1. Efficient Geophysical Research in Julia
Aaron Stanton and Mauricio D. Sacchi

2. Outline
Motivation
Julia
Seismic.jl
Examples

3. Motivation Matlab is a great prototyping language But…
easy to understand, compact code
many built in functions for linear algebra and plotting
But…
inefficient for large problems
not open source
Compiled languages are great for implementation
efficient for large problems
support all forms of parallelism
difficult to follow
inefficient to code and debug

4. Motivation
Julia presents a new opportunity with Matlab-like syntax and C-like performance.

5. Julia Released in 2012 Completely open source with MIT license
Just-In-Time compiler
compiled after execution begins
has access to more information than static compilers
Sophisticated type system
Multiple dispatch
Rich library of linear algebra and plotting functions
Distributed and shared memory parallelism
Pass-by-reference (pointers)
Directly call C-libraries with no overhead

6. Example: For-Loops Multi-level for-loop: Matlab: 5.1041 seconds
for j1=1:100;
for j2 = 1:100;
for j3=1:100;
for j4=1000;
a += 1.0;
end
Matlab: seconds
Julia: seconds

7. Example: POCS Matlab Julia
y = zeros(nx1,nx2,nx3,nx4); for iw = 1 : nw y(:) = d(iw,:) x = y for iter = 1 : Niter Y = fftn(y); Y = Threshold(Y,p(iter)); y = ifftn(Y); y = a*x + (1 - a*T).*y end d(iw,:) = y(:)
y = zeros(nx1,nx2,nx3,nx4); for iw = 1 : nw y[:] = d[iw,:] x = copy(y) for iter = 1 : Niter Y = fft(y); Y = Threshold(Y,p[iter]); y = ifft(Y); y = a*x + (1 - a*T).*y end d[iw,:] = y[:]

8. Seismic.jl

9. Installation
Pkg.add(“Seismic”)

12. Basic usage

13. Basic usage

14. Basic usage

15. Basic usage

16. I/O Reading Seismic Unix Files Writing Seismic Unix Files
SegyToSeis("foo.su","foo",{"format"=>su})
Writing Seismic Unix Files
SeisToSegy("foo","foo.su",{"format"=>su})
Also supports rsf and segy formats, can swap bytes and convert from IBM to IEEE.

17. Data format: foo.seisd
Ntraces x Nsamples of Binary IEEE floats

18. Header format: foo.seish
For each trace the header is stored as type Header
Ntraces x 31 Binary IEEE floats/integers
To see all fields type “names(Header)”

19. Package Contents
Utilities
Processing
Imaging
Solvers

20. Utilities Conversion to/from SEGY, SU, and RSF formats
Reading and writing of internal format
foo.seisd
foo.seish
Windowing
Geometry
Header statistics
Sorting
Display header statistics
Binning
Patching/UnPatching
Processing on groups of traces

21. Processing Semblance NMO Mute Stack Bandpass and FK fan filtering
Radon transform
5D interpolation
POCS
MWNI
Many others to come
Structural Smoothing
FX deconvolution
Plane wave destruction for dip estimation …

22. Imaging Pre-stack time migration
3D shot-profile angle computation using Poynting vectors
3D shot-profile acoustic/elastic one-way wave equation migration/modeling
Least squares shot-profile acoustic/elastic one-way wave equation migration

23. Solvers Dot product test
Memory or disk based preconditioned conjugate gradients
Iteratively Reweighted Least Squares (IRLS)
Fast Iterative Soft Thresholding Algorithm (FISTA)

24. Examples

25. Calling POCS Interpolation
using Seismic Param ={"Niter"=>100,"fmax"=>60,"padt"=>2,"padx"=>2,"dt"=>0.004} dpocs = Seismic.pocs(ddec,param);

26. Interpolation input

27. Interpolation output

28. Calling Plane Wave Destruction
using Seismic download(" SegyToSeis("kevin_0off_velocity.su","kevins_model",{"format"=>"su"}); d,h = SeisRead("kevins_model"); coh,pp,res = SeisPWD(d,{"w1"=>30,"w2"=>20,"dx"=>8,"dz"=>4});

29. Estimated reflector normals

30. Julia in my own research

31. ShotProfileLSEWEM

32. Conjugate Gradients …

33. Forward and adjoint operators

34. ShotProfileEWEM …

35. Conclusions
Julia can be used for fast prototyping as well as large scale production
Julia programs are easy to follow for implementation in other languages
We developed a package in Julia that is part of the ecosystem of Julia packages: Pkg.add(“Seismic”)
Utilities
Processing
Imaging
Inversion
We will continue to make additions and improvements to Seismic.jl

36. References

37. Acknowledgements
Thanks to the creators of Julia and to Sam Kaplan for showing us Julia
We thank the sponsors of the Signal Analysis and Imaging Group for their support