Remarkable ground uplift and reverse fault ruptures for the 2013 Bohol earthquake (Mw 7.1), Philippines, revealed by SAR pixel offset analysis
© Kobayashi; licensee Springer. 2014
Received: 5 December 2013
Accepted: 17 February 2014
Published: 17 April 2014
By applying a pixel offset analysis using RADARSAT-2 SAR data to an inland crustal earthquake that occurred on Bohol Island, Philippines on 15 October 2013, we succeeded in mapping a ground displacement associated with the earthquake. The most concentrated crustal deformation with ground displacement exceeding 1 m is located in the northwest part of the island. The crustal deformation is zonally distributed and extends a length of approximately 50 km in the ENE–WSW direction. The ground in the mountainous area moved toward the satellite, while the ground in the northern coastal zone moved away from the satellite. A clear displacement discontinuity with a length of about 5 km, probably corresponding to earthquake surface faults, can be identified in the northeastern region. Our fault model consisting of two rectangular planes shows nearly pure reverse-fault motion on south-southeast-dipping planes with moderate dip angles. A local rupture occurs in the northeast at shallow depths and produces surface ruptures. By applying an additive color process using SAR amplitude images, significant changes in backscatter intensity were detected along the coast from Maribojoc to Loon; these changes suggest that the seafloor uplifted and the shoreline resultantly shifted seaward. The area showing the shoreline change is in good spatial agreement with the locally distributed large ground uplift predicted from our fault model. We identified a good correlation between the ground upheaval produced by the reverse-fault motion and elevation in the mountainous area, which is consistent with the idea that repeated historical reverse faulting developed the present-day topography.
One of the notable features of the seismic event was remarkable ground surface changes, which were observed in field surveys . These changes included the appearance of earthquake surface faults with vertical offsets of several meters and shoreline changes caused by ground uplift. According to reports by the U. S. Geological Survey (USGS) and the Philippine Institute of Volcanology and Seismology (PHIVOLCS), among others, a reverse fault mechanism with a NW–SE compressive axis was inferred from seismic wave analyses, thus vertical ground movements associated with the reverse motion must have been involved in the ground surface changes. However, it remains unclear where and how the fault rupture contributed to these changes. Measurement of ground displacements around the epicentral area certainly plays a key role in answering these questions, but there is no geodetic data from which we could obtain the detailed crustal deformation.
Satellite synthetic aperture radar (SAR) data can provide detailed and spatially comprehensive ground information. Interferometric SAR (InSAR) analysis has the advantage of detecting ground deformation in a vast region with high precision (e.g., [6, 7]). However, for the Bohol event, the standard InSAR approach is not helpful for determining the details of the seismic rupture. Only C– or X-band SAR data are available for the event, thus it is not suitable to apply an InSAR method to measure ground displacement on Bohol Island, which is covered by forest [8–10]. We actually conducted an InSAR analysis using the C-band data we handle in this study, but a coherent loss area resultantly spread over the island. Thus, in order to reveal the unknown surface displacements, we conducted a pixel offset method that enabled us to robustly detect large ground deformation even in incoherent areas [11–13].
We used RADARSAT-2 data from the ascending orbit acquired on 12 January 2013 and 27 October 2013 for data analysis. This data pair provided the shortest temporal baseline among the SAR images covering the source region. The data obtained were strip-map imagery (Wide Multi-Look Fine mode) with an incidence angle of 34.1° at the scene center. The area analyzed is indicated by the frame in Figure 1. We processed the SAR data from SLC products using a software package Gamma . After conducting coregistration between two images acquired before and after the mainshock, we divided the single-look SAR amplitude images into patches and calculated the offset between corresponding patches by using an intensity tracking method. This method was performed by cross-correlating samples of backscatter intensity of a master image with those of a slave image . A pixel offset is feasible even for such incoherent areas provided that a large correlation window is used to track similar speckle patterns . We employed a nearly square search patch of 256 × 256 pixels (range × azimuth: ~680 m × ~640 m). We then reduced the artifact by applying an elevation-dependent correction incorporating NASA Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) data with a 3-arcsec resolution  in the same manner as used by Kobayashi et al. . The measured offset consisted of two components: (1) displacement along the line of sight (range offset) and (2) horizontal movement along the ground parallel to the satellite track (azimuth offset).
Results and discussion
Ground displacement field for the 2013 Bohol earthquake
The azimuth offset field shown in Figure 2b is rather noisy. Crustal deformation produced by reverse-fault motion, in which northward/southward ground movement should be dominant, cannot be identified clearly. However, significant ground movement can be observed near the displacement discontinuity area with a relatively high signal-to-noise ratio. In this area, ground movement opposite to the satellite flight direction (cyan), i.e., nearly southward horizontal displacement, of approximately 0.5 m can be recognized. The southward movement terminates at the displacement discontinuity observed in the range offset (Figure 3b).
Based on the obtained displacement data, we tried to construct a fault model under the assumption of a rectangular fault with uniform slip in an elastic half-space . A rectangular fault model has the advantage that it can represent a macroscopic feature of the source property with simple notation. A slip distribution model would have provided us with a more detailed picture regarding the fault rupture, but the result of the pixel offset analysis would not necessarily have enough measurement accuracy to estimate a more complex slip distribution. Thus, we here provide only a simple-shape fault model.
