A self-adaptive algorithm for choosing reference velocities in the presence of lateral velocity variations

Based on perturbation theory, the wave equation extrapolation operator with mixed domains has the ability to deal with lateral velocity variations. It is the image method that has undergone much research in seismology. All extrapolation operators face the problem of choosing the reference velocity due to continuation in depth. The wavefield extrapolation operator with a single reference velocity is suitable for media with weak lateral variation. The multi-reference velocity extrapolation operator can cope with severe lateral velocity variations and improve image accuracy. However, the calculation cost is large. We present a self-adaptive approach to automatically determine the number of selected reference velocities according to the complexity of structure and the given velocity threshold value. The approach can be used to construct the SSF, FFD, WXFD, and GSP multi-reference velocity wavefield extrapolation image algorithms. The result of a salt-dome model data test demonstrates that the self-adoptive multi-reference wavefield extrapolation algorithm has the ability to deal with severe lateral velocity variations and can also be used for structure edge detection. The method is flexible and computationally cost-effective.

Continuity and momentum equations for moist atmospheres

The moist atmosphere with occurring precipitation is considered to be a multiphase fluid composed of dry air, water vapor and hydrometeors. These compositions move with different velocities： they take a macroscopic motion with a reference velocity and a relative motion with a velocity deviated from the reference velocity. The reference velocity can be chosen as the velocities of dry air, a gas mixture and the total air mixture. The budget equations of continuity and momentum are formulated in the three reference-velocity frames. It is shown that the resulting equations are dependent on the chosen reference velocity. The diffusive flux due to compositions moving with velocities deviated from the reference velocity and the internal sources due to the phase transitions of water substances result in additional source terms in continuity and momentum equations. A continuity equation of the total mass is conserved and free of diffusive flux divergence if the reference velocity is referred to the velocity of the total air mixture. However, continuity equations in the dry-air and gas- mixture frames are not conserved due to the mass diffusive flux divergence. The diffusive flux introduces additional source terms in the momentum equation. In the dry-air frame, the diffusive flux of water substances and the phase transitions of water substances contribute to the change of the total momentum. The additional sources of total momentum in the frame of a gas mixture are associated with the diffusive flux of hydrometeors, the phase transitions of hydrometeors and the gas- mixture diffusive flux. In the frame of total air mixture, the contribution to the total momentum comes from the diffusive flux of all atmospheric compositions instead of the phase transitions. The continuity and momentum equations derived here are more complicated than the traditional model equations. With increasing computing power, it becomes possible to simulate atmospheric processes with these sophisticated equations. It is helpful to the improvement of precipitation forecast.