  In this study, we exhibit a number elementary strategies that might be at
disposal in diverse computational applications in the GEANT4 simulations with
the purpose of hemispherical particle sources. To further detail, we initially
generate random points on a spherical surface for a sphere of a practical
radius by employing Gaussian distributions for the three components of the
Cartesian coordinates, thereby obtaining a generating surface for the initial
positions of the corresponding particles. Since we do not require the half
bottom part of the produced spherical surface for our tomographic applications,
we take the absolute value of the vertical component in the Cartesian
coordinates by leading to a half-spherical shell, which is traditionally called
a hemisphere. Last but not least, we direct the generated particles into the
target material to be irradiated by favoring a selective momentum direction
that is based on the vector construction between the random point on the
hemispherical surface and the origin of the target material, hereby optimizing
the particle loss through the source biasing. In the end, we incorporate our
strategy by using G4ParticleGun in the GEANT4 code. Furthermore, we also
exhibit a second scheme that is based on the coordinate transformation from the
spherical coordinates to the Cartesian coordinates, thereby reducing the number
of random number generators. While we plan to exert our strategy in the
computational practices for muon scattering tomography, this source scheme
might find its straightforward applications in different neighboring fields
including but not limited to atmospheric sciences, space engineering, and
astrophysics where a 3D particle source is a necessity for the modeling goals.
