We have analyzed waveforms from an OBS and an island station recorded between September 2006 and July 2007. From the moment tensor catalog we found 60 Mw > 3.3 earthquakes occurred during this period. All of the 60 earthquakes have generated T-waves and are recorded by the OBS (Fig. 2). About 90% of the earthquakes have generated clear T-waves recorded by an island station.
The OBS (S004) contains a Guralp CMT-3TC seismic sensor with flat response between 20 Hz to 120 sec. Quanterra Q330 is used as the data logger, with sampling rate 40 sps. The sensor is decoupled from the OBS mainframe, and is leveled periodically during the deployment by a gimbal system with brakes [Thwaites et al., 2005]. There is also a differential pressure gauge (DPG) mounted on each OBS’s frame [Cox et al., 1984].
The DPG is acting as a hydrophone at a 20 Hz sampling rate.
The island station LYUB contains a broadband seismometer with flat response between 20 Hz to 120 sec. Quanterra Q330 is used as the data logger, with sampling rate 40 sps.
In order to study different paths and conversion points of waves, we classify T-waves into 3 different types (Fig. 1). Type 1 represents direct seismic wave to acoustic wave conversion at SOFAR-channel, a low acoustic-velocity zone in the water column formed due to the decreasing temperature and increasing pressure at depth. Type 2 has at least 2 conversions between elastic waves and acoustics waves. Type 3 has only one conversion point near the OBS station.
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For the Type 1 acoustic leg, the energy in the ocean leg is mostly trapped at about a depth of 1000 m in the SOFAR-channel. Type 2 either later than Type 1 enter to SOFAR-channel or earlier leakage from SOFAR-channel, in the result Type 2 stay longer in crustal propagation make it travel faster than Type 1 in a same profile. Type 3 T-waves have the shortest acoustic legs in the all kinds of T-waves. They are least studied or neglected because it is always contaminated with seismic P- and S- phases.
To calculate the travel times for Type 1 T-wave, we first assumed T-wave energy travels in three legs (Fig. 1): (1) solid earth seismic elastic wave with a regional 1D crustal velocity model [Table 1; Rau and Wu, 1995]; (2) horizontal hydroacoustic wave in SOFAR-channel at a water depth of 1000 m with a velocity of 1.48 km/s from a conversion point to directly above the OBS; and (3) a vertical path with a velocity of 1.5 km/s down to the OBS. The first leg was calculated using a Tau-P method [Crotwell et al., 1999].
Table 1. 1D velocity model used for Green's function
Thickness
Assuming different parts of the T-wave for this particular earthquake Event No.
46 (see Table 2) are associated with paths of different convergent points, we calculated
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the total travel time associated with one particular conversion point on the seafloor.
Similar calculations were performed for thousands of conversion points along the 1000 m contour line offshore Taiwan, and plotted in Figure 3. We have done similar analyses for all the 60 earthquakes (see Fig. 3 and Appendix). OBS waveforms from the earthquakes show clear T-waves, especially after a bandpass filter of 1 to 9 Hz. The durations of the T-waves ranges from 100 to 200 sec.
Table 2. Event list from September 2006 to July 2007 in Taiwan region Event
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Figure 3: T-wave generated by a thrust event (No. 46 in Table 1) near Hualien. (a) The color scheme plotted on the 1000 m bathymetry contour represents the combined S-T travel time in three legs; (b) Vertical seismic and (c) DPG waveforms have been band-pass filtered between 1-9 Hz. Again color bar represents the combined S-T travel time, and the gray color bar represents the combined P-T travel time. The black and green vertical lines depict the P and S arrival times, respectively.
The observed duration of Type 1 T-waves are consistent with our predicted combine P-T and S-T arrival times and duration.
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The arrival time and duration of the T-wave coincide with the paths of the
available P-T and S-T conversion points in this region. The early arrivals (about 105 sec of total traveltime) of T-wave have the P to T and S to T paths that went through the conversion points near latitude 22.5° N. The large amplitude of the T-wave for this near coast event arrived about 125 sec after the origin time, and had the short seismic elastic path, i.e. the conversion point is closer to the earthquake. The later phase (between 140 and 160 sec of travel time, green color) is more complicated because there were two paths: one with a conversion point at a latitude of 21.7° N, and another at 23.7° N. For the phases that arrive between 170 and 190 sec, there are three different paths: one with the conversion point at 21° N, another at 24.2° N, and the third one also at 24.2° N but at a longitude of 122.5° E, instead of 121.7° E. The latest arrivals (200-220 sec, neon color) are associated with furthest conversion points at 124° E and conversion points at 24.5° N, 122° E.
