A linear least-squares inversion is applied to the turning-ray first-arrival times of a shallow-marine seismic reflection data set to estimate the slowly varying (laterally and vertically) components of the near-surface velocity field. The velocity model is represented with a low-spatial-frequency parameterization (2D cubic B-splines) designed specifically for the predicted components of the data. This model parameterization effectively decouples the slowly varying background from the higher spatial-frequency component of the velocity field produced by shallow, low-velocity, gas-charged sands and allows the solution to be obtained in a single iteration. The observed first-arrival times (background and shallow anomaly-induced perturbations) and the slowly varying first-arrival times related to the background velocity are inverted separately. Similar velocity-model estimates result, demonstrating the decoupling imposed by the B-spline model parameterization. The background velocity and the low-velocity anomalies are best treated as separate inverse problems using very different model parameterizations. Ray tracing a synthetic model containing local low-velocity anomalies embedded in a smooth background does not accurately predict the anomaly-induced first-arrival time perturbations seen in the field data. Acoustic finite-difference waveform modeling shows that reflections and diffractions from the anomalies interfere with the diving-wave first arrivals. First-arrival times picked from the full-waveform synthetics more accurately predict the field data first-arrival times.