The 2D embedding map is shown in Fig. 5a. The distance in the embedding map reflects the similarity between earthquakes; that is, the shorter the distance on the embedding map, the greater the similarity between earthquakes. The characters A–H in Fig. 5a indicate the embedding location of the nine selected earthquakes shown in Fig. 4b and Table 1. The earthquakes in eastern Japan (Fig. 5a, Events A, B, C, D, and E) and those in western Japan (Fig. 5a, Events G, H, and I) were separately embedded along Component 1. Events A and C, which are interplate reverse-faulting earthquakes in eastern Japan, appear close in the embedding map. Event E is a shallow reverse-faulting inland earthquake in eastern Japan, and its embedding location is different from those of Events A and C because of the difference in spatial location and dip angle. Events B and D are normal-faulting earthquakes in eastern Japan, and their embedding locations differ along Component 2, which reflects the variety of their spatial locations and dip angles. Event F, a normal-faulting deep-focus earthquake occurring in the subducting plate, is located in the group of earthquakes in eastern Japan on the embedding map, which is reasonable because the occurrence of this event relates to the subduction of the Pacific plate. The embedding locations of Events G and I, which are shallow earthquakes in western Japan, are adjacent, although these events have different fault mechanism types. The focal mechanism of Event G is strike-slip-faulting, while that of Event I is normal-faulting. The reverse-faulting interplate earthquake H is embedded far from Events G and I along Component 2, despite the fact that the spatial location of Event H is close to that of Event G compared to Event I.
Table 1
List of earthquakes plotted in Fig. 5
ID
|
Origin time (JST)
|
Centroid depth (km)
|
Mw
|
Type*
|
A
|
2003-09-26 04:50
|
23
|
7.9
|
R, IP
|
B
|
2008-07-24 00:26
|
104
|
6.8
|
N, IS
|
C
|
2011-03-09 11:45
|
23
|
7.2
|
R, IP
|
D
|
2011-04-11 17:16
|
5
|
6.6
|
N, IL
|
E
|
2004-10-23 17:56
|
5
|
6.6
|
R, IL
|
F
|
2015-05-30 20:23
|
680
|
7.9
|
N, DF
|
G
|
2016-04-16 01:25
|
11
|
7.1
|
S, IL
|
H
|
2019-05-10 08:48
|
26
|
6.2
|
R, IP
|
I
|
2010-05-26 17:53
|
8
|
6.4
|
N, OR
|
*N: Normal-faulting earthquake, R: Reverse-faulting earthquake, S: Strike-faulting earthquake, IL: Inland earthquake, IP: Interplate earthquake, IS: Intraslab earthquake, OR: Outer-rise earthquake, DF: Deep-focus earthquake |
The relationships between the 2D dimensionality-reduced components and the five original source parameters are depicted in Fig. 6. Component 1 strongly corresponds to the spatial location of earthquakes and is larger than − 0.3 for earthquakes in eastern Japan and smaller than − 0.3 for earthquakes in western Japan. A large value of Component 1 corresponds to reverse-faulting interplate earthquakes with a low dip angle along the Japan Trench, whereas a small value of Component 1 corresponds to normal-faulting and reverse-faulting earthquakes in western Japan. Component 2 corresponds to the source depth and x of the source mechanism diagram. A large value of Component 2 corresponds to shallow normal-faulting earthquakes along the Izu-Ogasawara Trench and the Japan Trench as well as normal-faulting inland earthquakes in eastern Japan, whereas a small value of Component 2 corresponds to reverse-faulting interplate earthquakes with low dip angle along the Japan Trench, which have deeper depth and steeper dip angle than events with a large value of Component 1. Reverse-faulting interplate earthquakes in western Japan and deep-focus earthquakes also have a small value of Component 2.
Inverse transformation is useful for the interpretation of dimensionality reduction results, which is available in UMAP. Figure 7 shows the inverse transformation of UMAP, in which several representative positions of the embedding map are inversely transformed into the five source parameters. Here, 15 positions were selected so that the whole embedding map is sampled uniformly. Shallow reverse-faulting earthquakes in eastern Japan are classified into Groups 1 and 2. Most earthquakes of Group 1 are located along the Izu-Bonin Trench, while many events of Group 2 are located in the inland area of eastern Japan. Event E in Fig. 5 is close to Group 2. Interplate reverse-faulting earthquakes in eastern Japan are classified into Groups 3, 4, and 6, which have different horizontal locations and depths. Events A and C are close to Group 3. Group 5 consists of earthquakes along the Kuril Trench of which the reverse-faulting component is dominant. Shallow normal-faulting earthquakes in eastern Japan are distributed in Groups 7 and 8, and their rake angles differ slightly. Event D is close to Group 7. Shallow strike-slip-faulting earthquakes in eastern Japan are distributed in Group 9. Group 10 consists of intermediate-depth earthquakes with a down-dip compressional focal mechanism (Kawakatsu, 1986) in eastern Japan. Deep-focus events in the subducting Pacific plate including Event F are found in Group 11. Groups 12 and 13 include strike-slip-faulting and normal-faulting shallow earthquakes in western Japan, which correspond to Events G and I. The adjacency between Groups 12 and 13 on the embedding map could be caused by the adjacency of their spatial distribution, although their focal mechanism is different. Group 14 includes intermediate-depth earthquakes with a down-dip compressional focal mechanism around the islands of Taiwan. Reverse-faulting interplate earthquakes along the Ryukyu Trench are found in Group 15, which is close to Event H.
These embedding results demonstrate that earthquakes with similar characteristics can be projected on the embedding map by UMAP. The use of UMAP leads to uniformly re-distributing focal mechanisms as much as possible on the embedding map, although the distribution of focal mechanisms is collapsed in the direct mapping (Fig. 2). On the embedding map, earthquakes in eastern and western Japan were embedded separately and further embedded to reflect their characteristic fault mechanism and depth in each region. The degree of similarity of their groups was represented as the distance between the groups on the embedding map. The results indicate that this map can be useful for intuitively and objectively understanding the regional characteristics of earthquake mechanisms and the relationship among earthquake groups.
We also performed a dimensionality reduction of PCA to evaluate the usefulness of the non-linear dimensionality reduction method (Fig. 8). The distribution of PCA embedding is highly skewed, while earthquakes are distributed over the whole region with little bias in UMAP embedding (Fig. 5a). Moreover, earthquakes in eastern and western Japan are separately distributed in UMAP embedding, which is not the case in PCA embedding. Despite the fact that the spatial location differs among the three reverse-faulting interplate earthquakes (A, C, and H), they are concentrated in one place of the PCA embedding. These results suggest that 2D PCA embedding does not contain the data structure of the original moment tensor catalog, while non-linear dimensionality reduction methods such as UMAP are superior in terms of data visualization of geospatial data including the moment tensor catalog.
In this study, the strike information of the fault mechanism is not considered in the dimensionality reduction for simplicity. Because the consideration of strike information is important to know the direction of principal stress, the use of strike information in our dimensionality reduction could lead to obtaining new insight into the spatial variety of focal mechanisms through the explanatory analysis. Moreover, there are other source parameters that were not considered in this study such as time of earthquake occurrence, earthquake magnitude, and CLVD source. How to incorporate the other information into the dimensionality reduction is future work.