The complexity of the different paths from multiple conversions arriving at the same time is due to the geometry of the 1000 m contour line and the locations of the earthquake and the OBS. Some of the P and S waves propagate to the north, then converted to a T-wave to propagate back to SE. Such a path configuration made the arrival time increase dramatically for conversion points to the north. However, as the 1000 m contour line turns right near to the 24.6° N, the travel time started to decrease even though the conversion point was farther away. This is due to a shorter SOFAR path in which the propagation velocity is slower compared with that of the elastic waves. For convergent points further to the east, the increasing length of the elastic wave path finally took stronger effect, and increased the travel times. Overall, our model with the multiple paths from different conversion points can predict the duration of the T-wave.
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Next we want to study the factors affecting the amplitude envelope of the T-waves.
The factors we want to examine include the elastic wave propagations, source radiation patterns, and the availability of the conversion points.
In order to synthetic Type 1 T-wave amplitude, we have used the FK code [Zhu and Rivera, 2002] and a Taiwan average 1D crustal velocity model to generate synthetic
displacement ground motions using the moment tensor source parameters. The displacement waveforms then were converted into acceleration waveforms (Fig. 4). We have done this at the thousands of conversion points along the 1000 m contour line. Such calculations were done for all the 60 earthquakes in this study. We then calculated the inner product of the peak accelerations in the P and S wave time windows with a unit vector that is normal to the bathymetric slope at the conversion points. The time windows for P and S waves are starting with their theoretical arrival times with durations of 2 and 5 seconds, respectively. The short time window for P is to exclude S wave when the S-P time is short. We will treat the inner product as the peak amplitude of the acoustic wave that comes into the SOFAR-channel from that particular conversion point. We do not consider the T-wave attenuation in the SOFAR-channel due to the relatively short propagation distances for these earthquakes. We then can associate the amplitude to the arrival time. We have summed the P and S amplitudes together to derive a synthetic T-wave amplitude envelope. Such envelope then is compared with the envelopes derived from the DPG and the BHZ components (Fig. 5). The envelopes are smoothed using an 8 sec moving window.
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Figure 4: The predicted T-wave amplitudes at the different conversion points (Event No. 46) from (a) P-wave and from (b) S-wave. We have calculated the synthetic ground motions at each convergent points along the 1000 m contour lines. Vertical and horizontal scales represent 1x10-3 (m/s2) and 20 (sec), respectively. First we calculated the maximum P and S wave vector sums from the synthetic waveforms.
Next we calculated the inner product of the P and S vector sums with the unit vector that is normal to the bathymetry in order to get the predicted T-wave amplitudes.
Note that in this case, and in most of the other cases, S to T conversion generates larger T-wave amplitude.
Figure 5: We have plotted the amplitude envelopes of vertical ground acceleration (red) and DPG (blue) for the Event No. 46. The P-T synthetic conversion associated with traveltime is plotted in gray dashed line, and S-T in green dashed line. We then plotted the sum of both P-T and S-T conversion in black dashed line. We can fit the overall amplitude envelope to the first order. Some of the reduced T-wave amplitude (at 110 sec and 150 sec) are due to the gaps in the 1000 m contour lines in this region. The color and gray bars are the predicted travel time for the Type 1 S-T and P-T in this region. Note also the ratio between ground acceleration and water pressure changes (black line) are different during the arrival time of the P and S waves, and the arrival time of the T-wave. The observed amplitude envelopes are smoothed using an 8 sec moving time window.
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There are usually two energy pulses in the amplitude envelope plots of the 60 events that we studied. The first pulse is associated with the arrival time of the elastic wave phases, while the second pulse is associated with that of the T-wave energy. For the first pulse, the ratio between the observed vertical ground acceleration and pressure changes is larger than that in the second pulse (Fig. 5). In our simulation of P to T and S to T conversions, both have contributed on the durations and amplitudes of recorded waveforms. However, the S waves generally generate stronger T-waves. In later part (150 sec after the origin time) the predicted T amplitude decrease for a while before resuming back to larger amplitude. This is due to the gap in the 1000 m contour line in this region, between the latitudes of 22.2° N and 22.5° N (Fig. 3). Such pattern can also be found in the observed data, in both the vertical ground acceleration and the pressure changes (Fig.
