Figures showing focal depth constraints and HYPOINVERSE locations of 19 events of the sequence with error ellipse, as well as text and figures for the resolution tests of EGF (empirical Green's function) analysis method used in this study.
Fig. S1. Changes of the fitting error (E) and source mechanism as a function of focal depth for the Odaesan, Korea earthquake of 20 January 2007. The fitting error reaches a global minimum (Emin) at 11 km depth. The synthetics for the focal depths between 9 to 13 km fit observed data fairly well, indicating a range of acceptable depths, and are indicated as the horizontal dashed line representing 5% greater fitting error, i.e., 1.05 x Emin.
Fig. S2. Single event locations using HYPOINVERSE. 95% confidence error ellipse is plotted for each event. Foreshocks are indicated by red open circles and ellipses, whereas the aftershocks are indicated by blue open circles and ellipses. A star indicates the mainshock.
What is the resolution limit of the EGF analysis method employed in this study? In order to answer this question, we carried out a set of resolution tests by using the EGF analysis method and waveform data used in this study. Broadband seismic records used in this study are acquired with a sample rate of 100 samples/sec. So, the sampling interval is 0.01 sec and the maximum frequency available from the data is 50 Hz. In all tests, we used S-wave on transverse-component records. Since the corner frequency of S-wave, fc(S), is about 2/3 of that of P-wave (Madariaga, 1976), S-wave on transverse-component will provide better chance of resolving the corner frequency of small events from available band limited waveform data.
We assume that two events can be treated as if they are a mainshock—aftershock pair, and that we try to retrieve the source time function of the larger event (mainshock) by using the full bandwidth of the available data. Our EGF analysis method is simple and consists of following processes, assuming we analyze S waves on transverse-component from small earthquakes (M < 5.0).
We deconvolve records from a mainshock—aftershock pair in each case with itself by using the same procedure used in routine EGF analysis in this study. The resulting trace should produce a delta function.
Fig. S3. Deconvolution of records at short distance from the source. (a) Transverse-component (HHT) record at DGY (Δ=8.7 km) from event 8 is used as EGF event pair; (b) deconvolution of mainshock record by itself, records are only demeaned; (c) Transverse-component record at DGY (Δ=10.5 km) from event 3 is used as EGF event pair; (d) deconvolution of mainshock record by itself. This test is to check the resolution limit of the EGF analysis method used in this study. Results must be a delta function of minimum duration, that is, 0.02 sec (two samples). Sampling interval is 0.01 sec for all records used in these examples. Note that the amplitude of the delta function is unity, because it is normalized by the sampling interval.
Fig. S4. Deconvolution of records at local distance. (a) Transverse-component (HHT) record at CHC (Δ= 67.7 km) from event 8 is used as EGF event pair; (b) deconvolution of the mainshock record by itself, records are only demeaned; (c) Transverse-component record at CHC (Δ= 67.5 km) from event 3 is used as EGF event pair; (d) deconvolution of the mainshock record by itself. This test is to check the resolution limit of the EGF analysis method used in this study. Results must be a delta function of minimum duration that is, 0.02 sec (two samples).
We synthesize a mainshock record by convolving the EGF record with a known source pulse. The source pulse consists of four samples with amplitude (0, 2.5, 5, 0), hence, the duration of the source pulse width is 0.03 sec.
Fig. S5. (a) S wave on transverse-component (HHT) record at DGY (Δ=8.7 km) from event 8 convolved with source pulse of duration 0.03 sec is used as mainshock record (red trace) and itself is used as the aftershock record of an EGF event pair; (b) deconvolution of the mainshock- by aftershock-record; (c) S wave on transverse-component record at DGY (Δ=10.5 km) from event 3 convolved with source pulse of duration 0.03 sec is used as EGF event pair; (d) deconvolution of the mainshock- by aftershock-record. The source pulse is cleanly recovered with its slope (two samples up and one sample down) and amplitude. In this case, data are only demeaned before Fourier transform and no other data processing techniques are applied. It is important to have the same time window lengths for the EGF pair.
