3-D CO-Seismic Displacements using Point-Like Targets Offset Tracking
Hu, Xie1; Wang, Teng2; Liao, Mingsheng1
1Wuhan University, CHINA; 2Wuhan University; King Abdullah University of Science and Technology, CHINA
SAR Interferometry (InSAR) has been widely used to monitor the ground displacements, however, only along the line-of-sight (LOS) direction. On the other hand, offset tracking method offers an alternative approach to extract rapid and large displacements, e.g., glacier motion, dune migration, co-seismic deformation, etc. . It is achieved by locating the cross-correlation peak between the average distributed patches between the master and slave images. Despite being less accurate than InSAR technique, offset tracking provides displacement measurements in two directions (azimuth and range). Moreover, when both ascending and descending data are available, we are able to measure the pixel offsets in four different directions, allowing us to obtain the complete 3-D displacement fields by the least-square estimation . In addition, the phase unwrapping procedure can be avoided .
In order to reduce computational burden and to improve the accuracy of pixel offsets, we firstly detect image patches within bright point-like targets (PT) using a sinc-like template, and then perform offset tracking on them to obtain the pixel offsets, and this method is referred to as PT offset tracking . In this paper, we present the first result of deriving complete 3-D co-seismic displacement field only from PT offset tracking. SAR image pairs from ascending ALOS PALSAR and descending ENVISAT ASAR are used to map the co-seismic displacement of 2010 M7.2 El Mayor-Cucapah earthquake in Baja California, Mexico and Southernmost California, USA.
2. 3-D PT OFFSET TRACKING
The core idea of offset tracking is the cross-correlation algorithm, which obtains pixel offsets between the extended match patches from two SAR amplitude images . However, high relative Doppler centroid, large spatial baseline and long temporal intervals contribute to the loss of cross-correlation, which may lead to incorrect offset estimations. Nevertheless, high amplitude cross-correlation can be expected from PT, such as buildings, bare rocks, etc., implying more accurate pixel offset estimations .
Since the signal reflected from an ideal PT behaves as a 2-D sinc function , the cross-correlation between the master image and a sinc-like 2-D impulse response template can be used to identify the PT candidates. The normalized master-sinc cross-correlation can be used as the weight to enhance the amplitude of a PT and also to suppress the other high amplitude pixels, such as that from fore-shortening effects or side-lobes. Hence, the product of the correlation coefficient and the amplitude of the PT candidates should be much larger than that of the others, and then be easily identified . Afterwards, the locations of detected PT are used as the input for the pixel-offset tracking.
In order to obtain the complete 3-D displacements, we need the measurements in at least three different directions. However, even both ascending and descending SAR sensors pass over the same region, the deformation can be only measured along two LOS directions from the interferograms. Since measurements along four different directions (azimuth and range directions respectively) are available from the results of PT offset tracking using ascending and descending tracks, the complete 3-D displacements can be simply derived by the least-square estimation.
3. APPLICATION ON THE M7.2 EL MAYOR-CUCAPAH EARTHQUAKE
The presented method was applied on the M7.2 El Mayor-Cucapah earthquake on April 4th, 2010 that struck northern Baja California, Mexico, at a shallow depth along the principal transform boundary between the North American and Pacific plates.
Fig. 1. Setting of the 2010 El Mayor-Cucapah earthquake.
The study area was imaged by both C-band ENVISAT ASAR and L-band ALOS PALSAR image pairs. We used the pixel offsets from the pair of descending ASAR orbit (track 084) spanning a time interval of one week before, and one month after the earthquake (2010/03/28-2010/05/02), and the pair of ascending PALSAR orbit (track 211) spanning a time interval of approximately four months before, and one month after the earthquake (2009/12/17-2010/05/04).
PT offset tracking is applied to obtain pixel offsets for both data sets. A pixel is regarded as a PT candidate when the normalized master-sinc cross-correlation is larger than 0.2 and the product of the cross-correlation and the amplitude value is larger than an adaptive threshold, i.e., the mean of the amplitude plus 1.5 times the standard deviation (STD) in each block . When extracting the prominent PT, the minimum master-slave cross-correlation is set as 0.45 and the maximum variations in azimuth and range directions are set as 0.004 and 0.0015 according to their histograms.
At this moment, we are ready to measure the 3-D displacements from the obtained pixel-offsets. However, the number of prominent PT from ASAR images (93 909) is far larger than that of PALSAR images (25 955) as a result of larger spatial coverage. In order to match each point between the two sets of data, we firstly make a coarse co-registration on both data. Then, for each PALSAR patch, if the distance to the nearest point of an ASAR patch is less than 300 m, they are assumed to be measured from the same displacement, i.e. making an observation vector D. Finally, 10 972 matches were obtained from the two datasets (green dots in Fig. 1). Four measurements of each match are used to derive the complete 3-D displacements.
For the purpose of the better visualization, we make a more continuous displacement plane based on the discrete offsets. A discontinuity is expected near the rupture, while a simple interpolation may smooth the significant dislocation, and we use the idea of down-sampling, i.e., regular grid decomposition and quadtree decomposition.
Fig. 2. Regular grid decomposition: a) north-south, b) east-west and c) vertical, and positive means northward, eastward and uplift respectively.
The results show the northeast plate and the southwest plate moved to the opposite directions in all three dimensions. The clear asymmetry of near-surface strain with respect to the rupture plane indicates the complex fault geometry at depth.The approximate northwest endpoint of the rupture is located at 32.62deg N, -115.75deg W, and the rupture extended for ~60 km on a S36degE orientation to the southeast of the epicenter, which is consistent with the field report. According to the horizontal plane, i.e., north and east dimensions, we can clearly observe right-lateral motion near the rupture. On the vertical dimension, the southwest plate moves upward slightly, while the northeast plate moves with a more significant downward trend.