A long and short operator combination

Figure is using the same model as Figures and . However, the difference lies in the types of operators used for calculating the wave field. For derivating the field quantities a 16 point operator was used, while for derivating the medium parameters a 6 point wide operator was used. The 16 point operator smoothes the the propagating wave field more than the 6 point operator. The short operator is more local and smoothes the medium parameters less. It does not remove as many high spatial frequencies in the derivation process, as the longer 16 point operator does. The step discontinuity really has a very high frequency content and we prefer an accurate computation of the derivative of that discontinuity.

 

long+short
Figure 3 Trace 90 is taken from two wave fields. The results from the two different modeling equations are overlain. The smoother response is generated by the composite modeling equation with a fixed 16 point operator. The rougher response is produced by the split modeling equation , which leaves higher frequencies in the wave field, if the model itself contains those high frequencies. The modeling was carried out on a staggered grid. Again the source is located on top of the step and the receivers are located below. On the CD you are able to interactively experiment with different operator lengths yourself.