an unsophisticated look at curvelets and how to use them for seismic data...
TRANSCRIPT
![Page 1: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/1.jpg)
An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processing
Mostafa NaghizadehUniversity of Alberta(Currently at the University of Calgary)
CSEG Lunchbox Calgary
20th April 2010
![Page 2: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/2.jpg)
Outlines:
Introduction
Curvelet transform
Curvelet interpolation
Synthetic and real data examples
Curvelet ground-roll elimination
Synthetic example
Conclusion
![Page 3: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/3.jpg)
Introduction I:
Curvelet transform:
F-K filteringintegrated with
frame and operator theory
*** This talk focuses on f-k filtering concept and leaves out the frame theory part. This facilitates a physical understanding of curvelets rather than getting stuck in technical details of computing them.
![Page 4: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/4.jpg)
Introduction II:
Curvelet transformCandes and Donoho (2003) (http://www.curvelet.org/)
Curvelets in seismic data processing Interpolation
Hennenfent and Herrmann (2008)De-noising (random and coherent)
Yarham and Herrmann (2006)Multiple removal
Herrmann and Verschuur (2004)Imaging
Douma and de Hoop (2007)Chauris and Nguyen (2008)
…..
![Page 5: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/5.jpg)
Curvelet Transform
![Page 6: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/6.jpg)
Problem definition
Seismic data in T-X domain
Scale Angle Time Distance
Curvelet functions
![Page 7: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/7.jpg)
Curvelet coefficients
Inner product of data and curvelet functions
Forward curvelet transform
Adjoint curvelet transform
![Page 8: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/8.jpg)
F-K domain tiling of curvelet transform
0 0.25 0.5-0.25-0.50.0
0.25
0.5
Norm
alized frequency
Normalized wavenumber
scale 1
scale 3
scale 5
![Page 9: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/9.jpg)
Plotting Curvelet coefficientsa)
0 0.25 0.5-0.25-0.50.0
0.25
0.5
Nor
mal
ized
freq
uenc
y
Normalized wavenumber
1
23 4 5 6
7
8
b)
12345678
Curvelet panels have different sizes but for illustration purposes they can be scaled into a constant panel size (50x50 for plots in this presentation).
![Page 10: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/10.jpg)
Synthetic seismic section
![Page 11: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/11.jpg)
Curvelet windows in F-K domain
![Page 12: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/12.jpg)
Curvelet panels
![Page 13: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/13.jpg)
Synthetic example
T-X F-K Curvelets
![Page 14: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/14.jpg)
Only the 4th scale of curvelet domain
T-X F-KCurvelets
![Page 15: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/15.jpg)
Data with only one angle of the 4th scale of curvelets
T-X F-KCurvelets
One can built a super-redundant resemblances of curvelets by just applying F-K filtering for each curvelet tile in the F-K domain.
![Page 16: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/16.jpg)
A single curvelet coefficient at scale 4
T-X F-KCurvelets
![Page 17: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/17.jpg)
Curvelet interpolation*
*Accepted for publication in GEOPHYSICS. The article is accessible online at:http://www.phys.ualberta.ca/~mnaghi/Files/Research/Papers/curvelet_interpolation.pdf
![Page 18: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/18.jpg)
Introduction I:
Herrmann and Hennenfent (2008) used curvelets for interpolation of irregularly sampled seismic data.
They reported failure of curvelet interpolation for regularly sampled aliased data. They recommended using jitter sampling strategy in the acquisition stage in order to avoid having regularly sampled data.
![Page 19: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/19.jpg)
Introduction II:
In this presentation curvelets are used for interpolation of regularly and irregularly sampled aliased seismic data. The method can be considered as a combination of:
1.The F-X (Spitz,1991) or F-K (Gulunay,2003) interpolation methods which utilize the low frequency information for beyond-alias interpolation of high frequencies.
2.Minimum Weighted Norm Interpolation (MWNI) method with the exception that here we will use curvelettransform instead of Fourier Transform.
