I want to calculate the shortest distance between an earthquake (x,y,z) and a subducting plate interface (.grd file). I.e. not just the vertical distance, but the shortest distance between a point and a curved 3D surface

Does anyone have any ideas how I could do this?

Maybe `grdmath`

with one of the Xdist operator ?

That looks like a good starting point but as far as I can tell that will only calculate horizontal distance. So it wouldn’t consider the z value of the point (earthquake) and grd file (subducting plate)

I haven’t dug into it myself, but I think I’ve seen something in the gallery that might be relevant (?). The script uses `sphtriangulate`

A bit brute force, but what if you

- Use
`grd2xyz`

to convert the grid surface to a bunch of XYZ points
- Compute the distance between each of those XYZ points to your single earthquake epicentre
- Sort the distances, and get the shortest distance

Yeah that’s what I’ve ended up doing, here’s an example if anyone else would find it useful:

```
import pygmt
from geopy import distance
import math
plate = pygmt.grd2xyz('plate.grd', output_type='pandas')
# this code currently loops over an obspy Catalog containing earthquake info
for event in cat:
distances = []
for index, row in plate.iterrows():
hor_dist = distance.distance((event.origins[0].latitude, event.origins[0].longitude),
(row['y'], row['x'])).km
ver_dist = (event.origins[0].depth) - row['z']
threeD_distance = math.sqrt(hor_dist**2 + ver_dist**2)
distances.append(threeD_distance)
minimum_distance = min(distances, key=abs)
```

Ah cool, exactly that! You could probably optimize things a little bit using https://geopandas.org/en/v0.11.0/docs/reference/api/geopandas.GeoDataFrame.sjoin_nearest.html and compute the distance just once, but if it’s fast enough, then don’t worry about it.