Modern seismic imaging tools for oil and gas exploration and production (E&P) assume that seismic data contain responses only of waves that bounce (e.g., reflect, diffract) only once at each interface in the subsurface. This type of response is called a primary. Unfortunately, actual seismic data also contain responses of waves that bounce at several interfaces in the subsurface. This type of response is called a multiple. In general, multiples in seismic data fall into two categories: (1) events that bounce at least once at the free surface in addition to any other bounce in the sub- surface and (2) events that do not bounce at the free surface but instead inside the subsurface, at two or more interfaces. The first category has the greater amount of energy; therefore most of the research and development efforts in E&P have so far focused on attenuating this category of multiples accurately. At present, more knowledge of the subsurface is expected from seismic imaging. To avoid any misinterpretation of these details, there is a growing need in the E&P industry to also attenuate the second category of multiples, known as internal multiples. In this work I describe a new method of attenuation of internal multiples. The method consists of predicting the internal multiples and then subtracting them from the data. The prediction of internal multiples from seismic data is made possible by the discovery of a new type of seismic scattering event known as a virtual event. Seismic virtual events constitute a calculational device, which is becoming an important part of seismic data processing. Virtual events combine forward and back- ward wave propagation in such a way that their convolution with real events allows us to predict internal multiples. In addition to showing how virtual events can be constructed from real seismic events, I also show that virtual events obey physical laws, despite their counterintuitive wavepath. I have illustrated the findings in this thesis with synthetic examples. In particu- lar, I have shown the effectiveness of my internal-multiple-attenuation method for a 1D data set, which includes several primaries and internal multiple interferences.