The Dehoop‐Knopoff representation theorem as a linear inverse problem

The deHoop‐Knopoff representation theorem, which relates observed seismic waves to a displacement discontinuity s defined on a surface S, is posed so that seismograms may be directly inverted for estimates of s and of the spatial and temporal resolution of s . Solutions s can be constructed either by parametrizing the fault surface as a number of point double couples or by representing s as an expansion of orthogonal functions. Of the infinite number of possible solutions satisfying a single seismic‐data set, methods for constructing particular solutions (e.g., best fitting, or closest to a desired solution) are given. Application of inverse theory to the deHoop‐Knopoff representation theorem leads to a convenient way to include various types of seismic data—e.g., long‐ and short‐period teleseismic, near field accelerogram, and geodetic—into a single inversion.