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- 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. <ul><li>Example: Disk Formula </li></ul><ul><li>Seismic Waveform: Input Seismic Signal </li></ul><ul><ul><li>Homogenous Medium </li></ul></ul><ul><ul><li>Strong Interface </li></ul></ul><ul><li>Amplitude </li></ul><ul><ul><li>Minimum Phase Pulse </li></ul></ul><ul><ul><li>Zero Phase Pulse </li></ul></ul><ul><li>Acoustic Impedance </li></ul><ul><li>Coefficients of Reflection and Transmission </li></ul><ul><ul><li>Example: Air-water reflection </li></ul></ul><ul><ul><li>Example: Water-Air Reflection </li></ul></ul><ul><li>Reflection from Single Interface </li></ul><ul><li>Reflections from Several Interfaces </li></ul>Previous Lecture Introduction to Geophysics-KFUPM
- 3. Convolution <ul><li>Earth as a Filter of Seismic Energy </li></ul><ul><li>G(t) * F(t) = H(t) </li></ul><ul><li>Source Earth = Seismogram </li></ul><ul><li>Wavelet Ref. Coeff. </li></ul>Introduction to Geophysics-KFUPM
- 4. Source and Earth Response <ul><li>Mathematical Description of Filter </li></ul><ul><li>Convolution </li></ul>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
- 7. Introduction to Geophysics-KFUPM
- 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 <ul><li>Amplitude: the peak to trough height divided by two. </li></ul><ul><li>Wavelength: the distance over which the wave goes through one complete cycle. </li></ul><ul><li>Period: the time over which the wave is observed to complete a single cycle. </li></ul>V = Velocity = wavelength x frequency Introduction to Geophysics-KFUPM
- 13. Seismic Resolution <ul><li>Vertical – /4 to /2 wavelength </li></ul><ul><li>V = </li></ul><ul><li>V = 2000 m/sec = 25 Hz </li></ul><ul><li> = V / = 80 meters </li></ul><ul><li>Resolution 20 to 40 m </li></ul>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 <ul><li>In one typed page, discuss applications of </li></ul><ul><li>a) the seismic reflection method </li></ul><ul><li>b) the seismic refraction method </li></ul><ul><li>2. Calculating by hand </li></ul><ul><li>Convolve the spike function: </li></ul><ul><li>2 0 0 3 3 1 3 -1 1 -2 -1 </li></ul><ul><li>with the impulse response function: </li></ul><ul><li>1 2 1 -0.5 0 0.5 0 </li></ul><ul><li>Show your working for the hand calculated version. </li></ul>Introduction to Geophysics-KFUPM

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