Seismic Reflection 4: Acquisiton, Processing, and Waveform Analysis

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

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

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 =  