.rst .pdf

repository open issue suggest edit

Layer of prisms

One way to model three dimensional structures is to create a set of prisms that approximates their geometry and its physical properties (density, susceptibility, etc.). The harmonica.prism_layer offers a simple way to create a layer of prisms: a regular grid of prisms of equal size on the horizontal directions with variable top and bottom boundaries. It returns a xarray.Dataset with the coordinates of the centers of the prisms and their corresponding physical properties. The harmonica.DatasetAccessorPrismsLayer Dataset accessor can be used to obtain some properties of the layer like its shape and size or the boundaries of any prism in the layer. The methods of this Dataset accessor can be used together with the harmonica.prism_gravity to compute the gravitational effect of the layer.

import matplotlib.pyplot as plt
import numpy as np
import verde as vd

import harmonica as hm

# Create a layer of prisms
region = (0, 100e3, -40e3, 40e3)
spacing = 2e3
(easting, northing) = vd.grid_coordinates(region=region, spacing=spacing)
surface = 100 * np.exp(-((easting - 50e3) ** 2 + northing ** 2) / 1e9)
density = 2670.0 * np.ones_like(surface)
prisms = hm.prism_layer(
    coordinates=(easting[0, :], northing[:, 0]),
    surface=surface,
    reference=0,
    properties={"density": density},
)

# Compute gravity field of prisms on a regular grid of observation points
coordinates = vd.grid_coordinates(region, spacing=spacing, extra_coords=1e3)
gravity = prisms.prism_layer.gravity(coordinates, field="g_z")

# Plot gravity field
plt.pcolormesh(*coordinates[:2], gravity)
plt.colorbar(label="mGal", shrink=0.8)
plt.gca().set_aspect("equal")
plt.ticklabel_format(axis="both", style="sci", scilimits=(0, 0))
plt.title("Gravity acceleration of a layer of prisms")
plt.xlabel("easting [m]")
plt.ylabel("northing [m]")
plt.tight_layout()
plt.show()

Gravitational effect of topography Point Masses in Cartesian Coordinates