Digital calculations
Jump to navigation
Jump to search
 | |
| Series | Geophysical References Series |
|---|---|
| Title | Problems in Exploration Seismology and their Solutions |
| Author | Lloyd P. Geldart and Robert E. Sheriff |
| Chapter | 9 |
| Pages | 295 - 366 |
| DOI | http://dx.doi.org/10.1190/1.9781560801733 |
| ISBN | ISBN 9781560801153 |
| Store | SEG Online Store |
Problem
Fill in the values in Table 9.9a.
Solution
Table 9.9b shows Table 9.9a completed.
| $ t=-3 $ | $ t=-2 $ | $ t=-1 $ | $ t=0 $ | $ t=+1 $ | $ t=+2 $ | $ t=+3 $ | $ t=+4 $ | $ t=+5 $ | |
|---|---|---|---|---|---|---|---|---|---|
| $ a_{t}=\left[2,\;1\;,\;-2,\;1\right] $ | |||||||||
| $ b_{t}=-2a_{t} $ | |||||||||
| $ c_{t}{=3a_{t-2}} $ | |||||||||
| $ {\hbox{d}}_{t}{=a_{-t}}/2 $ | |||||||||
| $ e_{t}=\pi a_{3-t} $ | |||||||||
| $ f_{t}=\left[-1,\;1\right] $ | |||||||||
| $ g_{t}{=a_{t}*f_{t}} $ | |||||||||
| $ \delta _{t+2} $ | |||||||||
| $ \delta _{2-t} $ | |||||||||
| $ \phi _{ff}(t) $ | |||||||||
| $ \phi _{fa}(t) $ |
| $ t=-3 $ | $ t=-2 $ | $ t=-1 $ | $ t=0 $ | $ t=+1 $ | $ t=+2 $ | $ t=+3 $ | $ t=+4 $ | $ t=+5 $ | |
|---|---|---|---|---|---|---|---|---|---|
| $ a_{t}=\left[2,\;1\;,\;-2,\;1\right] $ | 0 | 0 | 0 | 2 | 1 | $ -2 $ | 1 | 0 | 0 |
| $ b_{t}=-2a_{t} $ | 0 | 0 | 0 | $ -4 $ | $ -2 $ | 4 | $ -2 $ | 0 | 0 |
| $ c_{t}{=3a_{t-2}} $ | 0 | 0 | 0 | 0 | 0 | 6 | 3 | $ -6 $ | 3 |
| $ {\hbox{d}}_{t}{=a_{-t}}/2 $ | 1/2 | $ -1 $ | 1/2 | 1 | 0 | 0 | 0 | 0 | 0 |
| $ e_{t}=\pi a_{3-t} $ | 0 | 0 | 0 | $ \pi $ | $ -2\pi $ | $ \pi $ | $ 2\pi $ | 0 | 0 |
| $ f_{t}=\left[-1,\;1\right] $ | 0 | 0 | 0 | $ -1 $ | 1 | 0 | 0 | 0 | 0 |
| $ g_{t}{=a_{t}*f_{t}} $ | 0 | 0 | 0 | $ -2 $ | 1 | 3 | $ -3 $ | 1 | 0 |
| $ \delta _{t+2} $ | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| $ \delta _{2-t} $ | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| $ \phi _{ff}(t) $ | 0 | 0 | $ -1 $ | 2 | $ -1 $ | 0 | 0 | 0 | 0 |
| $ \phi _{fa}(t) $ | 0 | 0 | 0 | $ -1 $ | $ -1 $ | $ -3 $ | 3 | $ -1 $ | 0 |
Continue reading
| Previous section | Next section |
|---|---|
| Calculating crosscorrelation and autocorrelation | Semblance |
| Previous chapter | Next chapter |
| Reflection field methods | Geologic interpretation of reflection data |
Also in this chapter
- Fourier series
- Space-domain convolution and vibroseis acquisition
- Fourier transforms of the unit impulse and boxcar
- Extension of the sampling theorem
- Alias filters
- The convolutional model
- Water reverberation filter
- Calculating crosscorrelation and autocorrelation
- Digital calculations
- Semblance
- Convolution and correlation calculations
- Properties of minimum-phase wavelets
- Phase of composite wavelets
- Tuning and waveshape
- Making a wavelet minimum-phase
- Zero-phase filtering of a minimum-phase wavelet
- Deconvolution methods
- Calculation of inverse filters
- Inverse filter to remove ghosting and recursive filtering
- Ghosting as a notch filter
- Autocorrelation
- Wiener (least-squares) inverse filters
- Interpreting stacking velocity
- Effect of local high-velocity body
- Apparent-velocity filtering
- Complex-trace analysis
- Kirchhoff migration
- Using an upward-traveling coordinate system
- Finite-difference migration
- Effect of migration on fault interpretation
- Derivative and integral operators
- Effects of normal-moveout (NMO) removal
- Weighted least-squares
External links
| find literature about Digital calculations |
|
|
|
|
|
|
|