To generate seismic waves a source function is required. This section develops the concept of a frequency band limited source function. Real seismic sources use an energy impulse or a vibration source to generate waves in the earth. Impulse sources include dynamite, a drop weight, a sledge hammer, a shot gun, or a rifle. The actual source used is dependent on the desired signal to noise ratio, the human environment, the target depth desired and the geological environment. The vast majority of land seismic data are generated by two methods, dynamite placed in shot holes drilled into the earth or by a truck mounted vibrating mass which shakes the earth in a vertical or horizontal direction. The method we will use in our simulation of seismic exploration is the impulsive dynamite source.
The source is finite in duration. This requires a time varying function. The following exponential equation is suitable, where and determine the maximum value and the length of time, . The required frequency content for the model is ; a typical value is 30 Hertz.
Now the source needs an oscillatory function and the symmetric Sine will do nicely,