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In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
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In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
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Achieving Robust Compressive Sensing Seismic Acquisition with a Two-Step Sampling Approach.

Anna Titova1, Michael B Wakin2, Ali C Tura1

  • 1Department of Geophysics, Colorado School of Mines, 1500 Illinois St., Golden, CO 80401, USA.

Sensors (Basel, Switzerland)
|December 9, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a two-step method for designing seismic surveys using compressive sensing (CS). This approach creates efficient sampling patterns, improving seismic data acquisition and analysis for field applications.

Keywords:
compressive sensingseismic acquisitionsignal samplingsurvey design

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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.