defined by Booth and Crampin (1985) as the range of incidence angles at the free-surface where shear-wave arrivals are not disturbed by S-to-P conversions.) Of these earthquakes, 17 (13%) were more than 30 different in polarisations and were considered unacceptable. The remaining 118 records (87%) were within 30 in polarisation and 64% were within ±3 sample points (±0.03s) of the visual measurements. Figure 6 shows histograms of the accuracies for different measurement errors. [FIGURE 6 HERE] The results suggest that ES technique for Qp, Qt = 1, 2 earthquake records provides good preliminary values of polarisations and time-delays for 87% and 64% of the records, respectively. 8
Excellent values are obtained for 52% and 17% of the records which do not require visual adjustment. 7. Conclusions We have shown that the ES technique is effective in identifying and measuring shear-wave splitting. The ES technique shows that: 1) The ES polarisation measurements are accurate for 81% of the data with errors less than 15 for all earthquake records, and are accurate for 95% of the data with errors less than 15 for earthquake records with Qt = 1. This means that the ES can provide reliable measurements of polarisations of shear-wave splitting with complete automatic identification. 2) The phase arrivals of fast and slow shear-waves (and consequently time-delays) are accurate for 64% of the data with errors less than 3 sample points for all earthquake records. However, for earthquake records with Qt = 1, the ES measurements are accurate for 78% of the data. 3) The accuracies in Figure 6 suggest that the ES measurements are not overly sensitive to quality factors. As long as the records are acceptable (Qp, Qt = 1, 2), both polarisations and time-delays can be easily be optimised by visual adjustment. The ES technique identifies polarisations, shear-wave arrival times, and hence time-delays, effectively, and results in a sufficiently accurate initial identification system for shear-wave splitting for the semi-automatic Shear Wave Analysis System developed by Gao et al (2006). It is believed to be an effective and efficient technique for measuring shear-wave splitting which avoids both the time-consuming visual measurements and the inadequate wholly automatic techniques. Acknowledgements This work was supported partly by: China NSFC Project 40274011; China MOST Project 2004BA601B01; China MOP Key Project 2003; European Commission PREPARED Project EVG1-CT2002-00073; and by a UK Royal Society Joint-Project with China. We thank Dr Heng-Chang Dai of the Edinburgh Anisotropy Project of the British Geological Survey, for fruitful discussions and comments. References: Booth, D.C., Crampin, S., 1985. Shear-wave polarizations on a curved wavefront at an isotropic free-surface. Geophysical Journal of the Royal Astronomy Society 83, 31-45. Crampin, S., Chastin, S., 2003. A review of shear-wave splitting in the crack-critical crust Geophysical Journal International 155, 221-240. Crampin, S., Gao, Y., 2006. A review of techniques for measuring shear-wave splitting above small earthquakes. Physics of the Earth and Planetary Interior, submitted. Crampin, S., Peacock, S., Gao, Y., Chastin, S., 2004. The scatter of time-delays in shear-wave splitting above small earthquakes. Geophysical Journal International 156, 39-44. Dai, H., MacBeth, C., 1994. Split shear-wave analysis using an artificial neural network? First Break 9
12, 605-613. Gao, Y., Zheng, S., 1995. Cross correlation function analysis of Shear wave splitting - method and example of its application. Journal of Earthquake Prediction Research 4, 224-237. Gao, Y., Wang, P., Zheng, S., Wang, M., Chen Y.-T., Zhou, H., 1998. Temporal changes in shear-wave splitting at an isolated swarm of small earthquakes in 1992 near Dongfang, Hainan Island, Southern China. Geophysical Journal International 135, 102-112. Gao, Y., Hao, P., Crampin, S., 2006. SWAS: a shear-wave analysis system for semi-automatic measurement of seismic shear-wave splitting above small earthquakes. Physics of the Earth and Planetary Interior, 159, 71-89. Jackson, P., 1999. Introduction to expert systems. 2 nd ed., Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA, 526pp. Murat, M.E., Rudman, J.R., 1992. Automated first arrival picking. Geophys. Prosp. 40, 587 604. Shieh, C.