Hi. My name is Xinxiang Zhu. Today I would like to talk about urban
geodesy along the Hayward Fault – automated detection of planar
primitives in mobile Lidar data and change detection.
The earthquake sheared the Earth with a unique a [inaudible] landform
caused by the faulting process. To study this process,
one of the initial observations one can acquire is measurement
of fault-related land deformation.
For example, shown in this figure,
a straight fence is deformed due to the strike-slip fault movement.
Ground displacement in the far field has an analytical form, shown on the left,
where the number of the contour shows the normalized displacement magnitude,
and arrows on the dashed lines shows the direction of the ground motion.
This analytical pattern has been confirmed by, for example,
the InSAR measurement of the 2003 Bam, Iran, earthquake.
In the near field, within hundreds of meters from the fault trace,
the ground displacement is not linear.
For example, the deformation of the fence is highlighted in red.
An analytical form of off-fault displacement profile is shown on the
left, where the X axis represent distances from a fault trace, and Y axis represent
ground displacement induced by various underlying rock properties.
This profile only exhibit distinguishable curvatures
in the near field from which we can study the shallow-slip deficit.
However, the corresponding geodetic signature is extremely hard to collect.
This is because the curvature require dense observations
in the near field to quantify, therefore limit the application
of traditional sparse geodetic observations.
And the scale of the change can be smaller than the
critical detection threshold of some geodetic tools.
In this study, we propose a new method using
mobile Lidar data to detect fault displacement in the near field.
Using mobile Lidar data sets, we explore the Lidar change detection
strategies and develop this method called modeling-based
change detection using geometric primitives.
Shown here are our change detection result for the 2014 South Napa
earthquake where point cloud are model are simple
geometric models that can be described by a few free parameters,
so-called geometric primitives.
By model the 1-yard rows as planar primitives, we were able to recover
25-centimeter coseismic displacement,
which agree with in situ and alignment array measurement at decimeter level.
By model the anchor posts as cylindrical primitives, we were able to recover the
postseismic displacement approximately one month after the main shock.
And the detected postseismic displacement agree with
co-located alignment array measurements at sub-centimeter scale.
Here shows the postseismic displacement profile revealed by
the cylindrical primitives, where the fault-parallel displacement
and the angular change are distributed against off-fault distances.
The reason that we achieve high accuracy change detection
is because we model point cloud as primitives.
Shown in this figure, the reference and the secondary point cloud can be treated
as Lidar measurements collected before and after a fault movement.
And, if we model point cloud as plane surface and calculate the point-to-point
distances, the model-to-model distances are a more robust estimator of the
true displacement compared with point-to-point distances.
This is because the point-to-point correspondence is highly unstable
due to the irregular format of the point cloud.
Here we show experiment where a displacement is randomly generated,
and the two change detection strategies
are performed to recover the simulated deformation.
The residual of the recovered deformation is found here.
And the modeling-based change detection result is smallest residual
compared with change detection using point-to-point distances,
which is the default metric behind a popular change detection
algorithm called iterative closest point, or ICP.
ICP is the dominant method processing Lidar point cloud
for the purpose of fault deformation monitoring.
And, as you can see, the modeling-based change detection outperformed the
ICP method by almost one order in this experiment.
Therefore, the modeling-based change detection using geometric primitives
is preferred to detect subtle fault creep displacement that is
characterized by steady and gradual deformation over years.
In order to model primitives in the urban environment, we adapted a
detector based on the classic random sample consensus, or RANSAC.
This new detector can extract corresponding planar primitives
parallelly from the reference and the secondary data sets
collected before and after the change.
For example, planar surface, like building walls, roofs, and garage doors
can be extracted parallelly by the detector to trace the fault creep deformation.
And the corresponding primitives are color-coded and ordered by
the number of points exist in both data sets.
Using the corresponding planar primitives, a shear deformation
represent fault creep displacement can be estimated
from augmentation of primitives.
In other words, the fault creep displacement of a house,
shown in the previous slide, can be estimated by tracking
the coincident movement of these walls, roofs, garage doors,
and other planar surfaces that are extracted by the new detector.
This estimation uses a combined least square regression
that is originally developed for Lidar sensor calibration.
