Using Forward Modelling in Calculating the Shortest Distance between the Shot Point and the First Geophone That Senses the Refracted Head Waves

Due to the importance of seismic waves and their multiple uses, especially in near-surface studies, the dependence of the data reverse modeling on direct modeling, and the reliance of the data accuracy on the array of geophones, simple mathematical forward modeling and the relationship among time, velocity and distance were used to formulate an equations and graphical relationships. They specify the shortest distance between shot-point and its first nearest geophone that can sense the critical refracted head waves in the cases of two and three layers. These relationships show that the largest distance between the source of the waves (shot- point) and the nearest geophone, which can detect the refracted head waves, should not be more than (nine times of the first layer's thickness) in the case of two layers, and it is doubled twice for each layer that is more than two subsurface layers above the refraction surface. This distance is steadily reduced with the variance of velocities increases. The total penetrated depth not only depends on the distance amongst shot point, the first and the last geophones, but also it depends on the differences of velocities between the layers.