CyberShake interpolation

This page documents research into techniques for interpolating various CyberShake data products, performed by 2024 SOURCES intern Amelia Kratzer.

Source Code

Hazard Curves

Procedure

Selection of Sites

• To start, I selected 4 sites (input sites), all in the basin, that formed a 10km by 10km square inside which there was at least 1 site to interpolate (interp site). This way I could compare the simulated values for that site to the interpolated to check the accuracy of my interpolation.

a) 1st chosen area: USC as there are three sites on the exterior for 1D linear interpolation and two sites on the interior for 2D linear interpolation

b) 2nd chosen area: CSDH

• Next, I selected two locations where some of the sites were not in the basin, to test how different velocity structures may affect the accuracy of the interpolation.

a) 1st location: STG

b) 2nd location: SGRTT

Linear Interpolation of Hazard Curves

• Download and plot the input sites' hazard curves.
• Query CyberShake database to get the X shaking values and Y probability values for input and interp sites.
• Use UTM to convert locations of sites to meters from lat/lon.
• Calculate the X’ and Y’ distances to my interpolated site from the left and top edge of my square since the 10km by 10km square is on a rotated axis.
• For each shaking value, use the probabilities of shaking at the input sites and these X’ and Y’ distances to perform bilinear interpolation.
• Plot the (shaking value, interpolated probability) points to form the interpolated hazard curve.
• Overlay the interpolated hazard curve and the simulated hazard curve on single plot for comparison.

Error Calculations

• I compared the simulated probabilities to the interpolated probabilities for the given site, and calculated the absolute percent difference at each acceleration value. Percent difference accurately models the accuracy of the hazard curve since it reflects the larger differences in the simulated and interpolated results at the higher acceleration values.

• I chose two metrics by which to compare the accuracy of my interpolations - max percent difference and average percent difference.

Results

1D Linear Interpolation
Note: no error metrics were calculated for the 1D linear interpolations, but overlayed plots helped to assess the accuracy of the interpolation.

2D Bilinear Interpolation

• 4 sites, all in basin

a) USC area

Maxdiff: 33.9%, avgDiff: 6.2%

Maxdiff: 40.4%, avgDiff: 4.1%

b) CSDH area

Maxdiff: 33.2%, avgDiff: 4.7%

Maxdiff: 39.5%, avgDiff: 10.3%

• 4 sites, not all in basin

a) SGRTT and STG locations

Maxdiff: 75.3%, avgDiff: 12.9%

Maxdiff: 91.1%, avgDiff: 19.8%

Findings: the bilinear interpolation was more accurate, with a lower max percent difference and average percent difference, when the 4 input sites were all in the basin compared to when I varied the velocity structures of the input sites.
For example, comparing USC, in which all 4 input sites are in the basin, to SGT, where some of the input sites are not in the basin, reveals that the max percent difference for STG was more than double that of USC, 40.4% to 91.1%, respectively. The average percent difference for STG was more than 4 times that of USC, 19.8% to 4.1%, respectively.

Next steps
I will next try to interpolate the shaking RotD50 values themselves to see if the interpolation is more accurate than that of the hazard curves.

Intensity Measures

Procedure

I followed a very similar procedure to the interpolation of the hazard curves. The selection of the sites process and linear interpolation method were identical.