Using this new method, we analyzed mobile Lidar data collected along
a 2-kilometer segment of the Hayward Fault, and we validate
the change detection result with fault creep measurements
of an alignment array located at Camellia Drive.
Here shows the 10-year fault creep displacement detected by
satellite surveys at the alignment array stations.
Again, here shows our study area and our change detection result.
For visualization purposes, let’s down-sample our displacement
vector a little bit and give it a imagery base layer.
Here shows the change detection result for the
Hayward Fault creep observed from July 2015 to June 2017.
The arrow represent the ground displacement vector
with the size proportional to the change.
If we project the displacement vector along the fault trace, we can get this
heat map where the color shows the normalized fault-parallel displacement.
From the change detection result, we find uniform strike-slip
displacement in the far field. And, in the near field,
we find this interesting rotationing pattern that are
rarely observed from other geodetic data sets.
To validate our change detection result, we compare the detected fault creep
displacement with co-located alignment array measurements at Camellia Drive.
Arrows shows in this plot represent fault creep displacement
detected by our method. And average fault-parallel displacement
near the alignment array benchmarks are calculated for validation.
The comparison results are reported here where the difference
between the two measurements is at sub-centimeter scale.
And it is also within the detection uncertainty of both data sets.
Referring to the fault trace profile of fault-parallel and fault-perpendicular
displacement can be generated and shown in the middle and bottom plot.
Alignment array measurements almost overlap with the detected fault-parallel
displacement, which validate our change detection result at this location.
It also appears that benchmark IS is located within the nonlinear
deformation zone such that the baseline of alignment array does not span the
entire near-field deformation zone, which indicated by the angular change
of the displacement vector across the fault trace.
This suggests that the ES-IS baseline does not span the entire creeping zone,
and the measurement of alignment array at this location and possibly
at other locations is under the risk of underestimating the
fault creep displacement detected in the near field.
To confirm that this rotational pattern and the nonlinear deformation zone are
not an artifact caused by the smoothing effect employed by the moving
window detection, a synthetic test was conducted.
In the synthetic test, at the same location of Camellia Drive,
we simulated a 4-centimeter strike-slip displacement that
matches the scale of real fault creep with instant transition of slip amount
and direction at the fault trace.
Shown in this plot are the change detection response
of the simulated deformation.
This experiment represent a conservative estimation of the
smoothing effect where elastic fault displacement pattern at the
ground surface is assumed. In reality, a gradual transition
is expected due to plastic deformation or the buried slip front,
which could cause less smoothing effect within the searching window.
There is no bias found in the directions of the detected displacement.
And the angular variation of the detected result is
about 10 degrees for 1 sigma.
The synthetic result confirms that the moving window detection
does introduce a smoothing artifact into the change detection.
However, the smoothing effect should be no larger than 10 meters.
Therefore, the nonlinear deformation detected in the real data sets shown
in the previous slide is unlikey induced by a detection artifact.
Whereas, a nonlinear deformation zone detected in real data set is
at least 50 meters wide with noticeable systematic rotation pattern
that are not observed in the simulation.
Here shows the overall off-fault displacement profile where the
fault-parallel and fault-perpendicular ground displacement are distributed
versus off-fault distance.
A 2.5-centimeter dextral displacement is detected in the far field.
On the right shows the most recent UAVSAR change detection result
provided by Eric Fielding from NASA JPL.
As you can see, the two measurements agree well in terms of the detected
fault-parallel displacement in the near view.
In conclusion, in this study, we have shown that geometric
primitive model from mobile Lidar point clouds is not only an effective
feature to track the change but also can be combined as persistent
geodetic markers to improve the change detection performance.
Our new method detects centimeter-level change with
sub-centimeter level accuracy, which enable the detection of aseismic
fault creep ground displacement over two years of observations.
Validation with alignment array confirms the uncertainty of the
detection and suggests that the baseline of an alignment array
might not be long enough to span the entire creeping zone.
For more information, please refer to our two publications.
Finally, I would like to acknowledge my co-authors, Craig Glennie,
who is also my Ph.D. adviser; Ben Brooks and Todd Ericksen
from USGS; and we would also like to thank Eric Fielding from
NASA JPL for providing the UAVSAR change detection result.
Thank you.