I present an overview of full-waveform inversion (FWI), focusing on its use in seismic exploration. I consider the typical data acquisition scenarios used by industry, and discuss the progression of velocity model building and imaging techniques that have been employed to extract increasing amounts of information from seismic data. FWI has the potential to make the most complete use of seismic data, providing information ranging from improved imaging velocities to maps of rock and fluid properties on sub-wavelength scales.
While the basic mathematics of FWI has been known for decades, only in the last ten years or so have algorithm and compute-power advances made practical application to seismic problems possible. A number of these advances are discussed, following a brief discussion of the basic mathematical techniques used in FWI. Several synthetic examples illustrating the performance of FWI in ideal conditions are then shown. Finally, I look at some examples of the challenges that must be overcome to make FWI usable in real-world scenarios, and present examples of research aimed at solving these problems.