Reflection seismic waveform tomography

In seismic waveform tomography, if using reflection data with limited source‐receiver offsets, it is difficult to reconstruct the deep part of the subsurface velocity model. We present two approaches to tackle this problem: layer stripping and weighted updating. In a layer‐stripping procedure, we replace the top portion of seismic data with synthetics generated from the previous‐layer inversion and make the current inversion focus on the minimization of the data misfit corresponding to the deep part of the model. To improve efficiency, we use only sparsely sampled frequency data in the deeper‐layer inversions, unlike the first‐layer inversion where we use densely sampled frequency data as usual. The sparsely sampled frequencies together have the full wave number coverage for effective imaging. Combined use of dense and sparse sampling in frequency is a compromise between resolution and efficiency, as it reduces the number of iterations needed in layer‐stripping inversion while still producing a good image. In the second scheme, we apply depth‐dependent weights to model updates in order to improve the convergence in an iterative solution. The weighting is inversely proportional to the ray density variation along the depth and is mathematically equivalent to the application of an inverse Hessian matrix which sharpens the gradient vector for model updating. For real seismic data, we transfer point source shot records to line source records, by partial amplitude compensation and phase adjusting, before inputting it to the waveform tomography. We perform traveltime inversion to generate a reliable layered velocity model and then waveform tomography to produce a high‐resolution image of the subsurface model through frequency domain iteration.