-F., 1997. Estimation of shear-wave splitting time using orthogonal transformations. Geophysics 62, 657-661. Stefánsson, R. et al., 1993. Earthquake prediction research in South Iceland Seismic Zone and the SIL Project. Bulletin of the Seismological Society of America 83, 696-716. Teanby, N.A., Kendall, J.-M., van der Baan, M., 2004. Automation of shear-wave splitting measurements using cluster analysis. Bull. Seism. Soc. Am. 94, 453-463. Tong, C., Kennett, B.L.N., 1996. Automatic seismic event recognition and later phase identification for broadband seismogram. Bulletin of the Seismological Society of America 86, 1896-1909. Zhu, Y., Vogel, A., Hao, P., 1996. Expert System for Earthquake Hazard Assessment: ESEHA. In Earthquake Hazard and Risk, Kluwer Academic Publishers, 199-209. 10
FIGURE CAPTIONS Figure 1. Flow chart for measuring shear-wave splitting by Expert System, ES, analysis. Figure 2. An example of an initial ES pick of a shear-wave arrival illustrating Rule 4, Section 3. Figure 3. Screen image from SWAS before ES processing. Three-component seismogram at 100 samples-per-second of a magnitude 0.55 earthquake recorded at Station BJA of the SIL seismic network in Iceland. The time axis is in seconds. Header top-left shows earthquake and seismogram details. Header top-left shows splitting parameters, which in this image are blank before processing. From the top, seismograms are EW-, NS-, Vertical-, and rotated horizontal Radial- and Transverse-components for locations in the SIL seismic catalogue. The P- and S-wave arrivals (from SIL seismic catalogue) are spanned by 0.1s time-intervals for the polarisation diagrams in Figure 5. Figure 4. Screen image of fast and slow split shear-waves identified by ES. The right-hand header shows: ES-derived polarisations (with directions for adjustment) and (re-assignable) quality (Qp = 1, 2); times of ES-derived fast and slow arrivals, from start of screen image (with directions for adjustment); and time-delays, difference between fast and slow picks, with (re-assignable) quality (Qt = 1, 2). Notation as in Figure 3, with the lower two seismograms are horizontal seismograms rotated into the ES-derived fast and slow shear-wave polarisations, and the fast and slow shear-wave picks are marked by vertical lines on the seismograms. Figure 5. Screen image of polarisation diagrams for possible adjustment of polarisation and time-delay. Header information as in Figure 4. Horizontal seismograms have been rotated into radial and transverse directions as in the original seismograms in Figure 3. From the top, mutually-orthogonal polarisation diagrams are: sagittal section (Up, Down, Towards, and Away from the source); horizontal view (Up, Down, Left, and Right from the source), and horizontal section (Away and Towards the source, and Left and Right from the source). Each column of the polarisation diagrams shows particle motion in 0.1s (10 sample points) time-intervals, marked in the Figure 3 and 4 seismograms, spanning the P- and S-wave arrivals. The x n marked above each column indicates relative scaling. ES fast and slow shear-wave picks are marked by circles in the horizontal polarisation diagrams in time interval 1S and 2S. At the bottom is an enlarged horizontal polarisation-diagram spanning the selected fast and slow arrivals, where the circled picks can be visually adjusted in the template on the right. The template shows current selection of row, column, first and last points of the time-delay, and directions for visual adjustment. The polarisation of the fast shear-wave is calculated from equation (13). Small ticks mark time-series samples, which are outward facing for clockwise rotation, and inward facing for anti-clockwise rotation. Figure 6. Comparing ES measurements with visual measurements of 135 earthquakes (January to August, 2004) within the shear-wave window of Station BJA with Qp, Qt = 1, 2. a) Histograms of percentages of ES and visual measurements of polarisations differing by less than 5, 10, 15, 20, and 30 (histograms are cumulative to the right). b) Histograms of percentages of ES and visual measurements of shear-wave phase arrival times, which differ by less than or equal to 0, 1, 2, and 3 time-series samples (histograms are cumulative to the right). 11
Figure 1 Figure 2 12
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An Figure 6 16