Draft gravity point spherical kernel

choclo/point/__init__.py

@@ -19,3 +19,15 @@
     gravity_u,
     gravity_uu,
 )
+from ._forward_spherical import (
+    gravity_e_spherical,
+    gravity_ee_spherical,
+    gravity_en_spherical,
+    gravity_eu_spherical,
+    gravity_n_spherical,
+    gravity_nn_spherical,
+    gravity_nu_spherical,
+    gravity_pot_spherical,
+    gravity_u_spherical,
+    gravity_uu_spherical,
+)

choclo/point/_forward_spherical.py

@@ -0,0 +1,375 @@
+# Copyright (c) 2022 The Choclo Developers.
+# Distributed under the terms of the BSD 3-Clause License.
+# SPDX-License-Identifier: BSD-3-Clause
+#
+# This code is part of the Fatiando a Terra project (https://www.fatiando.org)
+#
+"""
+Forward modelling function for point sources
+"""
+import numpy as np
+from numba import jit
+
+from ..constants import GRAVITATIONAL_CONST
+from ..utils import distance_spherical_core
+
+
+@jit(nopython=True)
+def gravity_pot_spherical(
+    longitude_p,
+    cosphi_p,
+    sinphi_p,
+    radius_p,
+    longitude_q,
+    cosphi_q,
+    sinphi_q,
+    radius_q,
+    mass,
+):
+    """
+    Kernel function for potential gravitational field in spherical coordinates
+    """
+    distance, _, _ = distance_spherical_core(
+        longitude_p,
+        cosphi_p,
+        sinphi_p,
+        radius_p,
+        longitude_q,
+        cosphi_q,
+        sinphi_q,
+        radius_q,
+    )
+    kernel = 1 / distance
+    return GRAVITATIONAL_CONST * mass * kernel
+
+
+#  Acceleration components
+#  -------------------
+
+
+@jit(nopython=True)
+def gravity_u_spherical(
+    longitude_p,
+    cosphi_p,
+    sinphi_p,
+    radius_p,
+    longitude_q,
+    cosphi_q,
+    sinphi_q,
+    radius_q,
+    mass,
+):
+    """
+    Upward component of the gravitational acceleration due to a point source
+
+    Returns the upward component of the gravitational acceleration produced by
+    a single point source on a single computation point
+
+    Use spherical coordinates
+    """
+    distance, cospsi, _ = distance_spherical_core(
+        longitude_p,
+        cosphi_p,
+        sinphi_p,
+        radius_p,
+        longitude_q,
+        cosphi_q,
+        sinphi_q,
+        radius_q,
+    )
+    delta_z = radius_p - radius_q * cospsi
+    kernel = -delta_z / distance**3
+    return GRAVITATIONAL_CONST * mass * kernel
+
+
+@jit(nopython=True)
+def gravity_e_spherical(
+    longitude_p,
+    cosphi_p,
+    sinphi_p,
+    radius_p,
+    longitude_q,
+    cosphi_q,
+    sinphi_q,
+    radius_q,
+    mass,
+):
+    """
+    Easting component of the gravitational acceleration due to a point source
+
+    Returns the upward component of the gravitational acceleration produced by
+    a single point source on a single computation point
+
+    Use spherical coordinates
+    """
+    distance, _, _ = distance_spherical_core(
+        longitude_p,
+        cosphi_p,
+        sinphi_p,
+        radius_p,
+        longitude_q,
+        cosphi_q,
+        sinphi_q,
+        radius_q,
+    )
+    delta_e = radius_q * cosphi_q * np.sin(longitude_q - longitude_p)
+    kernel = delta_e / distance**3
+    return GRAVITATIONAL_CONST * mass * kernel
+
+
+@jit(nopython=True)
+def gravity_n_spherical(
+    longitude_p,
+    cosphi_p,
+    sinphi_p,
+    radius_p,
+    longitude_q,
+    cosphi_q,
+    sinphi_q,
+    radius_q,
+    mass,
+):
+    """
+    Northing component of the gravitational acceleration due to a point source
+
+    Returns the upward component of the gravitational acceleration produced by
+    a single point source on a single computation point
+
+    Use spherical coordinates
+    """
+    distance, _, coslambda = distance_spherical_core(
+        longitude_p,
+        cosphi_p,
+        sinphi_p,
+        radius_p,
+        longitude_q,
+        cosphi_q,
+        sinphi_q,
+        radius_q,
+    )
+    delta_n = radius_q * (cosphi_p * sinphi_q - sinphi_p * cosphi_q * coslambda)
+    kernel = delta_n / distance**3
+    return GRAVITATIONAL_CONST * mass * kernel
+
+
+#  Tensor components
+#  -------------------
+
+
+@jit(nopython=True)
+def gravity_ee_spherical(
+    longitude_p,
+    cosphi_p,
+    sinphi_p,
+    radius_p,
+    longitude_q,
+    cosphi_q,
+    sinphi_q,
+    radius_q,
+    mass,
+):
+    """
+    Easting-easting component of the gravitational acceleration due to a point
+    source
+
+    Returns the upward component of the gravitational acceleration produced by
+    a single point source on a single computation point
+
+    Use spherical coordinates
+    """
+    distance, _, _ = distance_spherical_core(
+        longitude_p,
+        cosphi_p,
+        sinphi_p,
+        radius_p,
+        longitude_q,
+        cosphi_q,
+        sinphi_q,
