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# E-101 - Signal Processing

5 days GEP/SIGNAL
Level
Audience
• E&P Geoscientists with experience in Signal Processing
Purpose
• To provide a thorough introduction to concepts and mathematical tools of signal processing used in seismic surveys, from acquisition, processing to interpretation
Learning Objectives
• To understand fundamentals of signal processing algorithms (Fourier, etc.), and their application in geophysics
• To use appropriate sampling and filtering techniques, with correlation and deconvolution processes to improve geophysical data
• To assess application constraints and limits of the methods
Prerequisite
• It is highly recommended to have a good knowledge of fundamentals in mathematics and signal processing
Ways and means
• Interactive presentations, exercises and document analysis
• 90% of the training duration is devoted to workshop on PC, using Signal Processing Software
Observation
Number of seats limited to 14 Tuition fees include deliverables on DVD

Overview on seismic acquisition and processing
The Fourier transform
• Fourier transform
• Time domain versus Frequency domain
• Field record analysis in (x,t) and (f, k) domains
Common functions in spectral analysis
• The Dirac function
• The boxcar function
• The Hanning function
• The exponential decay function
• The signals composed of carriers and envelopes
• The Dirac comb, used to sample a continuous function or make a signal periodic
• Approximation of a Dirac comb by the sum of cosines
• Periodicities in time
• Multiplication by a Dirac comb
Time and spatial sampling
• Mathematical representation of time sampling
• Conservation of the spectrum H(f). Shannon theorem
• Sampling the Fourier transform. The Discrete Fourier Transform (DFT)
• Sampling the Dirac function. Under-sampling. Spectral wrap-around (Aliasing)
• Over-sampling. Multiplexing. Spatial sampling
• Application to 2D and 3D spread designs
Correlation
• Analog and digital definitions. Interpreting the correlation. Properties of the correlation
• Autocorrelation of various functions. Measuring delays, phase and periods
• Noise attenuation by using cross correlations
Filters
• Properties. The Z-transform (ZT). Some examples of filters. Reject filters. Non-linear filters
• Spectral density: Raw cross-power spectrum. Smoothing
• Averages, methods of estimating energy levels. Random signals, white noise. Applications
• The Hilbert transform. Applications
Wave separation
• Description of separation methods with examples
• Different separation methods are described: F-K, SVD, SMF, Wiener, Polarization
• Application for wave separation on field records (body waves, surface waves, multiplesâ€¦)
Deconvolution and filter estimation
• Minimum and maximum phase causal and anti-causal signals
• Deconvolution
• Application: increasing of vertical resolution, multiple attenuation, stratigraphic deconvolution, Wiener filter and monitoring