This paper discusses the generation of synthetic 3D seismic data for training neural networks to solve a variety of seismic processing, interpretation, and inversion tasks. Using synthetic data is a way to address the shortage of seismic data, which are required for solving problems with machine learning techniques. Synthetic data are built via a simulation process that is based on a mathematical representation of the physics of the problem. In other words, using synthetic data is an indirect way to teach neural networks about the physics of the problem. An important incentive for using synthetic data to solve problems with artificial intelligence methods is that with real seismic data the ground truth is always unknown. When generating synthetic seismic data, we first build the model and then calculate the data, so the answer (model) is always known and always exact. We describe a methodology for generating on-the-fly simulated postmigration (1D modeling) synthetic data in 3D, which are high resolution and look similar to real data. A wide range of models is covered by generating an unlimited number of data examples. The synthetic data are built from impedance models that are constructed through geostatistical simulation of real well logs. With geostatistical simulation, we can describe various geologic variance models in 3D and obtain realistic images. To cover a broad range of scenarios, we need to generalize the seismic data story by randomly perturbing many parameters including structures, conformity styles, dip-strike directions, variograms, measured input logs, frequencies, phase spectra, etc.