**5.1 Full moment tensor inversion for the** *M***<sup>W</sup> 7.9 Earthquake**

Using the method outlined above, we performed the full moment tensor inversions for the Rat Islands earthquake using a range of focal depths and provided the moment tensor solution obtained using a focal depth of 105 km.

#### *5.1.1 Rayleigh wave records*

Since the Rat Islands *M***<sup>W</sup> 7.9** earthquake was very large, it generated very strong Rayleigh waves, recorded at stations throughout the world. Hundreds of these waveform records were on the LHZ (long period, high gain, and vertical component) channel. We selected vertical records from 57 stations, filtered those records with a band-pass filter of 135 s to 500 s, and decimated the sampling interval from 1 s to 10 s. When the velocity of the mantle waves is assumed to be on the order of 3 km/s, the shortest wavelength is on the order of 400 km, which was approximately seven times of the rupture length of this *M*<sup>W</sup> 7.9 earthquake. For such long-period mantle waves, the earthquake source can be treated as a point source.

#### *5.1.2 Full moment tensor inversions*

We conducted the following tests using a depth range from 80 km to 120 km with a depth increment of 5 km. For each focal depth, (1) we calculated the Green's functions, (2) took the same length for the observed Rayleigh wave record aligned with the synthetic seismogram, calculated at the focal depth, and (3) performed a full moment tensor inversion. The used source time function was three overlapping triangles. The time length of each bottom side was 20 s. **Table 1** lists the obtained

*Studies on the Source Parameters of the 23 June 2014 Rat Islands, Alaska… DOI: http://dx.doi.org/10.5772/intechopen.104600*

parameters for the full moment tensor solution using our preferred focal depth of 105 km. Compared to the scalar moment of the major DC in **Table 1**, the isotropic (ISO) is 2.88%. At all other depths from 80 km to 120 km (not listed), the ISO as a percentage of the total seismic moment was less than 6%. The smallest ISO occurred at the depth of 95 km.

The trace (trace = 3 ISO; e.g., [11]) obtained in our inversions was small. As the trace quantifies a volume change in the source region (e.g., [11]), the small trace implied that the change of the earth's material volume in the source region was small. Compared to the major DC moment in **Table 1**, the minor DC moment was only 3.64%. The small minor DC and small ISO moments imply that the Rat Islands mainshock was dominated by a major DC event.

To evaluate the creditability of the solutions we need to compare the synthetic seismograms with those of the observed ones. **Figure 7** shows the moment tensor projection and the waveform comparison for the first four pairs of seismograms. The similarities between the synthetic and observed seismograms in both the waveform shapes and the maximum amplitude ratios were good. Other pairs at the remaining 53 stations had a similar quality. The good waveform fit implies that the moment tensor solution obtained is reasonable.

#### **Figure 7.**

*(a) The lower hemispherical projection of the moment tensor solution obtained using a depth of 105 km. (b) Comparison between the first 4 observed and synthetic seismograms used in the inversion. For each pair, the upper trace is the observed (solid line), and the lower trace is the synthetic (dashed-line), generated with the solution displayed in panel (a). Both the observed and synthetic waveforms were filtered with a band-pass filter in the range of 135 s to 500 s. The symbols and numbers on the left side of each pair from the top to the bottom indicate the station name, vertical component, station distance in degree, station azimuth in degree, and the ratio between the observed and synthetic maximum amplitudes. The waveform shape similarity and the small bias of the ratios from an ideal case (ratio = 1) show that the fit is good.*

## **5.2 Relocation of aftershocks with magnitude** ≥ **4.5**

There are two nodal plane solutions in **Table 1**. One nodal plane is close to the rupture plane of the *M*<sup>W</sup> 7.9 mainshock. The hypocentral distribution of the aftershocks could help us to identify which nodal plane is close to the rupture plane. The requirement is that the errors in the hypocenters should be small. To obtain a distribution of hypocenters with small error, the aftershocks with magnitude ≥ 4.5 were relocated.

The error in the focal depth obtained using a conventional method may be large. The reason is that the travel times of the P and S phases are dominated by the station distance, not the focal depth. We used a combined procedure to relocate the aftershocks.

