We use the wide-angle wavefield to constrain estimates of the seismic velocity and thickness of basalt flows overlying sediments. Wide angle means the seismic wavefield recorded at offsets beyond the emergence of the direct wave. This wide-angle wavefield contains arrivals that are returned from within and below the basalt flows, including the diving wave through the basalts as the first arrival and P-wave reflections from the base of the basalts and from subbasalt structures. The velocity structure of basalt flows can be determined to first order from traveltime information by ray tracing the basalt turning rays and the wide-angle base-basalt reflection. This can be refined by using the amplitude variation with offset (AVO) of the basalt diving wave. Synthetic seismogram models with varying flow thicknesses and velocity gradients demonstrate the sensitivity to the velocity structure of the basalt diving wave and of reflections from the base of the basalt layer and below. The diving-wave amplitudes of the models containing velocity gradients show a local amplitude minimum followed by a maximum at a greater range if the basalt thickness exceeds one wavelength and beyond that an exponential amplitude decay. The offset at which the maximum occurs can be used to determine the basalt thickness. The velocity gradient within the basalt can be determined from the slope of the exponential amplitude decay. The amplitudes of subbasalt reflections can be used to determine seismic velocities of the overburden and the impedance contrast at the reflector. Combining wide-angle traveltimes and amplitudes of the basalt diving wave and subbasalt reflections enables us to obtain a more detailed velocity profile than is possible with the NMO velocities of small-offset reflections. This paper concentrates on the subbasalt problem, but the results are more generally applicable to situations where high-velocity bodies overlie a low-velocity target, such as subsalt structures.