Interval VTI Parameter Estimation With Well Control: One-Pass Delta and Epsilon Update

Summary The general flow for an anisotropic imaging project is to iteratively migrate with tomographic updates of the interval velocity V_nmo and e until the gathers are flat. The migrated stack is used to obtain interpreted horizons at every spatial location for key geologic markers as found in the available well logs. At each (sparse) well location and for each layer, using the known events, we interpolate the depth correction Δz across the grid. Now for each grid location, using our set of seismic horizons and well horizons, the traveltime through the isotropic and anisotropic slabs must match for every layer. Assuming V_P0 to be a stretched/squeezed version of V_nmo between the appropriate seismic and well horizons, equations for both V_P0 and δ are derived by application of the formula for integration by substitution. Since we know from our initial migration the e that produced flat gathers for V_nmo and δ=0, we devise a method to numerically invert for the e that will produce flat gathers for V_P0 and the new δ. This procedure is applied for each location of the inline and crossline grid, resulting in full delta and epsilon volumes.