  The idea of curvature analysis has been widely used in subsurface structure
interpretation from three-dimensional (3D) seismic data (e.g., fault/fracture
detection and geomorphology delineation) by measuring the lateral changes in
the geometry of seismic events. However, such geometric curvature utilizes only
the kinematic information (two-way traveltime) of the available seismic
signals. While analyzing the dynamic information (waveform), the traditional
approaches (e.g., complex trace analysis) are often trace-wise and thereby fail
to take into account the seismic reflector continuity and deviate from the true
direction of geologic deposition, especially for steeply dipping formations.
This study proposes extending the 3D curvature analysis to the waveforms in a
seismic profile, here denoted as the waveform curvature, and investigates the
associated implications for assisting seismic interpretation. Applications to
the F3 seismic dataset over the Netherlands North Sea demonstrate the added
values of the proposed waveform curvature analysis in four aspects. First, the
capability of the curvature operator in differentiating convex and concave
bending allows automatic decomposition of a seismic image by the reflector
types (peaks, troughs and zero-crossings), which can greatly facilitate
computer-aided horizon interpretation and modelling from 3D seismic data.
Second, the signed minimum curvature offers a new analytical approach for
estimating the fundamental and important reflector dip attribute by searching
the orientation associated with least waveform variation. Third, the signed
maximum curvature makes it possible to analyze the seismic signals along the
normal direction of the reflection events. Finally, the curvature analysis
promotes the frequency bands of the seismic signals and thereby enhances the
apparent resolution on identifying and interpreting subtle seismic features.
