INTRODUCTION

The most important linear operator in exploration seismology is normal moveout and stack. Here we review this combined operator and its adjoint modeling. We particularly investigate velocity increasing with depth making moveout curves cross. This problem is traditionally solved by ``muting'', an ad hoc process of throwing away information at wide offset. To better understand crossing events and the stacking operator, I set up some synthetic data. Much to my surprise, I found that preconditioning transformations (scaling before and after transformation) give a theoretical basis for a process resembling muting. The preconditioning transformation differs from muting in that data is gained unexpectedly downward with time before stack and then upward after stack.