Monitoring of Tsunami/Earthquake Damages by Polarimetric Microwave Remote Sensing Technique

3.1 Y4R and S4R

Y4R and S4R decompose the target by linearly expanding matrix T′on the four canonical scattering models, as illustrated in Figure 1:

where TS′, TD′, TV′, and TC′denote the surface scattering model, the double-bounce scattering model, the volume scattering model, and the helix scattering model, respectively:

Parameters fS, fD, fV, and fCin Eq. (8) represent the contributions of the four components; βand αin TS′and TD′are complex parameters; a, b, c, and din TV′are real constants satisfying a+b+c=1, which involve in four volume scattering models and are adaptively selected according to the branch conditions [27, 28]. Combining Eqs. (8) and (9), the S4R/Y4Rscattering balance equation system on unknowns fS, fD, fV, fC, α, and βis formulated [26, 27]:

Nevertheless, we obtain no scattering balance equation on T13′in Eq. (10). Hence, there always exists a T13′-related unaccounted residue in Y4R and S4R.

3.2 G4U

To model T13′, G4U uses U3φto conduct unitary transformation to both sides of Eq. (10) first and then eliminates the influence of φ[28]. As a result, an additional balance equation is brought into G4U, and we obtain the following scattering balance equation system [30]:

Comparing Eq. (11) with Eq. (10), we can find that Eq. (11–2) gives a dichotomy to Eq. (10–2). The redundancy makes Eq. (11) have no such exact solution like Eq. (10) but some approximate ones. In G4U, Singh et al. preferred the first equation of (11–2) only.

3.3 GG4U: generalization of G4U

Obviously, Eq. (11) provides us a generalized G4U (GG4U). Here we focus on the general solution to (11) for the unknowns fS, fD, fV, fC, α, and β. Let

where μis a real constant. Then Eq. (11) can be rearranged as

Eq. (13) comprises of five equations and six unknowns. Following Freeman-Durden [23] and Yamaguchi et al. [24], we can fix αor βin terms of the sign of S−Dfor the superior between surface scattering and double-bounce scattering:

where BC=S−D. Combining Eqs. (13) and (14), we can then simply obtain the scattering power of each of the four components, i.e., the surface scattering power PS, the double-bounce scattering power PD, the volume scattering power PV, and the helix scattering power PC:

where H·denotes the Heaviside step function, which is used here to adjust the value of PCfor nonnegative PVruling [27]. It can be easily validated that PS+PD+PV+PC=T11′+T22′+T33′. Thus GG4U gives a decomposition of scattering power.

3.4 Special decompositions

By taking appropriate value to μ, we can have some different decompositions, which are denoted as Gμ. Here we are particularly interested to the following special cases of Gμ.

Case (1): G+1≔G4U

This is just the parameter Cused in G4U. GG4U changes to G4U in this case.

Case (2): G−1≔DG4U

This acts as the complement of case (1); thus we name it the dual G4U (DG4U).

Case (3): G0≔S4R

This is the parameter Cused in S4R, i.e., S4R also shows a special form of GG4U. Hence, the essential difference between S4R and G4U just lies in the different definition of parameter Cin Eqs. (16) and (18). The unitary transformation is just to enable the T13′entry contained in CG4Uand finally in PSand PD. Parameter Cdefined in Eq. (12) is a generalization of CG4Uand CS4R.

3.5 Theoretical evaluation of S4R and G4U

S4R can improve Y4R by strengthening the double-bounce scattering in urban area [27]. Singh et al. [28] indicated that G4U could further improve S4R in this aspect by strengthening surface scattering in the area where surface scattering is preferable to double-bounce scattering, while increasing the double-bounce scattering in the urban area where the double-bounce scattering is preferable to surface scattering. By combining the ruling in Eq. (14), we can formulate these observations as

In terms of the general expression of PSand PDin (15), here we give a simple validation to Eq. (19) by combining μ=0and μ=1into Eqs. (12) and (15):

From Eq. (20) we have

Then Eq. (19) will hold if 2C12−C1+C22≥0. Obviously, this condition is not always tenable. Hence, despite better performance in some areas, G4U cannot improve S4R for every target area. To tackle this, the extended G4U (EG4U) will be developed in the following as an adaptive combination of G4U and DG4U.

3.6 EG4U: adaptive combination of G4U and DG4U

Combining μ=−1into Eqs. (12) and (15), DG4U surface and double-bounce scattering powers can be formulated as

Combining Eqs. (20) and (22), after some simple deduction, we obtain

We can immediately obtain from Eq. (23) that

From Eq. (24) we obtain

where BC1=C1−C2. Eq. (26) just lays the foundation for EG4U:

As the adaptive combination of G4U and DG4U, EG4U is also a special case of GG4U. So we denote it as G±1. By bringing μ=+1or μ=−1into Eqs. (12) and (15) based on the branch condition BC1, we can achieve the scattering powers of four components in EG4U. Furthermore, from Eqs. (25) to (27), we have

Compared with S4R and G4U, EG4U increases surface scattering in area where surface scattering is superior to double-bounce scattering and strengthens double-bounce scattering in area where double-bounce scattering is preferable to surface scattering. Therefore, EG4U achieves not only a nice improvement to S4R, but also an effective extension to G4U. This may make EG4U more suitable to the remote sensing of tsunami/earthquake. We will investigate this in Section 4. The procedure of EG4U is outlined in Algorithm 1.

