spharpy.spatial¶
Functions:
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The matrix describing the propagation of a plane wave from a direction of arrival defined by the azimuth and elevation angles of the source points to the receiver points. |
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Green's function for point sources in free space in matrix form. |
- spharpy.spatial.greens_function_plane_wave(source_points, receiver_points, wave_number, gradient=False)[source]¶
The matrix describing the propagation of a plane wave from a direction of arrival defined by the azimuth and elevation angles of the source points to the receiver points. The phase sign convention reflects a direction of arrival from the source position.
- Parameters
source_points (Coordinates) – The source points defining the direction of incidence for the plane wave. Note that the radius on which the source is positioned has no relevance.
receiver_points (Coordinates) – The receiver points.
wave_number (double) – The wave number of the wave
speed_of_sound (double) – The speed of sound
gradient (bool) – If True, the gradient will be returned as well
- Returns
M – The plane wave propagation matrix
- Return type
ndarray, complex, shape(n_receiver, n_sources)
- spharpy.spatial.greens_function_point_source(sources, receivers, k, gradient=False)[source]¶
Green’s function for point sources in free space in matrix form. The phase sign convention corresponds to a direction of propagation away from the source at position $r_s$.
\[\begin{split}G(k) = \\frac{e^{- k\\|\\mathbf{r_s} - \\mathbf{r_r}\\|}} {4 \\pi \\|\\mathbf{r_s} - \\mathbf{r_r}\\|}\end{split}\]- Parameters
source (Coordinates) – source points as Coordinates object
receivers (Coordinates) – receiver points as Coordinates object
k (ndarray, double) – wave number
- Returns
G – Green’s function
- Return type
ndarray, double