The fault planes provided by the NSHM are approximations for the actual fault interface, simplified to allow for easier simulation.
In most cases the differences between the approximation and the actual interface are insignificant, however for faults with large curvature this may introduce a large error.
As the Hikurangi subduction fault is the largest fault we simulate, the fault has been extensively investigated and the subduction interface has a lot of curvature, this makes it a prime candidate for fitting the NSHM plane to a curved surface.
NHM faults
In the NHM the Hikurangi subduction fault is broken down into three sections, each with two sizes:
HikHBay (In the area of Hawkes Bay), HikRauk (In the area of Raukawa), HikWgtn (In the Wellington Region)
Each has the suffix of min and max, representing the smallest and largest ruptures expected. The min fault planes are subsets of the max fault planes, and so are not investigated to begin with.
Curved surface
For this investigation and application we will use the interface model from Charles Williams et al.
The original model comes from a 2013 paper, with a further update provided by Williams.
Verification of deformation
Using a function to place a marker at the center of curvature for the middle strike index, this point was then used to plot points on the surface of the cylinder. These showed that the deformations are occuring as expected, and that any visual distortion is as a result of inconsistent scaling in each dimension.
A greatly exaggerated deformation to verify the deformation curvature.
Curvature value calculation
In order to calculate the radius of curvature for each fault, the center strike transect was taken, and at each point along the transect the depth of the nearest (By surface distance) surface point is taken. For each triple of adjacent points with unique depth the distance between each pair of points is taken and the radius of the circle they define calculated. The mean of these radii was then taken for use.
Testing demonstrated that the algorithm works for ideal data.
The faults have the following curvatures calculated (km):
HikHBaymax | 5194.11 |
HikHBaymin | 7777.27 |
HikRaukmax | 476.70 |
HikRaukmin | 566.43 |
HikWgtnmax | 67.05 |
HikWgtnmin | 39.51 |
Current status
As the HBay fault curvatures are clearly far too large (Resulting in small deformations) they were reduced by an order of magnitude.
The current state of the deformations is visible below
The first four have worked relatively well. However Wgtnmax has not deformed at all, and Wgtnmin has deformed, much too far.
The next step is to apply the appropriate dip to each fault and then a vertical shift to move them into alignment with the given surface.