Algorithm 1: EG4U

01: Input: T

02: Conduct deorientation to Tfor T′

03: Compute helix power PC=2ImT23′HT33′−ImT23′

04: Calculate branch condition BC

05: Determine volume scattering model based on branch condition

06: Obtain volume scattering power PV=2T33′−PC/2c

07: Compute parameters S, D, C1, and C2, as well as branch condition BC1

08: Implement SPANreservation ruling based on S+D

09: if S+D>0

10: Adaptively select between G4U and DG4U based on BC1

11: if BC1>0

12: C=C1

13: else

14: C=C2

15: end if

16: Calculate surface scattering power PSand double-bounce scattering power

PDaccording to BC

17: if BC>0

18: PS=S+C2/S,PD=D−C2/S

19: else

20: PS=S−C2/D,PD=D+C2/D

21: end if

22: Implement nonnegative PSand PDruling

23: else

24: PS=PD=0,PV=T11′+T22′+T33′−PC

25: end if

26: Output: PS,PD,PV,PC

4.1 Great Tohoku earthquake and tsunami

The great Tohoku earthquake is also known as the great Sendai earthquake or the great East Japan earthquake, which was a magnitude 9.0–9.1 (Mw) undersea megathrust earthquake off the coast of northeast Japan (the epicenter is shown in Figure 2 as “”) that occurred on March 11, 2011, the most powerful earthquake ever recorded in Japan [34]. The earthquake triggered powerful tsunami, which swept the mainland of Japan, killed over 10,000 people (mainly through drowning), and damaged over 1,000,000 buildings (half of them are collapsed and even totally collapsed) [35].

4.2 Datasets

The Advanced Land Observing Satellite (ALOS) was launched in 2006 by the Japanese Space Agency (JAXA). It has three remote sensing payloads, i.e., the Panchromatic Remote-sensing Instrument for Stereo Mapping (PRISM) for digital elevation mapping, the Advanced Visible and Near Infrared Radiometer type 2 (AVNIR-2) for precise land coverage observation, and the Phased Array type L-band SAR (PALSAR) for all-day/all-weather land observation [36].

To demonstrate the capability of polarimetric remote sensing for damage monitoring, we choose two quad-polarization single-look complex-level 1.1 (ascending orbit) datasets acquired around Miyagi Prefecture, Japan, before and after the earthquake/tsunami with 138 days’ temporal baseline, as summarized in Table 1. The ALOS-PALSAR footprint of the two datasets is shown in Figure 2.

4.3 Method

The flowchart of EG4U-based monitoring and evaluation of damages caused by tsunami/earthquake disaster is illustrated in Figure 3. We first co-register the two datasets based on the image features [37, 38, 39, 40]. The boxcar filtering [9] is then carried out to both datasets to suppress the speckles. To ensure the pixel size in both image directions comparable, the window size for ensemble average is chosen as 2 pixels in ground-range direction and 12 pixels in azimuth direction, i.e., we integrate the scattering matrix Sof a total of 24 pixels for the estimation of a coherency matrix Tin Eq. (2). From Twe calculate the orientation angle θaccording to Eq. (4) and implement the deorientation operation for the deoriented coherency matrix ⟨[T′]⟩ according to Eq. (5). Finally, EG4U is used to decompose ⟨[T′]⟩ to extract scattering powers PS, PD, PV, and PCand construct the RGB pseudo-color scattering power visualization result by encoding RGBwith PDPVPS. This process is executed on each cell of the two datasets until we obtain the complete pre- and post-event scattering power images shown in Figure 4, based on which we evaluate EG4U on monitoring of the tsunami/earthquake disaster in the following.

4.4 Evaluation and analysis

For better comparison and analysis, we also display the optical image of the study area obtained from ©Google Earth in Figure 5. Our intuitive impression of Figure 4(a) and (b) is their consistency and nice correspondence to the optical image. The blue color mainly appears in the water and land areas because of the dominant surface scattering there. The red color mainly arises in the urban area, such as the Ishinomaki City and Higashi-Matsushima City, with a large number of buildings. The ground and the vertical walls of buildings constitute the dihedral corner structures, which generally reflect the dominant double-bounce scattering. Mountain presents the green color, i.e., the dominant volume scattering. The well-developed branch and crown structures of trees on the mountain complicate the scattering process, depolarize the scattering wave, and show themselves as the complex mixed volume scattering in PolSAR image. Therefore, by color-coding the scattering powers obtained by EG4U, we can achieve a nice discrimination of the ground objects.