The offset field has ground surface changes over a vast range, and so produces too many values to be easily assimilated in a modeling scheme. Thus, to reduce the number of data for the modeling analysis, we downsampled the data beforehand, using a quadtree decomposition method. Essentially, we followed an algorithm presented by Jónsson et al. . For a given quadrant, if, after removing the mean, the residue is greater than a prescribed threshold (25 cm in our case), the quadrant is further divided into four new quadrants. This process is iterated until either each block meets the specified criterion or the quadrant reaches a minimum block size (8 × 8 pixels in our case). Upon application of the above-mentioned procedure, the size of the data set was reduced from 471070 to 405 for the range offset data. We also applied the method in the same manner to the azimuth offset data. The azimuth offset data, however, were too noisy to incorporate into the modeling. Therefore, we used only the data in the northeastern area, ranging from 124.00°E to 124.15°E and from 9.95°N to 10.10°N, where the signal-to-noise ratio was relatively high.
For the modeling, we applied a simulated annealing method for searching the optimal fault parameters [19, 20]. We assumed a two-segment model that consists of a main fault producing the majority of the crustal deformation and a local but essential fault located in the northeast producing clear surface offsets. For the main fault, we randomly assigned parameters within the search range of 123.75°–124.00° in longitude, 9.8°–9.9° in latitude, 0–20 km in depth, 0–70 km in length, 0–30 km in width, 0°–90° (180°–270°) in strike, 0–90° in dip, 0°–180° in rake, and 0.0–10.0 m in slip amount. For the northeast fault, the clear displacement offsets reflecting surface ruptures strongly suggested that the fault rupture is rather shallow, thus we here fixed the fault top to be near the ground surface. With knowledge of the displacement discontinuity line, the search range of strike could be strongly limited to within 55°–65° (235°–245°) so as to fit the boundary line. We randomly assigned the other parameters within the search range of 124.10°–124.15° in longitude, 9.85°–10.01° in latitude, 0–10 km in length, 0–30 km in width, 0–90° in dip, 0°–180° in rake, and 0–10.0 m in slip amount. To estimate the individual confidence of each inferred parameter, we employed a bootstrap method .
Fault parameters of our preferred model for the 2013 Bohol event
Shoreline changes revealed by SAR analysis
The major source of error of this method is a tide-level difference between the two SAR data acquisition times. Thus, to confirm the validity of our analysis, we calculated it using Some Programs for Ocean-Tide Loading (SPOTL) software . As a result, the difference in tide level is approximately 9 cm in and around the sea area, thus there would be no serious affect in the analysis result.
Figure 6d shows the model-calculated vertical displacement in and around Maribojoc and Loon, where our fault model predicts a large ground uplift of approximately 1.2 m (at maximum). Compared with other coastal areas, this area is locally subjected to large upheaval. A dotted line indicates the coastal zone showing the increase of backscatter intensity (Figure 7b). The locally distributed large uplift can account for the fact that shoreline changes occurred only in this area.
Relationship between ground movement and topography
There is a good spatial correlation between the range shortening area (warm-colored area) and the mountainous area (Figure 2). In particular, the relationship is obvious in the area from the coast to the north-facing slope of the mountain (lines 1 and 2 in Figure 4). The correlation between the two caused us to think about the landform evolution and whether the spatial correlation could be true. As mentioned in Section Methods, we applied an elevation-dependent correction to reduce the artifact displacement correlating with elevation, but the correction was often insufficient because of the large amount of topographic relief and the accuracy of the DEM data . Thus, we had to consider carefully whether or not the spatial correlation is true. We here confirmed the potential error caused by the topography. For the SAR data pair that we analyzed, the perpendicular baseline of satellite orbit was estimated to be approximately −47 m at the scene center. In this case, the artifact, calculated using a formulation presented by Kobayashi et al. , should be at most 8 cm at the elevation of 500 m. Thus, we concluded that the error produced by the topographic effect can be ignored in this analysis.
Intensive deformation with ground displacement exceeding 1 m extends in the northwest part of the island.
The crustal deformation zone has a length of approximately 50 km in the ENE–WSW direction.
The ground on the southern side of the crustal deformation area moved toward the satellite, while the ground on the northern side moved away from the satellite.
A clear displacement discontinuity with a length of about 5 km, probably corresponding to earthquake surface faults observed in field surveys, can be identified in the northeastern part of the source region.
Our fault model shows nearly pure reverse-fault motions on south-southeast-dipping planes with moderate dip angle. In the northeast, a local fault rupture occurs at shallow depths, causing the appearance of surface ruptures.
Remarkable changes in backscatter intensity were detected along the coast from Maribojoc to Loon by applying an additive color process, and these changes suggest that the seafloor uplifted and the shoreline resultantly shifted seaward.
The ground displacements produced by the reverse-fault motion are correlated with elevation, possibly suggesting that reverse-fault motions on the North Bohol fault have repeated historically and have contributed to the development of the present-day topography.
We used Generic Mapping Tools (GMT) provided by Wessel and Smith  to construct the figures. We are grateful to Dr. Toto, staff member at PHIVOLCS, for providing valuable information on the 2013 Bohol earthquake. We thank two anonymous reviewers and the editor (Prof. Satake) for their helpful comments to improve our manuscript.
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