Achieving Robust Compressive Sensing Seismic Acquisition with a Two-Step Sampling Approach.

Area of Science:

• Geophysics
• Signal Processing
• Seismic Survey Design

Background:

• Traditional seismic surveys often require dense, alias-free sampling, which can be costly and logistically challenging.
• Compressive sensing (CS) offers a framework for acquiring signals at a lower sampling rate than traditional methods.
• Designing CS-based seismic acquisition requires specialized sampling patterns that meet both theoretical requirements and practical constraints.

Purpose of the Study:

• To propose and evaluate a novel two-step design process for generating compressive sensing-based seismic sampling schemes.
• To ensure the generated sampling patterns adhere to CS theoretical properties while controlling spatial sampling characteristics.
• To demonstrate the applicability and robustness of the proposed method for practical 3D seismic survey design.

Main Methods:

• A two-step sampling strategy is employed: initial uniform random sampling guided by the restricted isometry property, followed by targeted sample addition.
• The second step, justified by the null space property, adds samples to control the maximum distance between adjacent sources or receivers.
• The method allows for flexible control over active and omitted samples, and its robustness is tested with reallocated samples and CS reconstruction.

Main Results:

• The proposed two-step sampling method successfully generates seismic sampling patterns with a strong CS theoretical foundation.
• The method provides control over the maximum distance between adjacent sampling points and allows for flexible sample distribution.
• CS reconstruction tests and analysis of a designed 3D seismic survey (fold maps, rose diagrams) confirm the suitability of the two-step scheme.

Conclusions:

• The developed two-step sampling design is effective for creating compressive sensing-based seismic acquisition schemes.
• The method balances theoretical CS requirements with practical geophysical and logistical considerations for seismic surveys.
• The proposed approach is suitable for CS-based seismic surveys and demonstrates practical utility in field applications.