+        radius_q,
+    )
+    delta_e = radius_q * cosphi_q * np.sin(longitude_q - longitude_p)
+    kernel = -1 / distance**3 + 3 * delta_e**2 / distance**5
+    return GRAVITATIONAL_CONST * mass * kernel
+
+
+@jit(nopython=True)
+def gravity_nn_spherical(
+    longitude_p,
+    cosphi_p,
+    sinphi_p,
+    radius_p,
+    longitude_q,
+    cosphi_q,
+    sinphi_q,
+    radius_q,
+    mass,
+):
+    """
+    Northing-northing component of the gravitational acceleration due to a
+    point source
+
+    Returns the upward component of the gravitational acceleration produced by
+    a single point source on a single computation point
+
+    Use spherical coordinates
+    """
+    distance, _, coslambda = distance_spherical_core(
+        longitude_p,
+        cosphi_p,
+        sinphi_p,
+        radius_p,
+        longitude_q,
+        cosphi_q,
+        sinphi_q,
+        radius_q,
+    )
+    delta_n = radius_q * (cosphi_p * sinphi_q - sinphi_p * cosphi_q * coslambda)
+    kernel = -1 / distance**3 + 3 * delta_n**2 / distance**5
+    return GRAVITATIONAL_CONST * mass * kernel
+
+
+@jit(nopython=True)
+def gravity_uu_spherical(
+    longitude_p,
+    cosphi_p,
+    sinphi_p,
+    radius_p,
+    longitude_q,
+    cosphi_q,
+    sinphi_q,
+    radius_q,
+    mass,
+):
+    """
+    Upward-upward component of the gravitational acceleration due to a point
+    source
+
+    Returns the upward component of the gravitational acceleration produced by
+    a single point source on a single computation point
+
+    Use spherical coordinates
+    """
+    distance, cospsi, _ = distance_spherical_core(
+        longitude_p,
+        cosphi_p,
+        sinphi_p,
+        radius_p,
+        longitude_q,
+        cosphi_q,
+        sinphi_q,
+        radius_q,
+    )
+    delta_z = radius_p - radius_q * cospsi
+    kernel = -1 / distance**3 + 3 * delta_z**2 / distance**5
+    return GRAVITATIONAL_CONST * mass * kernel
+
+
+@jit(nopython=True)
+def gravity_en_spherical(
+    longitude_p,
+    cosphi_p,
+    sinphi_p,
+    radius_p,
+    longitude_q,
+    cosphi_q,
+    sinphi_q,
+    radius_q,
+    mass,
+):
+    """
+    Easting-northing component of the gravitational acceleration due to a point
+    source
+
+    Returns the upward component of the gravitational acceleration produced by
+    a single point source on a single computation point
+
+    Use spherical coordinates
+    """
+    distance, _, coslambda = distance_spherical_core(
+        longitude_p,
+        cosphi_p,
+        sinphi_p,
+        radius_p,
+        longitude_q,
+        cosphi_q,
+        sinphi_q,
+        radius_q,
+    )
+    delta_e = radius_q * cosphi_q * np.sin(longitude_q - longitude_p)
+    delta_n = radius_q * (cosphi_p * sinphi_q - sinphi_p * cosphi_q * coslambda)
+    kernel = 3 * delta_e * delta_n / distance**5
+    return GRAVITATIONAL_CONST * mass * kernel
+
+
+@jit(nopython=True)
+def gravity_eu_spherical(
+    longitude_p,
+    cosphi_p,
+    sinphi_p,
+    radius_p,
+    longitude_q,
+    cosphi_q,
+    sinphi_q,
+    radius_q,
+    mass,
+):
+    """
+    Easting-upward component of the gravitational acceleration due to a point
+    source
+
+    Returns the upward component of the gravitational acceleration produced by
+    a single point source on a single computation point
+
+    Use spherical coordinates
+    """
+    distance, cospsi, _ = distance_spherical_core(
+        longitude_p,
+        cosphi_p,
+        sinphi_p,
+        radius_p,
+        longitude_q,
+        cosphi_q,
+        sinphi_q,
+        radius_q,
+    )
+    delta_e = radius_q * cosphi_q * np.sin(longitude_q - longitude_p)
+    delta_z = radius_p - radius_q * cospsi
+    kernel = 3 * delta_e * delta_z / distance**5
+    return GRAVITATIONAL_CONST * mass * kernel
+
+
+@jit(nopython=True)
+def gravity_nu_spherical(
+    longitude_p,
+    cosphi_p,
+    sinphi_p,
+    radius_p,
+    longitude_q,
+    cosphi_q,
+    sinphi_q,
+    radius_q,
+    mass,
+):
+    """
+    Northing-upward component of the gravitational acceleration due to a point
+    source
+
+    Returns the upward component of the gravitational acceleration produced by
+    a single point source on a single computation point
+
+    Use spherical coordinates
+    """
+    distance, cospsi, coslambda = distance_spherical_core(
+        longitude_p,
+        cosphi_p,
+        sinphi_p,
+        radius_p,
+        longitude_q,
+        cosphi_q,
+        sinphi_q,
+        radius_q,
+    )
+    delta_n = radius_q * (cosphi_p * sinphi_q - sinphi_p * cosphi_q * coslambda)
+    delta_z = radius_p - radius_q * cospsi
+    kernel = 3 * delta_n * delta_z / distance**5
+    return GRAVITATIONAL_CONST * mass * kernel