Virtual reflector representation theorem (acoustic medium).

Area of Science:

• Geophysics
• Seismic Imaging
• Wave Propagation

Background:

• Seismic exploration relies on analyzing wave propagation to understand subsurface structures.
• Simulating seismic responses is crucial for interpreting geological formations and identifying potential resources.
• Existing methods may face limitations in imaging complex geological scenarios or absent reflectors.

Purpose of the Study:

• To introduce and detail the virtual reflector method for seismic signal simulation.
• To provide a theoretical framework for generating virtual reflected signals using recorded seismic traces.
• To extend the method's applicability to acoustic media with and without boundaries, and to variable reflection coefficients.

Main Methods:

• The virtual reflector method is based on the cross-convolution of recorded seismic signals from multiple sources and receivers.
• The theory is grounded in the Kirchhoff integral representation theorem for wave propagation.
• The method is generalized to account for variable reflection coefficients in scattered wavefields.

Main Results:

• The virtual reflector method successfully simulates new seismic signals by processing existing data.
• It enables the retrieval of the Green's function for virtual reflected signals, mimicking the presence of a reflector.
• The approach is theoretically validated for acoustic media and extended for scattered wavefields with variable reflection coefficients.

Conclusions:

• The virtual reflector method offers a novel approach to seismic data processing and subsurface imaging.
• It provides a powerful tool for generating virtual seismic reflections, enhancing the interpretation of geological structures.
• This technique has the potential to improve seismic exploration by imaging absent or poorly defined reflectors.