Method of imaging in an underground formations steep-sloping geologic interfaces, giving rise to prismatic reflections

A method of imaging, in an underground formation, at least one steep sloping geologic interface forming with primary reflectors dihedra whose faces are not necessarily plane and giving rise to prismatic seismic reflections, from time-dependent seismic records of waveforms received by seismic receivers coupled with the formation, in response to the emission of seismic waves in a subsoil by a seismic source, comprising:

• determining a subsurface model described by a velocity distribution in the formation, and a geometry of each primary reflector contributing to the formation of the prismatic seismic reflections;
• choosing on the seismic record arrival times of seismic events corresponding to prismatic seismic reflections impacting at impact points on the sloping geologic interface and on each primary reflector, for source-pickup pairs of the seismic receivers;
• forming an arrival time vector from traveltimes corresponding to signatures;
• and
• constructing an image of the subsoil by applying a reflection traveltime tomography technique to determine geometry of the at least one steep sloping interface;
• and wherein the reflection traveltime tomography technique comprises:
• minimizing a difference between traveltimes generated by tracing rays through the subsurface model and traveltimes forming the arrival time vector;
• and
• constraining the minimization by guaranteeing an existence of a ray for each signature which is considered by means of constraints defined by seeking the path along which the traveltime is a minimum by imposing at the impact points position constraints on the reflectors so as to satisfy the signature which is considered.