Systems and methods create velocity models for a single well or for a set of wells. In one implementation, a system optimizes a time-depth relationship applied to data points from a single well to estimate coefficients for a linear-velocity-in-time function that models the data points. The system optimizes by reducing the influence of outlier data points, for example, by weighting each data point to decrease the influence of those far from the velocity function. The system also reduces the influence of top and bottom horizons of geological layers by applying data driven techniques that estimate the velocity function in a way that reduces dependence on the boundary conditions. The systems and methods can also create velocity models based on data from a set of wells, applying a well weights method to reduce the influence of outlier wells and thereby prevent wells with aberrant data from degrading a correct velocity model.