Fig. S6. (a) S wave on transverse-component (HHT) record at CHC (Δ=67.7 km) from event 8 convolved with source pulse of duration 0.03 sec is used as the mainshock record (red trace) and itself is used as the aftershock record of an EGF event pair; (b) deconvolved record. Source pulse is recovered with negligible oscillations; (c) S wave on transverse-component record at CHC (Δ=67.5 km) from event 3 convolved with source pulse of duration 0.03 sec is used as EGF event pair; (d) deconvolved record. The source pulse is cleanly recovered with its slope (two samples up and one sample down) and amplitude (0 2.5, 5, 0). These records did not require applying the water-level method or filters. In this test, data are only demeaned before Fourier transform and no other processes are applied.
Fig. S7. We applied 0.5% water-level to the records to compare them with results in Figures S6b and S6d. (a) the same as in Figure S6a; (b) deconvolved record. We applied a water-level of 0.5% to spectral amplitudes of the Green's function before taking spectral ratios and Fourier inverse transform. Notice that small oscillatory signals in Figure S6b are reduced somewhat, but the improvement is not significant; (c) the same as in Figure S6c; (d) the same as in Figure S6d, but records are demeaned and we applied a water-level of 0.5%. There is no significant change from Figure S6d in which no water-level was applied. The result indicates that small oscillatory signals in Figures S6b and S6d are very slightly reduced.
Fig. S8. (a) S wave on transverse-component record at DGY (Δ=8.7 km) from event 8 convolved with source pulse of duration 0.06 sec is used as the mainshock record (red trace) and itself is used as the aftershock record of the EGF event pair; (b) deconvolved record. Notice low amplitude oscillations near the source pulse, records are only demeaned; (c) S wave on transverse-component record at DGY (Δ=10.5 km) from event 3 convolved with source pulse of duration 0.06 sec is used as EGF event pair; (d) deconvolved record. The source pulse is cleanly recovered with its slope (three samples up and three samples down) and amplitudes (0, 2.5, 3.75, 5.0, 3.75, 2.5, 0). In this test, data are only demeaned before Fourier transform and no other processes are applied.
Fig. S9. The same tests as in Figure S8, but we applied a 0.1% water-level to the EGF signal before taking the spectral ratios and Fourier inverse transform (deconvolution). The STF duration and shape are cleanly recovered. (a) the same as in Figure S8a; (b) deconvolved record. We applied a water-level of 0.1% of the maximum spectral amplitude on aftershock record (Green's function) after the Fourier transform before taking spectral ratios before Fourier inverse transform (deconvolution). Notice the oscillatory signals around the source pulse in Figure S8b are reduced from the source pulse record, and the shape and duration — 0.06 sec of the initial source pulse is recovered; (c) the same as in Figure S8c; (d) the same as in Figure S8d, but records are demeaned and we applied water-level of 0.1%. There is no significant change from Figure S8d in which no water-level was applied. Note that applying some band-pass filters made the source time function records less clear.
Fig. S10. The STFs are not well recovered when no signal processing technique is applied (Fig. S10b and S10d). (a) S wave on transverse-component record at CHC (Δ=67.7 km) from event 8 convolved with source pulse of duration 0.06 sec is used as the mainshock record (red trace) and itself is used as the aftershock record of the EGF event pair; (b) deconvolved record. The source pulse is poorly recovered. Records are only demeaned before Fourier transform; (c) S wave on transverse-component record at CHC (Δ=67.5 km) from event 3 convolved with source pulse of duration 0.06 sec is used as EGF event pair; (d) deconvolved record. The source pulse is poorly recovered. Data are only demeaned before Fourier transform and no other processes are applied.
Fig. S11. A simple cosine split box-car taper with 5% of the record length produced the fairly good results as shown in Figure S11b. For event 3 (Fig. S11c), the STF is fully recovered when 5% cosine split box-car taper is applied (Fig. S11d). Note that the Nyquist frequency is 50 Hz. (a) the same as in Figure S10a; (b) deconvolution of the mainshock- by aftershock-record. We applied 5% cosine split box-car tapering at the beginning and end of both records before Fourier transform. The shape and duration — 0.06 sec of the initial source pulse is fairly well recovered; (c) the same as in Figure S10c; (d) the same as in Figure S10d, but records are demeaned and we applied 5% cosine split box-car tapering at the beginning and end of both records before the Fourier transform. The shape and duration — 0.06 sec of the initial source pulse is well recovered. Slope (three samples up and three samples down) and amplitudes (0, 2.5, 3.75, 5.0, 3.75, 2.5, 0).
