1. Objective
2. Problem
3. Experiments on B4 dataset
4. Experiments on El Mayor Cucupah dataset
5. Finding the right window size
6. Detecting regions containing the fault
7. Further directions
8. Related publications
9. Source code and Test dataset

Objective

The objective of this project is to determine 3-dimensional, local ground displacements caused by an earth-quake. The technique requires pre- and post-earthquake point cloud datasets, such as those collected using air-borne Light Detection and Ranging (Lidar) or SFM generated point clouds from aerial images. A typical aerial point cloud data of a terrain is shown in the figure below.

We used the publicly available B4 Lidar and El Mayor Cucupah datasets. B4 dataset covers the San Andreas Fault System of Central and Southern California. El Mayor Cucupah dataset gives the pre and post earthquake data of the April 4 2010 earthquake that was felt throughout Southern California, Arizona, Nevada, and Baja California Norte, Mexico.
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Problem

This problem is formulated as a point cloud registration problem in which the full point cloud is divided into smaller windows, for which the local displacement that best restores the post earthquake point cloud onto its pre-earthquake equivalent must be found. We used the ICP algorithm to register point clouds.

Initially we introduced a synthetic earthquake on the B4 lidar dataset wherein displacement vectors were introduced on different regions of the terrain and the resulting displacement vectors from ICP were compared with the input displacement vectors. Later we proceeded to test this approach on the El Mayor Cucupah dataset (a real earthquake dataset) and some observations on the resulting displacements were made.
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Experiments on the B4 dataset (Synthetic Earthquake)

Two experiments were conducted with different displacement fields and the results are shown in the figures below.  Black arrows are horizontal displacements and coloured circles denote vertical displacements. The artificial fault introduced is shown as a dotted line, and points on the right side of the fault were given a south east transformation and the points to the left were given a north west transformation. A vertical z displacement was also introduced.

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Experiments on the El Mayor Cucupah dataset (Real Earthquake dataset)

We considered a 2 km x 2 km region in this dataset and presented initial results for the same. The figure below shows the results after registration wherein. The differences in these displacements are clear on either side of the fault (shaded in green).

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Finding the right window size

In the above experiments we assume a fixed window size for registration. We also  investigated an algorithmic way of finding the right window size for registration. We began by choosing an arbitrary window size in the source cloud (e.g. 200 m × 200 m). For each of these windows, the corresponding window in the target data is identified based on x and y coordinates. Next, we computed the rigid body transformation between the source and target windows using the ICP algorithm. This window is split into four smaller windows of equal size and the rigid body transformation is computed on every child window. The transformation is validated after each split and the associated error computed. Based on the differences in error after consecutive splits, we decide whether further splitting is necessary. We verified experimentally that we cannot have small errors for very small window sizes (∼10 m) given the point cloud densities and input displacements. An analysis of this error indicates when to stop splitting yielding the right window size. A detailed description of this approach can be seen in our paper.
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Detecting regions containing the fault

An interesting question to answer in earthquake datasets is ‘Can we find the regions containing a fault?’. Our windowing approach to change detection enabled us to examine this and we came up with an information theoretic approach to classify the windows containing a fault. The following image shows the dataset being split up into multiple windows with the thick black line showing the fault. The results of the information theoretic approach extracting windows containing the fault is shown in the right. A detailed description of this approach can be seen in our paper.

These results were submitted to the International Symposium of Experimental Robotics, 2012 and is under review.
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Further directions

We are now running experiments on the entire dataset covering 850 sq km. One more direction we are looking at is to use SFM generated point clouds instead of Lidar. This offers significant advantages in terms of the cost involved.

The following image shows the point cloud generated using aerial image sequences over a  strip of land obtained from a helicopter. This strip of land coincides with a part of the data in the B4 lidar dataset.

 

The B4 lidar and SFM pointclouds have different co-ordinate systems and before we do change detection, the first task is to align the two point clouds globally. We are considering this problem as a template fitting problem. The best fit for the SFM point cloud in the lidar point cloud is computed and change detection is done after the template fit. We are still working on the results.
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Related publications

• Change detection using Airborne Systems : Applications to Earthquakes   Aravindhan K Krishnan, Edwin Nissen, Srikanth Saripalli and Ramon Arrowsmith. International Symposium on Experimental Robotics (ISER) 2012

• Three-dimensional coseismic surface displacements and rotations from pre- and post-earthquake Lidar point clouds
  Edwin Nissen, Aravindhan K Krishnan, Ramon Arrowsmith and Srikanth Saripalli
  Geophysical Research Letters, 2012

Source code and Test dataset

The source code can be downloaded here. The test dataset can be downloaded here.