![Page 20: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/20.jpg)
Problem definition
Sampling matrix
Interpolated data
Available data
Inverse Curvelet
Mask function
Curvelet coefficients
![Page 21: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/21.jpg)
Least-squares curvelet interpolation
Cost function
Mask function
Maximum alias-free scale
![Page 22: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/22.jpg)
Synthetic example 1(Regularly sampled aliased data)
![Page 23: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/23.jpg)
Original synthetic data
T-X F-K
![Page 24: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/24.jpg)
Decimated data by factor of 4
T-X F-K
![Page 25: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/25.jpg)
Zero-interlaced data
![Page 26: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/26.jpg)
F-K panel of zero-interlaced data
![Page 27: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/27.jpg)
F-K panel of zero-interlaced data
![Page 28: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/28.jpg)
F-K panel of zero-interlaced data
![Page 29: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/29.jpg)
Curvelet panels of zero-interlaced data
![Page 30: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/30.jpg)
The mask (weight) function
![Page 31: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/31.jpg)
Curvelet panels of interpolated data
![Page 32: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/32.jpg)
Interpolated data using curvelets
T-X F-K
![Page 33: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/33.jpg)
The difference section
Interpolated DifferenceOriginal
![Page 34: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/34.jpg)
Synthetic example 2(Irregularly sampled data)
![Page 35: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/35.jpg)
Curvelet interpolation of irregularly sampled data
original interpolated
missing difference
![Page 36: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/36.jpg)
F-K panels of data
original interpolatedmissing
![Page 37: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/37.jpg)
Curvelet panels
missing
interpolated
![Page 38: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/38.jpg)
Synthetic example 3(Data with conflicting dips)
![Page 39: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/39.jpg)
Synthetic example with conflicting dips
original interpolateddecimated
![Page 40: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/40.jpg)
Zero-interlaced data
F-K
T-X
![Page 41: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/41.jpg)
Curvelet panels of zero-interlaced data
![Page 42: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/42.jpg)
The mask (weight) function
![Page 43: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/43.jpg)
Curvelet panels of interpolated data
![Page 44: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/44.jpg)
Real data example 1(Shot record)
![Page 45: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/45.jpg)
Original shot gather from the Gulf of Mexico
![Page 46: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/46.jpg)
Interpolated shot gather
![Page 47: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/47.jpg)
F-K panel of data
original interpolated
![Page 48: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/48.jpg)
Curvelet panels of zero-interlaced data
![Page 49: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/49.jpg)
The mask (weight) function
![Page 50: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/50.jpg)
Curvelet panels of interpolated data
![Page 51: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/51.jpg)
Real data example 2(Near-offset section)
![Page 52: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/52.jpg)
Original near-offset section
![Page 53: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/53.jpg)
Interpolated near-offset section
![Page 54: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/54.jpg)
F-K panel of data
original interpolated
![Page 55: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/55.jpg)
Curvelet panels of zero-interlaced data
![Page 56: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/56.jpg)
The mask (weight) function
![Page 57: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/57.jpg)
Curvelet panels of interpolated data
![Page 58: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/58.jpg)
Ground-roll elimination
![Page 59: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/59.jpg)
Synthetic data contaminated by ground-roll
![Page 60: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/60.jpg)
Synthetic data contaminated by ground-roll
![Page 61: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/61.jpg)
Curvelet panels of data
![Page 62: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/62.jpg)
Mask function (from high to low frequency)
Projecting maskfunction fromhigher scales
to lower scales
![Page 63: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/63.jpg)
Filtered curvelet panels using mask function
![Page 64: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/64.jpg)
Ground-roll eliminated section using curvelets
![Page 65: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/65.jpg)
F-K dip filtered data
![Page 66: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/66.jpg)
Conclusions:Curvelet transform is a local decomposition of data based on
some predefined scales and directions. It can be conceived as an F-K filtering combined with frame theory principles to obtain an optimal and efficient redundant representation of data.
For Interpolation of data in curvelet domain:Extract a mask function from alias-free scales (low frequencies) and
project it to alias-contaminated scales (high frequencies).Form a least-squares fitting algorithm using the sampling operator
and mask function. In the case of irregularly sampled data, iterative thresholding of
curvelet coefficients (IRLS) suffices for interpolation purposes.For Ground-roll elimination in Curvelet domain:
Extract mask function from non-contaminated scales (high frequencies) and use it to eliminate ground-roll in the contaminated area (low frequencies).
![Page 67: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/67.jpg)
Acknowledgments:
Dr. Mauricio Sacchi for his insightful supervision during my PhD program and after.
Authors of CurveLab [http://www.curvelet.org/], Emmanuel Candes, Laurent Demanet, David Donoho, and Lexing Ying for providing access to their curvelettransform codes.
Sponsors of SAIG for their financial support.
![Page 68: An Unsophisticated Look at Curvelets and How to use them for Seismic Data Processingmostafan/Files/Presentations/mostafa... · An Unsophisticated Look at Curvelets and How to use](https://reader034.vdocuments.mx/reader034/viewer/2022051601/5ad1e3747f8b9a05208c0a60/html5/thumbnails/68.jpg)