Automatic velocity analysis

The exponential growth in seismic data volumes requires automation of seismic velocity analysis and imaging. Migration velocity analysis exploits the redundancy in the data to estimate the background velocity model. Data for different shot-receiver distances or offsets should provide the same image of the subsurface. Its implementation for the full wave equation invokes action at distance via a subsurface shift in space or time. The figure shows a real-data example. The corresponding cost functional tries to focus energy at zero subsurface shift, thereby suppressing the unphysical action at distance.

Example of seismic velocity inversion with focusing based on horizontal shifts in the depth domain, starting from the best velocity model that increases linearly with depth. The left panel shows the extended image at a lateral position of x = 1.95 km, as a function of horizontal subsurface offset h_x and depth z. The iteration count is displayed in the left upper corner. The central panel displays the migration image. The right one shows the reconstructed smooth background velocity model.