On the Retrieval of Forward-Scattered Waveforms From Acoustic Reflection and Transmission Data With the Marchenko...

Area of Science:

• Geophysics
• Seismic Imaging
• Wave Propagation

Background:

• Green's function retrieval from reflection data is crucial for seismic imaging.
• The Marchenko equation is a key tool for this retrieval.
• Current methods using only direct waves often miss forward-scattered waveforms and multiple reflections.

Purpose of the Study:

• To mitigate the problem of missing forward-scattered waveforms in Green's function retrieval.
• To investigate the incorporation of transmission data to improve Green's function estimates.
• To enhance the accuracy and completeness of seismic imaging.

Main Methods:

• Solving a multidimensional Marchenko equation using reflection data.
• Utilizing a priori knowledge of the initial focusing function.
• Deriving and solving an auxiliary equation for forward-scattered components using transmission data.
• Applying the method in an acoustic medium with mass density contrast and constant propagation velocity.

Main Results:

• Successfully derived an auxiliary equation for forward-scattered components.
• Demonstrated the solvability of the auxiliary equation in a specified acoustic medium.
• Showcased the inclusion of forward-scattered waveforms in Green's function estimates by solving auxiliary and Marchenko equations successively.
• Validated the enhanced Green's function retrieval with a numerical example.

Conclusions:

• Incorporating transmission data effectively mitigates the loss of forward-scattered waveforms in Green's function retrieval.
• The proposed method enhances seismic imaging by providing more complete Green's functions.
• This approach offers a significant improvement over traditional direct-wave approximations.