Gravitational effect of topographyΒΆ

One possible application of the harmonica.prisms_layer function is to create a model of the terrain and compute its gravity effect. Here we will use a regular grid of topographic and bathymetric heights for South Africa to create a prisms layer that model the terrain with a density of 2670 kg/m^3 and the ocean with a density contrast of -1900 kg/m^3 obtained as the difference between the density of water (1000 kg/m^3) and the normal density of upper crust (2900 kg/m^3). Then we will use harmonica.prism_gravity to compute the gravity effect of the model on a regular grid of observation points.

Gravitational acceleration of the topography
import pyproj
import numpy as np
import verde as vd
import harmonica as hm
import matplotlib.pyplot as plt
import as ccrs

# Read South Africa topography
south_africa_topo = hm.datasets.fetch_south_africa_topography()

# Project the grid
projection = pyproj.Proj(proj="merc", lat_ts=south_africa_topo.latitude.values.mean())
south_africa_topo = vd.project_grid(south_africa_topo.topography, projection=projection)

# Create a 2d array with the density of the prisms Points above the geoid will
# have a density of 2670 kg/m^3 Points below the geoid will have a density
# contrast equal to the difference between the density of the ocean and the
# density of the upper crust: # 1000 kg/m^3 - 2900 kg/m^3
density = south_africa_topo.copy()  # copy topography to a new xr.DataArray
density.values[:] = 2670.0  # replace every value for the density of the topography
# Change density values of ocean points
density = density.where(south_africa_topo >= 0, 1000 - 2900)

# Create layer of prisms
prisms = hm.prisms_layer(
    (south_africa_topo.easting, south_africa_topo.northing),
    properties={"density": density},

# Compute gravity field on a regular grid located at 4000m above the ellipsoid
coordinates = vd.grid_coordinates(
    region=(12, 33, -35, -18), spacing=0.2, extra_coords=4000
easting, northing = projection(*coordinates[:2])
coordinates_projected = (easting, northing, coordinates[-1])
prisms_gravity = prisms.prisms_layer.gravity(coordinates_projected, field="g_z")

# Make a plot of the computed gravity
plt.figure(figsize=(8, 8))
ax = plt.axes(projection=ccrs.Mercator())
maxabs = vd.maxabs(prisms_gravity)
tmp = ax.pcolormesh(
ax.set_extent(vd.get_region(coordinates), crs=ccrs.PlateCarree())
plt.title("Gravitational acceleration of the topography")
    tmp, label="mGal", orientation="horizontal", shrink=0.93, pad=0.01, aspect=50

Total running time of the script: ( 1 minutes 8.408 seconds)

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