content
Seismic Signal Analysis and Noise Characteristics
Page 4: Signal Types and Mathematical Treatment
Stationary Signals
Defined as signals with statistical properties that do not change over time.
Example: Marine microseisms can be treated as stationary within a seismogram's time frame but may vary over days due to meteorological conditions.
Fourier transformation does not exist for stationary signals, but analysis can be performed over finite time intervals.
Focus is on Power Spectral Density (PSD) rather than detailed waveforms.
Transient Signals
Characterized by complicated waveforms influenced by the earthquake source, Earth's structure, and seismograph properties.
Waveforms can be deterministic, following mathematical relationships, unlike stochastic seismic noise.
Page 5: Fourier Transformation of Signals
Fourier Transformation Basics
Transient signals can be represented in the frequency domain using Fourier integrals.
The relationship between time domain and frequency domain is established through Fourier integral transformations.
The amplitude spectrum and phase spectrum are derived from the Fourier transform.
Frequency Filtering
Connected to analog signal processing and Fourier transformations.
Filtering modifies signal amplitudes and can change the amplitude of desired signals in the time domain.
Page 6: Discrete Fourier Transformation
Discrete Fourier Transformation (DFT)
A simpler formulation for harmonic analysis suitable for computer processing.
Involves equidistant samples of a continuous signal and results in complex Fourier coefficients.
Page 7: Spectral Analysis of Stationary Signals
Power Spectral Density (PSD) vs. Energy Spectral Density (ESD)
PSD is used for stationary signals, while ESD is used for transient signals.
The relationship between PSD and ESD is mathematically defined, with specific calculations for each.
Page 8: Energy and Power Densities
Calculating Spectral Densities
Energy and power densities are determined through Fourier transformations.
The total energy of a signal can be expressed as an integral of its spectral density.
Page 9: Spectral Analysis Techniques
Autocorrelation Method
Spectral density can also be determined by calculating the Fourier transformation of the autocorrelation of a signal.
Page 10: Signal Derivatives and PSD Representation
Changing Between Displacement, Velocity, and Acceleration
The Fourier transform of a signal can be adjusted to represent its derivatives.
PSD can be represented in decibels for easier comparison.
Page 11: Cross-Correlation and Coherence
Cross-Correlation
Measures the similarity between two stationary signals and can be expressed as a coherence spectrum.
Page 12: Uncertainty Principle
Fourier Transformation Uncertainty Principle
States that an impulsive signal must have a large bandwidth, and vice versa.
Page 13: Global Models for PSD of Seismic Noise
Noise Models
The New High Noise Model (NHNM) and New Low Noise Model (NLNM) define expected limits of seismic noise.
Variations in noise levels are observed across different periods.
Page 14: Noise Power Spectral Densities
Noise Power Spectral Densities
Tables provide values for noise power spectral densities at selected periods.
Page 15: Instrumental Self-Noise
Sources of Instrumental Noise
Modern seismographs produce self-noise due to electronic components.
Huddle tests can help identify the contributions of different instruments to self-noise.
Page 16: Comparing Spectra of Transient and Stationary Signals
Bandwidth and Amplitude
The relationship between bandwidth and amplitude is crucial for understanding signal power.
Page 17: Dynamic Range of Seismographs
Dynamic Range Definition
Defined as the range of amplitudes between the smallest and largest recordable signals.
Influenced by ambient noise and the instrument's technical properties.
Page 18: Representing Clip Levels and Noise
Graphical Representation
Seismic signals, noise levels, and clip levels can be represented in the same diagram for comparison.
Page 19: Power Densities and Recording Amplitudes
Conversion of Power Densities
Approximations for converting power densities into recording amplitudes are discussed.
Page 20: Bandwidth and Noise Characteristics
Bandwidth Considerations
The relationship between bandwidth and noise characteristics is essential for accurate seismic measurements.
Page 21: Seismograph Response and Waveform
Empirical Case Studies
Case studies illustrate the effects of bandwidth on the amplitude and timing of seismic signals.
Page 22: Signal Distortion in Seismic Records
Theoretical Considerations
Signal distortion due to seismograph response characteristics is discussed.
Page 23: Seismograph Response to Impulsive Signals
Transient Response
The transient response of seismographs affects the recording of impulsive signals.
Page 24: Seismic Noise Characteristics
Ocean Microseisms
Ocean waves generate microseisms, which are significant sources of seismic noise.
Page 25: Seismic Noise on the Ocean Floor
Broadband and Short-Period Noise
Noise characteristics differ between land and ocean floor environments.
Page 26: Seismic Noise on Land
Long-Period and Short-Period Noise
Various sources of noise on land, including natural and man-made, are discussed.
Page 27: Noise Characteristics and Sources
Cultural Noise
Man-made sources of noise significantly impact seismic recordings.
Page 28: Noise Reduction Techniques
Improving Signal-to-Noise Ratio
Techniques for reducing noise levels in seismic recordings are explored.
Page 29: Seismic Noise Characteristics
Noise Levels and Environmental Factors
Environmental factors influence noise levels and recording quality.
Page 30: Seismic Noise and Sensor Installation
Installation Considerations
Proper installation of sensors is crucial for minimizing noise and improving data quality.
Page 31: Seismic Noise and Environmental Conditions
Seasonal and Diurnal Variations
Noise levels can vary significantly based on environmental conditions.
Page 32: Summary of Seismic Noise Characteristics
Overall Noise Characteristics
A comprehensive overview of the characteristics and sources of seismic noise