Enhancing Seismic Imaging: A Python Tool for Understanding Migration with Simple Geometries

Spatial resolution of seismic data is prone to limitation in presence of diffractions which are caused by dipping events and fault planes/edges. Different migration techniques are applied to collapse the scattered diffraction energy on their true spatial locations and hence increase the spatial resolution. Hagedoorn migration (wavefront construction) is a simple technique applied on the unmigrated data (seismic data with diffractions) to reposition all the scattered diffraction energy to their actual subsurface position.

The diffracted energy of a point source, with consideration of constant velocity model, will lie on a semi circle passing through the point. The energy on this semi-circle is also called impulse response of point diffractor. When combining the impulse response of adjacent events on seismic data (e.g. dipping reflector) will constructively interfere at the true subsurface location(Figure-01). In this way all the diffractions can be repositioned / migrated to correct subsurface location.

The python code results by author describes the simple geometry solution to the diffraction problem (unmigrated events), which could be simply moved to their true subsurface locations by finding the constructive interference points of semi-circular wavefronts of each unmigrated event. All the other points will cancel out due the destructive interference leaving only the migrated event in the data. Figure-02 shows the migration of an anticline which is narrower then its unmigrated geometry. In case of broader synclines the migration events are broadened (Figure-03). In case of narrow synlines, which are apparent as bow-tie geometries, the migrated reflection are also broadened (Figure-04).