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Least squares migration of elastic data Aaron Stanton and Mauricio Sacchi PIMS 2015.

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Presentation on theme: "Least squares migration of elastic data Aaron Stanton and Mauricio Sacchi PIMS 2015."— Presentation transcript:

1 Least squares migration of elastic data Aaron Stanton and Mauricio Sacchi PIMS 2015

2 Outline Motivation Least squares migration of elastic data Adjoint (migration) operator – Wavefield de composition – Extrapolation – Imaging condition Forward (de-migration) operator – Adjoint of Imaging condition – Extrapolation – Wavefield re composition Preconditioning via Poynting vectors Example

3 Motivation To improve the imaging of converted wave data in the presence of noise, missing data, and poor illumination

4 Least squares migration with quadratic regularization L  extrapolates P & S potentials and recompose into data components

5 The forward operator Extrapolation and wavefield recomposition: Split-Step Padé Fourier propagator Blending of wavefields into data components

6 What is H -1 ? H -1 blends wavefield potentials into data components

7 What is H -1 ? H -1 blends wavefield potentials into data components

8 What is H -1 ? H -1 blends wavefield potentials into data components

9 What is H -1 ? H -1 blends wavefield potentials into data components If we assume isotropy we can use Helmholtz decomposition

10 Helmholtz decomposition

11 Etgen, 1988

12 Helmholtz recomposition Etgen, 1988

13 The forward operator Extrapolation and wavefield recomposition:

14 The adjoint operator wavefield decomposition and extrapolation: implies that the adjoint operator could result in some crosstalk artifacts

15 Quadratic Regularization

16 Angle domain regularization By a change of variables z = Dm we write Where D -1 is smoothing across angles within each angle gather

17 Poynting vector method Imaging is done without spatial lags Vectors are calculated from source and receiver side wavefields independently From the source and receiver side Poynting vectors the angle can be defined in many different ways Higginbotham et al, 2010

18 Poynting vectors Typically implemented in RTM: This approximation leads to a technique to calculate Poynting vectors in WEM (Dickens and Winbow, 2011) (Yoon and Marfurt, 2006)

19 Poynting vectors in WEM 1.calculate gradient components for the source side wavefield: 2.inverse Fourier transform over the spatial axes (x and z) 3.obtain that corresponds to the time of reflection by calculating the zero- lag cross correlation with the receiver wavefield: 4.normalize the elements of 5.repeat steps 1 to 4 for the z-component of the source side wavefield to obtain 6.repeat steps 1 to 5 for the receiver side wavefield

20 Unit vectors

21 Angle with respect to vertical: Angle with respect to reflector normal: Sign of angle (Duan and Sava 2014): Conversion from unit vectors to angle

22 Three Interfaces

23 m ps for 1 shot gather

24 Angles for 1 shot gather

25 Corrected gather

26 MARMOUSI 2 Synthetic data example

27 vpvp

28 vsvs

29 Shot gathers

30 Migration: m pp 25˚ incidence angle

31 LS Migration: m pp 25˚ incidence angle

32 Migration: m ps 25˚ incidence angle

33 LS Migration: m ps 25˚ incidence angle

34 ANTICLINE MODEL Synthetic data example

35 Simulated OBC Acquisition ★ osx = 100m ; dsx = 100m ; nsx = 69 ; sz = 10m ; dgx = 8m ; gz = 550m ; recording aperture = 6608m

36 X-Component

37 Z-Component

38 Angles for 1 migrated shot

39 Adjoint Mpp Constant Incidence angle of 10˚

40 Least Squares Mpp Constant Incidence angle of 10˚

41 Adjoint Mpp CIG @ x = 1600m

42 Least Squares Mpp CIG @ x = 1600m

43 Adjoint Mps Constant Incidence angle of 10˚

44 Least Squares Mps Constant Incidence angle of 10˚

45 Adjoint Mps CIG @ x = 1600m

46 Least Squares Mps CIG @ x = 1600m

47 Misfit Iteration number Relative misfit

48 Conclusions We implemented elastic least squares migration using the one way wave equation The forward operator consists of scalar extrapolation of P and S potentials followed by wavefield recomposition The method has application in imaging, regularization and wavefield separation of multicomponent data

49 Acknowledgements We gratefully acknowledge the sponsors of the Signal Analysis and Imaging Group for their generous support


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