This dataset contains 100,000 3D matrices representing S-wave velocity profiles with random fields. The spatial resolution corresponds to a grid of 9.6 x 9.6 x 9.6km with a spatial step of 300m (matrices are of size 33 x 33 x 33). Velocities go from 1,071 to 4,500m/s. Each profile contains a 1.8km-thick bottom layer at constant velocity 4500m/s. Above, the profile contains between 1 and 6 layers of random thickness. In each layer, the mean velocity is chosen uniformly in [1,785; 3,214m/s] and the coefficient of variation follows a Gaussian distribution N(0.2; 0.1). Then, a correlation length is chosen randomly among 1.5, 3, 4.5, 6 km in all three directions for each layer. The random fields' kernel has a von Karman correlation with a Hurst exponent of 0.1 and log-normal marginal distributions.