ÖNCEL AKADEMİ: INTRODUCTION TO GEOPHYSICS
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This document discusses seismic reflection acquisition, processing, and waveform analysis. It introduces key concepts like reflection coefficients, convolution, and how the earth acts as a filter on seismic energy. Examples are provided to illustrate convolution and how it is used to model seismic reflections within the earth. Key wave properties like amplitude, wavelength, velocity and their relationships are also defined. Homework problems at the end ask about wave properties and applications of seismic reflection and refraction methods.
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ÖNCEL AKADEMİ: INTRODUCTION TO GEOPHYSICS
- 1. Introduction to Geophysics Ali Oncel [email_address] Department of Earth Sciences KFUPM Seismic Reflection 4: Acquisiton, Processing, and Waveform Analysis Introduction to Geophysics-KFUPM
- 2. Example: Disk Formula Seismic Waveform: Input Seismic Signal Homogenous Medium Strong Interface Amplitude Minimum Phase Pulse Zero Phase Pulse Acoustic Impedance Coefficients of Reflection and Transmission Example: Air-water reflection Example: Water-Air Reflection Reflection from Single Interface Reflections from Several Interfaces Previous Lecture Introduction to Geophysics-KFUPM
- 3. Convolution Earth as a Filter of Seismic Energy G(t) * F(t) = H(t) Source Earth = Seismogram Wavelet Ref. Coeff. Introduction to Geophysics-KFUPM
- 4. Source and Earth Response Mathematical Description of Filter Convolution Introduction to Geophysics-KFUPM See pp. 353 of Reynolds, 2002
- 5. Convolutional Model for the Earth SOURCE * Reflection Coefficient = DATA (input) (earth) (output) where * stands for convolution Reflections in the earth are viewed as equivalent to a convolution process between the earth and the input seismic wavelet. Introduction to Geophysics-KFUPM
- 6. Introduction to Geophysics-KFUPM (MORE REALISTIC) Convolutional Model for the Earth
- 8. Example 1: Convolution Introduction to Geophysics-KFUPM 1) Folding 2) Shifting 3) Multiplication 4) Summation The process of convolution consists of 4 simple mathematical operations Seismic Wavelet (1, -1/2, 1/2) Reflectivity Sequence (1, 1/2, 1/2)
- 9. Solution Reflectivity Output Sequence Response 1 1/2 1/2 1/2 -1/2 1 1x1= 1 1/2 -1/2 1 -1/2x1+1/2x1= 0 1/2 -1/2 1 1/2x1+1/2x-1/2+1/2x1= 3/4 1/2 -1/2 1 …………………= 0 1/2 -1/2 1 …………= 1/4 1/2 -1/2 1 …………= 0 Introduction to Geophysics-KFUPM
- 10. Convolution Output Response Plot amplitudes as a seismogram using travel times 1 , 0 , 3/4 , 1/4, 0 Introduction to Geophysics-KFUPM
- 11. Introduction to Geophysics-KFUPM For example, a double spike function , 2, 0, 1 convolved with an impulse response function 4, 3, 2, 1 . Example 2: Convolution From Kearey, Brooks, and Hill, 2002
- 12. Recall: Elastic waves Amplitude: the peak to trough height divided by two. Wavelength: the distance over which the wave goes through one complete cycle. Period: the time over which the wave is observed to complete a single cycle. V = Velocity = wavelength x frequency Introduction to Geophysics-KFUPM
- 13. Seismic Resolution Vertical – /4 to /2 wavelength V = V = 2000 m/sec = 25 Hz = V / = 80 meters Resolution 20 to 40 m Introduction to Geophysics-KFUPM
- 14. What is their period? 12 sec What is the amplitude of these waves? 1mm What is their frequency? 1/12 Hz = 0.083 Hz Example 1 Introduction to Geophysics-KFUPM V =
- 15. What is the amplitude of these waves? 1.2 mm What is their wavelength? 1.75 m If the frequency of these waves is 5 Hz, what is their speed? v = 1.75 m • 5Hz= 8.75 m/sec = 0.00875 km/sec Example 2 Introduction to Geophysics-KFUPM V =
- 16. Homework, Due to April 26 What is the amplitude of these waves? What is their period? These waves were recorded in rock with a seismic velocity of 5km/sec. What is their wavelength? Introduction to Geophysics-KFUPM V =
- 17. Homework, Due to April 26 What is the amplitude of these waves? What is their period? What is their frequency? Introduction to Geophysics-KFUPM V =
- 18. Homework, Due to April 26 In one typed page, discuss applications of a) the seismic reflection method b) the seismic refraction method 2. Calculating by hand Convolve the spike function: 2 0 0 3 3 1 3 -1 1 -2 -1 with the impulse response function: 1 2 1 -0.5 0 0.5 0 Show your working for the hand calculated version. Introduction to Geophysics-KFUPM