5). This demonstrates the efficiency of the conversion points at 1000 m water depth for exciting strong T-waves.
Not all the T-waves are excited by the conversion points along the 1000 m contour line. Next we will show T-waves excited by an abyssal earthquake that is far away from the 1000 m bathymetry contour line. From the traveltime analysis (Fig. 6) we found some T-wave energy arriving before the predicted P and S to T conversion at the 1000 m contour line. This suggests that there is T-wave energy that has shorter acoustic path than the Type 1 T-wave. By definition this means that there is Type 2 T-wave energy observed for such an abyssal earthquake. We have calculated the travel time for the path that goes from the earthquake to the hypocenter, then to the SOFAR-channel before going down sub-vertically to the OBS site. Such T-wave can also be identified in DPG (Fig. 6c). We see increase T-wave energy at this arrival time (Fig. 6c & d), especially on the DPG channel. Note that there is still an increase of the T-wave amplitude in the predicted P and S to T conversion at 1000 meter contour line. To sum, this demonstrated that it is
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possible for T-wave energy to enter into the water column not only at 1000 m bathymetric contour lines but also at any points on the seafloor.
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Figure 6: An example of T-waves excited by an abyssal earthquake (Event No. 27).
(a), (b) and (c) same as the configuration in Fig. 3; (d) same as the configuration in Fig. 5. We interpret that there are some T-wave energy arriving from the water column to the OBS starting at 25 second after the earthquake origin time, based on the barely decayed signal after S-phases. We also calculated the travel time for a path with a SOFAR-channel leg from the above the earthquake to above the OBS, and marked the time as “a” with purple vertical line. It coincides with a time when we see an increase of apparent water pressure change in (c) and (d). We also see an increase of T-wave energy at the arrival time of the Type 1 T-wave.
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Next we show an example of the Type 3 T-wave using the same event used in Figures 3, 4 and 5. We have plotted the spectrograms of the vertical ground acceleration and pressure changes (e.g. Fig. 7, and Appendix). In Figure 7, the first pulse of the T-wave energy is correlated with the elastic T-wave arrival times at the OBS site. The DPG also recorded water pressure changes at the same time. Usually we see strong energy at frequency bands between 6 and 8 Hz in the ground motions. For the BDH channel, we see stronger energy between 2 and 6 Hz. Overall, weak T-wave energy can be see between 1 and 10 Hz. It has higher ground acceleration to pressure change ratio compared with the second pulse of the T-wave energy that fits with the Type 1 T-wave travel time (Fig.
7e). Such feature can be observed in all the 60 events we have studied (see Appendix). In later section we will analyze the possible mechanism for such change of ratio between Type 1 and Type 3 T-waves.
Figure 7: Waveforms of the (a) acceleration ground motions and (b) DPG for Event No. 46. We have also plotted their frequency spectra (c) and (d) respectively, in addition to a transfer function defined as the (e) ratio of the acceleration over the pressure changes. We have marked Type 1 and Type 3 T-wave in (d). For the transfer function (e), its values are higher during the P- and S-waves, but lower during the T-wave.
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For all the 60 events, we have also studied the T-waves recorded by the island seismic station. We found T-wave in about 54 events, and the T-wave energy is weaker than that in the OBS. We see T-wave energy in the predicted P and S to T conversion time window. Here we use an earthquake Event No. 7 as an example. There is a clean energy occurred in the predicted T-wave arrival time window (Fig. 8). And there is a gap in the T-wave energy, correlating to the conversion points between latitudes 22.6° N to 24° N. These conversion points do not have direct line of sight to the seismic station because part of the 1000 m contour line has blocked them. The first section predicted P to T arrival time is earlier than that of the S arrival. S-waves are always contaminated with first section of Type 1 T-wave, e.g. higher amplitude before S arrival and long duration. The shapes of the T-waves recorded by LYUB are very different. For earthquakes occur to the west of these conversion points, we also observe smaller or no T-wave energy. But earthquakes to the north of this shadow zone usually generate clear T-wave recorded by this island station.
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Figure 8: T-wave recorded by the island station LYUB (Event No. 7). The acceleration waveforms were filtered between 1 and 9 Hz. Note that the predicted P to T arrival time is earlier than that of the S arrival. There is a gap in the T-wave energy, correlating to the conversion points between latitudes 22.6° N to 24° N.
