Introduction

Well logs can be used to interpret geologic features at much higher resolution than that of the seismic data. Consequentially, well logs are often used to calibrate seismic images which have lower resolution but much higher spatial coverage to understand the distribution of subsurface rock properties (White and Simm, 2003). This calibration is referred to as a seismic-well tie, where reflectors from a well log modeled synthetic seismicogram are aligned with common reflectors in the seismic data. Any mis-ties between the modeled synthetic seismograms and seismic data are used to update the well's time to depth relationship (TDR) and are often related to inaccuracies in the seismic migration velocities (White, 1998).

In an attempt to reduce the mis-tie between well log information, which is taken as ground truth, and the seismic image, well log measurements are often injected into migration velocity model building to provide constraints in an otherwise non-unique problem (Bakulin et al., 2010). Morice et al. (2004) show that combining well log, borehole and surface seismic data can provide an understanding of seismic velocities, anisotropy, attenuation and interbed multiples which can aid in building a velocity model consistent between all datasets. Egozi et al. (2006) show that mis-tie surfaces generated from multiple picks in multiple wells can be used to iteratively update a TTI velocity field thus driving the cumulative average mistie of all wells towards zero. Using well marker-related workflows in velocity model building removes or reduces nonuniquness and may allow for simultaneous estimation of velocity and anisotropy parameters which can be used to constrain tomography problems that focus on flattening the residual moveout of seismic events (Bakulin et al., 2010; Woodward et al., 2008).

Although well marker-related workflows help integrate well log interpretations with seismic velocity model building; these methods are limited to updates related to discrete pre-selected well markers. Several methods have been proposed to automatically perform the seismic-well tie and provide a continuous mis-tie function along the entire length of the modeled synthetic seismogram. Some authors (Wu and Caumon, 2017; Muñoz and Hale, 2012) use dynamic time warping (DTW) (Hale, 2013; Berndt and Clifford, 1994) to automatically align real and synthetic seismograms. Herrera et al. (2014) show that local similarity (LSIM) (Fomel, 2007a) can be an alternative approach to successfully compute a seismic-well tie and compares the results with DTW. Bader et al. (2018) use LSIM to semi-automatically tie several wells to a 3D seismic dataset and provide a technique for cross validation to ensure consistency and accuracy of seismic-well ties. In each case, the mis-tie function is converted to an update applied to the velocity log.

In workflows where updates are not based on the tomographic principle, the velocity model update is dependent on the quality of the interpolation algorithm and horizon picks (Gupta et al., 2013). Several methods have been proposed to interpolate information along local seismic structures. Hale (2010) uses image guided blended neighbor interpolation (Hale, 2009) for seismic guided well log interpolation. Karimi et al. (2017) apply predictive painting (Fomel, 2010) to interpolate log data along seismic structures to generate accurate starting models for post stack inversion.

To understand and remove the inconsistencies between the migration velocity, well logs, migrated seismic image and modeled synthetic seismogram, we propose a method that uses LSIM to measure the mis-tie from the seismic-well tie and uses the result to update the migration velocity at the well log positions. A complete, updated, velocity model is then interpolated along seismic structures using predictive painting. We test our method on several synthetic datasets. The results indicate that the proposed workflow provides an effective method for incorporating well log data in velocity model building workflows.