Conclusions

The wave operator can formally and numerically be split into parts that involve taking derivatives of either model parameters or propagating field quantities. For identical derivative operators this is the same as the conventional method which takes nested derivatives of those quantities. However, the main advantage lies in the possibility to treat the two parts differently. I have given the splitting for completely anisotropic media. By assuming different a priori properties of the medium, the operators can be adjusted to match the medium. A possible topic of future research is the use of wavelet transform for derivative calculations for medium and field variables.