On optimal NMO and generalised Dix equations for velocity determination and depth conversion

Abstract

Abstract The classical Earth model used to process seismic data assumes plane layers and a velocity analysis based on a hyperbolic approximation of the reflection events, where basically one parameter (the stacking velocity) is used to perform the normal move-out (NMO) correction to obtain the stacked section. We explore the possibility of using alternative approaches, other than the standard Dix equation based on the root-mean-square (RMS) velocities, to obtain the interval velocities and perform the depth conversion in order to locate the interfaces. Specifically, we consider traveltime equations as a function of offset using different NMO approximations, based on the average, RMS and root-mean-quartic (RMQ) velocities. A generalised form of Dix's equation is used for this purpose. Moreover, we analyse the model-dependency of the different NMO equations. We consider a simple 4-layer model and a model based on data from the Cooper basin, South Australia, to test the NMO equations. We build an elastic-velocity model and compute a common midpoint (CMP) synthetic seismogram. The reflection events are identified and traveltimes are picked to perform a non-linear inversion with the conventional (one parameter) hyperbolic approximation, the 3-term Taner and Koehler equation and approximations based on the average, RMQ and RMS velocities, also using two parameters. The model has a velocity inversion which poses a challenge to the approximations. The performance of the approximations is model dependent, so a-priori information of the velocity profile can be useful to perform a suitable inversion, or an optimal stack of the reflection events is required to test the NMO correction. Moreover, the results show that the inversion based on the RMS velocities yields better results than those based on the RMQ velocities, but this is not always the case. On the other hand, the inversion using the average velocity performs a worse velocity–depth estimation, even compared to the RMS results from the hyperbolic approximation.