We searched tele-depth phase pP from the vertical component (BHZ) of teleseismic P-wave records retrieved from IRIS for 23 aftershocks that occurred


*Note: lat. means latitude (°); lon., longitude (°); depth in km; m, magnitude; t-err, error in the origin time (s); lat-err, error in latitude (km); lon-err, error in longitude (km). The magnitude values are from the IRIS database. The bold text shows the 5 larger aftershocks.*

#### **Table 2.**

*Catalog of the 23 relocated aftershocks.*

### *Studies on the Source Parameters of the 23 June 2014 Rat Islands, Alaska… DOI: http://dx.doi.org/10.5772/intechopen.104600*

between June 23 and July 11, 2014, with magnitude ≥ 4.5, and determined focal depths for these 23 aftershocks using depth phase pP [16]. Then the arrival times of the recorded P and S phases at the same four regional stations for these 23 aftershocks were carefully measured, and the SEISAN [24, 25] was used to locate the epicenters at the focal depth obtained using the depth phase pP. The re-located 23 aftershocks were listed in **Table 2**.

The bird-view distribution of the obtained 23 hypocenters in **Figure 8** shows that the hypocenters are separated into two groups. Group 1 was formed by the hypocenters with the lighter color, while group 2 was formed by the hypocenters with the deeper color. **Figure 9a** shows the hypocenter projection onto a vertical plane perpendicular to the steep-dip plane (nodal plane 2). Eleven (11) aftershocks in group 2 formed a linear trend in the steep-dipping direction. The other hypocenters are scattered. **Figure 9b** shows the hypocenter projection onto a vertical plane, perpendicular to the shallow-dip plane, indicated with P1 projection (nodal plane 1). No linear trend was formed by the hypocenters at the dipping (27.1°) direction of the shallow-dip plane.

In order to observe a spatial trend, we simulated a plane using the hypocenters of the 23 well relocated aftershocks. **Figure 10** shows the simulated spatial plane. Its strike is at Az 258.2°; its dip angle is 44.8°. To clearly observe the dipping of the simulated plane we projected the hypocenters of the mainshock and the 23 aftershocks onto a vertical plane which is along the simulated dipping direction. **Figure 11** shows that most hypocenters were distributed along the tilted line, the projection of the simulated plane, at dip angle 44.8°. This angle is close to the one (47.7° in Figure 4a)

#### **Figure 8.**

*Distribution of the epicenters for the mainshock and the 23 relocated aftershocks. Each solid circle shows an epicenter. It was color-coded with focal depth. A deeper color shows a deeper depth. The size of each circle is proportional to the magnitude. The epicenters are separated into a shallower group (group 1) and a deeper group (group 2). The strike and the dipping directions of two nodal planes of the mainshock were indicated with strike 1 and dipping 1(shallow-dip plane); strike 2 and dipping 2 (steep-dip plane), respectively. The latitude and longitude of each epicenter were converted to a Cartesian coordinate system for distance comparison. The star with Mw 7.9 shows the epicenter of the mainshock.*

#### **Figure 9.**

*Hypocenter projections. (a) The hypocenters of the mainshock and the 23 relocated aftershocks projected onto a vertical plane that is perpendicular to the steep-dip nodal plane (P2). The tilted dashed line indicated with 84.2° is the projection of the steep-dip plane. The number 84.2 is the dip angle. Eleven (11) aftershocks in group 2 formed an about 15 km linear trend along the steep-dip plane. (b) The hypocenters of the mainshock and the 23 relocated aftershocks are projected onto a vertical plane that is perpendicular to the shallow-dip plane (P1). The tilted dashed line indicated with 27.1° is the projection of the shallow-dip plane. It was found that no linear trend was formed along a nodal plane (P1).*

#### **Figure 10.**

*The simulated spatial plane uses the hypocenters of the 23 well-relocated aftershocks (Table 2). The simulated strike is Az 258.2°; the dip angle is 44.8°. The plane dips at Az 348.2° (from north to west 11.8°). The red star shows the initial location of the mainshock.*

*Studies on the Source Parameters of the 23 June 2014 Rat Islands, Alaska… DOI: http://dx.doi.org/10.5772/intechopen.104600*

#### **Figure 11.**

*The hypocenters of the mainshock and the 23 relocated aftershocks are projected onto a vertical plane that is along the simulated dipping direction (perpendicular to the simulated spatial plane. The tilted dashed line indicated with 44.8° (dip angle) is the projection of the simulated plane. The red star shows the initial location of the mainshock. The relatively narrow seismicity belt may be assumed to be close to the boundary between the Pacific Plate and the North American plate beneath the Rat Islands region.*

obtained by simulating hypocenters of the earthquakes occurred before the mainshock. They are neither close to the steep-dip angle 84.2° nor the shallow-dip angle 27.1°. The trend may be close to the boundary between the Pacific plate and the north America plate beneath the Rat Islands region.
