To determine the range of geocentric angles in which the modeled and observed P-wave arrival times are noticeably different, we need to consider the factors that affect P-wave propagation through the Earth's interior.
P-waves travel at different velocities in different Earth materials, and this velocity depends on the density and elasticity of the material. When a P-wave encounters a boundary between two Earth layers with distinct properties, it can change direction and velocity, leading to variations in arrival times.
The noticeable difference in arrival times between modeled and observed P-waves typically occurs in the transition zone between the Earth's crust and mantle, known as the Mohorovičić discontinuity or Moho.
This is where there is a significant change in seismic velocity. P-waves slow down as they enter the less rigid mantle from the more rigid crust.
The specific range of geocentric angles where this occurs can vary depending on the local geological conditions and the depth of the Moho.
In general, the noticeable difference in P-wave arrival times due to this transition can occur within a range of geocentric angles from roughly 0 degrees to 30 degrees.
This range represents the shallow angle at which P-waves enter the Earth's interior.
Beyond this range, the P-wave velocities tend to stabilize as they propagate through the mantle.
It's important to note that the exact range of noticeable differences can vary depending on the seismic model being used and the specific geological conditions of the region under study.
Therefore, for more precise results, it's advisable to consult seismic data and models specific to the region of interest.