In the past few years, significant progress has been made on new velocity analysis algorithms. In the first part of this paper, we will briefly summarize recent advances on velocity analysis. Then we describe a new model-based globally-optimized residual curvature analysis algorithm we have just developed. Like conventional residual curvature analysis, the algorithm is based on the principle that after prestack migration with a correct velocity model, an image in the common image point (CIP) gather is aligned horizontally regardless of structure. Unlike conventional residual curvature analysis, this algorithm uses not only the interpreted CIP gathers, but also the interpreted migrated depth section as input. The algorithm is model-based, and uses modelbased CIP ray tracing to relate residual moveouts in CIP gathers to errors in the velocity model. Residual moveouts measured in CIP gathers are globally used in the optimization process for updating the whole velocity model. Also model-based normal incident ray tracing is used for updating the reflector boundaries. REVIEW OF RECENT ADVANCES OF VELOCITY ANALYSISRecent advances of velocity analysis can be summarized into two categories: 1) traveltime inversion; 2) migration velocity analysis. Traveltime inversionTraveltime Inversion (TI) (Bishop et al., 1985; Stork and Clayton, 1991) estimates a depth velocity model from traveltimes picked from prestack data. The main advantage of TI is that it is formulated as an optimization problem and therefore model updating is very effective and efficient. However, in areas of complex geological structure, picking prestack traveltimes in surface seismic data is almost unfeasible. Picking prestack traveltimes may have the following problems: 1) in the case of complex reflector geometry, seismic energies reflected from different parts of a reflector may arrive at the same receiver location; 2) reflection arrivals contaminated by diffraction energy; 3) low signal-to-noise ratio often associated with complex structure.In the past few years, a few researchers tried to solve the traveltime picking problem. IFP (Institut Francais du Petrole) developed a method called SMART (Sequential Migration Aided Reflection Tomography) (Delprat-Jannaud and Lailly, 1993) to solve the traveltime picking problem. The main idea of SMART is to use an approximate velocity model to migrate seismic data, then pick the imaged reflectors in the cube of migrated shot gathers, finally trace rays that propagate in the same velocity model as the one used for the migration and that are reflected on the picked imaged reflectors. They claimed that because the ray tracing undoes what the migration has done, even with an approximate velocity model they can recover traveltimes. More recently DATAID (1994) used a similar approach as IFP, but performed migration and raytracing in the common-offset gather instead of common-shot gather. The main point of these approaches is that instead of directly picking events in the time domain, picking is done after depth migration...

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A linear time-varying filtering process usually is realized by applying a number of time-invariant filters to overlapping time regions of a trace and transitionally merging these different regions. We describe the design of a different type of linear time-varying filter where the frequency spectrum of the filter is shifted along the frequency axis as a function of time without appreciable change in the spectrum shape. The design is based on a given time-invariant tilter with the desired spectrum shape.For long filter length, the design procedure is rather complicated. Furthermore, only a constant rate of frequency shift is possible. However, for many practical situations where the frequency shift over the filter length is much less than the bandwidth of the filter, the process of time-varying filtering can be further simplified without appreciable frequency error. In fact, time-varying filtering is achieved through modifying the complex signal representation of the original time invariant filter by a preapplication of a specified time-varying frequency-shifting operator and a post-application of a corresponding frequency restoration operator. Under this short filter approximation. the more general time-varying filter in which the rate of frequency shift is nonuniform can be realized. Behavior of the convolutional time-varying filters is demonstrated by examples of filtering of sampled sinusoidal signals.If,, the filtered trace can be calculated as follows: Let a(t) and o(t) denote the input signal and the final output signal, respectively. Let o,(t) and 02(t) denote the intermediate filtered signals using filters J' ,(T) and fi(7), respectively. Then, Linear merging requires that