Despite the consistency, we can also observe the obvious difference between the pre- and post-event scattering power images. A lot of red pixels in Figure 4(a) change to blue pixels in Figure 4(b), particularly in the urban areas of Ishinomaki and Higashi-Matsushima, which illustrate the change from the dominant double-bounce scattering to the dominant surface scattering, denote the decrease of the dihedral structures, and indicate the collapse of buildings. Take Ishinomaki City framed in Patch A for instance; it is interesting to observe that the strong change mainly arises in the area by the seaside, while tiny change occurs in the area away from the coast. This finding is also validated by the corresponding optical images acquired before and after the event shown in Figure 6(a) and (b). Therefore, the severe damages brought by the Tohoku tsunami/earthquake are probably mainly due to the flooding rather than the earthquake. Flooding from the Onagawa Bay and the Mangokuura Sea also swept the town of Onagawa framed in Patch B, as shown in Figure 6(c) and (d) in terms of the pre- and post-event optical images. A large majority of red pixels of Patch B in Figure 4(a) change to blue pixels or even green pixels in Figure 4(b), which indicates that nearly all the buildings in Onagawa were badly damaged by the flooding except for a few buildings constructed in high elevation. The collapsed buildings not only present the dominant surface scattering here, but also the dominant volume scattering because of the complex scattering in such mountain area. The biggest change caused by flooding appears in the area along the Kitakami River. Take the town of Kamaya framed in Patch C, for example, as shown in Figure 6(e), besides several buildings, the most part of Kamaya is farmland. This area can be clearly distinguished from the Kitakami River in Figure 4(a) before the disaster. However, after the disaster, nearly all the land and buildings in Kamaya are flooded by the water from Kitakami River as shown in Figure 6(f), which present in Figure 4(b) as the wide distribution of blue pixels and show the dominant surface scattering here. Therefore, by decomposing the pre- and post-event PolSAR datasets with EG4U to construct the color-coded scattering power images, we can achieve a simple but accurate monitoring of the damages caused by tsunami/earthquake disaster.

From the above analysis, we can obtain that flooding which resulted from tsunami is the main contributor to the severe damages in the 3.11 great Tohoku earthquake. The flooding destroyed the buildings and inundated the lands. All these damages present themselves in the polarization domain as the change of the dominant scattering mechanism from double-bounce scattering to surface scattering and in the image domain as the change of pixel color from red to blue. The boundary condition BChas been widely used in model-based decomposition as a crucial feature to discriminate surface scattering and double-bounce scattering [23, 24, 26, 27, 28]. As expressed in Eq. (14), BC>0indicates stronger surface scattering than double-bounce scattering, while BC≤0denotes stronger double-bounce scattering than surface scattering. Therefore, besides the qualitative evaluation in terms of color, we can further achieve an quantitative evaluation of the damages by analyzing the dominant scattering according to BC. Figure 7(a) and (b) show the binary images of BCbefore and after the disaster, respectively. The white pixel denotes BC>0, i.e., the dominant surface scattering, which mainly occupies the water and land areas, while the black one denotes BC≤0, i.e., the dominant double-bounce scattering, which mainly occupies the urban and mountain areas. Before disaster, the black pixels account for 15.1641%of the whole image, while this ratio decreases to 13.0785%after the disaster, i.e., the dominant scattering mechanism of about 2.0856%area of the scene is changed from double-bounce scattering to surface scattering. As shown in Figure 7, the change mainly arises in the urban area like the Ishinomaki City and Higashi-Matsushima City, in the land area like the town of Kamaya, as well as in the water area like the Mangokuura Sea, Onagawa Bay, and Kitakami River. This further provides us a consistently quantitative evaluation of the damages. All these demonstrate the importance and value of polarimetric microwave remote sensing technique in the monitoring of tsunami/earthquake damages.

Singh et al. [28] indicated that G4U could enhance double-bounce scattering over urban area while strengthen surface scattering contribution over water and land area. This establishes G4U the state-of-the-art four-component scattering power decomposition and enables its wide application to the remote sensing of forestry, agriculture, wetland, snow, glaciated terrain, earth surface, manmade target, environment, and damages caused by earthquake, tsunami, and landslide [29, 30]. Nevertheless, the rigorous derivation in Eq. (21) validates that G4U cannot always enhance the double-bounce scattering nor strengthen the surface scattering power unless we adaptively integrate G4U and its duality, i.e., DG4U, for EG4U based on another boundary condition BC1. As expressed in Eq. (27), G4U is selected only when BC1>0; otherwise, we should turn to DG4U. The binary images Figure 8(a) and (b) further show the pre- and post-event BC1, respectively, where the white pixels (i.e., BC1>0) indicate the area where G4U operates and the black pixels (i.e., BC1≤0) give the area where DG4U operates. The white pixels account for 46.4260%of the pre-event image, which conveys that G4U achieves better result than S4R only for 46.4260%area. As for the rest 53.5740%area, we should resort to DG4U for improvement. The ratio of white pixels increases to 49.5247%after the disaster. Nevertheless, there are still half a little more areas where G4U will underestimate the surface or double-bounce scattering. If we adopt G4U in this area to evaluate damages caused by tsunami/earthquake, the reduced double-bounce scattering from G4U may lead to the underestimation of building scale and overestimation of damage level. EG4U can adaptively increase the surface scattering or double-bounce scattering. Hence, it definitely improves the competence and performance of G4U in the remote sensing of damages caused by earthquake/tsunami.