These conversion points do not have direct line of sight to the seismic station, thus might need to have additional conversions, causing a weaker T-wave. We see similar effects for many earthquakes to the north.
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It will be helpful if we can differentiate the main energy that arrives to the OBS from the water column (Type 1 and some Type 2) or from the crust (Type 3). Because the ground motion and water pressure energies arrive at the same time, such ambiguity makes travel path determination difficult. To solve this problem, we had developed a method to differentiate these two cases using a transfer function between the ground accelerations and water pressure changes.
Seafloor is an interface between sea water and solid crust (Fig. 9). These two materials have different modulus. Thus the conversion from acoustic to elastic should have different conversion efficiency than the elastic to acoustic conversion. We had observed that Type 1 and Type 3 T-waves have different ratios between vertical seismic component and DPG-component. If we applied Hooke’s Law in Figure 9, that Type 1 and Type 3 T-waves have different ratios due to the different moduli between crust and sea water.
Figure 9: Two ways of conversions between crust and water column at the seafloor.
Note that we have used a unit energy source while the amplitudes of the transmitted energy for the elastic to acoustic and acoustic to elastic might be different.
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We have plotted the ground acceleration over pressure-change ratios as a function of time for all the 60 events (Fig. 10). We found higher ratios during the P-wave arrivals, and even higher ratios during the S-wave arrivals. However, the ratios during the Type 1 T-wave arrival times are generally low, the results ratios similar to the spectrum ratio in Figure 7e.
All of the spectrograms of 60 events in our OBS station have showed this two different of ratios between two dominant energy pulses, one correlating with the elastic wave arrival times, while the other correlating with the Type 1 T-wave arrival time (Fig.
7 and Appendix). To further exam the ratio between elastic ground acceleration and acoustic pressure in time domain, we had plotted the ratios of all of the events in Figure 11. To choose the time windows of Type 3 P to T, S to T and Type 1 combined T-waves, we have chosen a three-second time window that is 0 to 3 sec after the first arrivals of the phases using the average absolute amplitudes of the OBS waveforms. We can see that
Figure 10: The ground acceleration over pressure-change ratios as a function of time for all the 60 events. The ratios have been normalized. The events are sorted according to the epicentral distance. We found higher ratios during the P wave arrivals, and even higher ratios during the S wave arrivals. However, the ratios for the Type 1 T-wave arrivals (not marked because they are not a function of the epicentral distance) are generally low.
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Type 3 P-T and S-T have wider ranges of ratios than that of the Type 1 T-wave. Overall, Type 1 T-wave has smaller ratios, while the average Type 3 P-T have higher ratios, and Type 3 S-T even higher.
Based on Newton’s second Law, forcing is directly proportional to the acceleration, so we use acceleration rather than velocity ground motions.
p h a
(1)
In our calculation in Figure 11, it may be written as an equation below.
Figure 11: A transfer function defined as the ratio between ground acceleration and water pressure changes. We have studied 60 earthquakes, and plotted such transfer function for the time windows of the travel time P (red), S (green), and Type 1 T-waves (yellow). Note that the Type 1 T-wave has very small transfer functions, while the others have higher ones.
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a a
p h a
(2)
Equation 2 gives a relation between observation and the physical insights. The left side of the equation can be derived from the observed seismic and DPG waveforms.
Equation 1 shows that there might be a linear relationship between the differential pressure changes and the ground acceleration. And in the case of energy propagating from water column to the crust (Type 1 T-wave), the left side has a dimension similar to a kind of transfer function called the seafloor compliance [e.g. Crawford et al., 1991], in which the source is in the denominator while the response is in the numerator. This ratio is relatively constant for Type 1 T-wave. For the case of wave propagating from the crust to the water column at the OBS site, as the case of Type 3, the left side implies that the source is in the numerator while the response is in the denominator. The ratio between the ground acceleration and the water pressure changes becomes another type of transfer function. Figure 11 shows that most of the acceleration over pressure change ratios range between 0.005 to 0.02 for Type 1, 0.01 to 0.1 for Type 3 P-T and 0.01 to 0.3 for Type 3 S-T, respectively.
Next we can derive a dimensionless parameter that we have informally called
Next we can derive a dimensionless parameter that we have informally called