Fig. S12. (a) S-wave on transverse-component record at DGY (Δ=8.7 km) from event 8 (Mw 2.3) as the mainshock (red trace) and record from event 3 (Mw 1.3) as the Green's function (blue trace) are the EGF event pair; (b) deconvolved record. The source pulse is fairly well constrained with a total duration of ~0.03 sec which is about three samples (τ½ = 0.014 sec). This is similar to the tests shown in Figure S5. That is, deconvolution of S-wave on transverse-component with source pulse of very short duration.
This is an ideal case in which we could utilize the high-frequency S-wave signals nearly up to the Nyquist frequency of the data (50 Hz), because EGF pair is the event doublet, and the signal-to-noise ratio is very high even for the EGF signal at high frequencies due to its short source-receiver path of 8.7 km.
(c) S wave on transverse-component record at CHC (Δ=67.5 km) from event 8 (red trace) and record from event 3 as the Green's function (blue trace); (d) deconvolved record. The source pulse is clearly constrained with its duration of about 0.07 sec and τ½ = 0.035 sec. This is similar to the tests shown in Figure S11c and S11d. That is, deconvolution of S-wave on transverse-component with source pulse of long duration.
These actual data, the S waves on transverse-component from the EGF pair, are only demeaned before the fast Fourier transform and deconvolution, no additional signal processing technique was needed, in fact, a set of deconvolutions with water-level method yielded worse results with diminished high frequency resolution.
| N |
Station code |
Distance (km) |
Azimuth (°) |
θ (°) |
τ½ (s) |
Radius (km) |
|---|---|---|---|---|---|---|
| 1 | DGY | 8.7 | 81 | 52.0 | 0.014 | 0.103 |
| 2 | CHC | 68.8 | 280 | 6.0 | 0.035 | 0.104 |
Although the duration of STFs recovered from EGF analysis at two stations are a factor 2.5 different (see Table S1), the radius calculated by using the equation (1) with the rupture velocity Vr = 0.8 x Vs are within 10% of each other (see Table S1). Radius estimated from DGY records with the rise time, τ½ = 0.014 sec is 0.103 km, whereas the radius estimated from CHC records with τ½ = 0.035 sec is 0.104 km, with an average radius of ~0.10 km. This consistent radius estimate may be due to the fact that we have good knowledge on rupture geometry (strike and dip), focal depth and event location as shown in Figure 5. Duration of the STF depends upon the position of the stations and rupture velocity.
Three sets of resolution tests with synthetic mainshock records suggest that as long as the mainshock—aftershock pair for EGF analysis is a true event pair such as repeating events with different size - nearly colocated and have a common focal mechanism, and the seismic signals have high signal-to-noise ratios at high frequencies — then the data can be used up to the Nyquist frequency, because we are taking spectral ratios of the records with the same instrument response, site condition, and common source-receiver path.
When the EGF event pair satisfies the above conditions as a repeating event pair, deconvolution can proceed from a simple to gradually more complex signal processing techniques such as: demean, detrend, tapering, high- or band-pass filtering, application of water-level to EGF spectra. Applying water-level and filtering may all introduce diminished resolution of available band-limited data. If the simple processes do not work, one may question if the signals are from the true EGF event pair.
We argue that the S-wave on transverse-component record is preferred to define the source spectrum corner frequency or to determine the rise time of the source pulse of small earthquakes over the P wave on vertical records, because the corner frequency of the P-wave is greater than the corner frequency of the S-wave by an average factor of 1.5 (Madariaga, 1976). Hence, the use of S-wave provides a better chance to constrain the corner frequency of small earthquakes than the P-wave when available data have finite, limited high-frequency bands and the corner frequency approaches the Nyquist frequency of the records available for analysis.
Madariaga, R. (1976). Dynamics of an expanding circular fault, Bull. Seism. Soc. Am. 66, 639-666.
