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Multisource Least-squares Migration and Prism Wave Reverse Time Migration

Multisource Least-squares Migration and Prism Wave Reverse Time Migration

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## Multisource Least-squares Migration and Prism Wave Reverse Time Migration

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**Multisource Least-squares Migration and Prism Wave Reverse**Time Migration Wei Dai Oct. 31, 2012**Outline**Introduction and Overview Chapter 2: Multisource least-squares migration Chapter 3: Plane-wave least-squares reverse time migration Chapter 4: Prism wave reverse time migration Summary**Introduction: Least-squares Migration**• Seismic migration: Given: Observed data • modelling operator Migration velocity Goal: find a reflectivity model to explain by solving the equation • expensive Direct solution: Conventional migration: • Iterative solution:**Introduction: Motivation for LSM**• Problems in conventional migration image 0 Z (km) migration artifacts 3 0 X (km) 6 0 X (km) 6 imbalanced amplitude**Problem of LSM**• Least-squares migration has been shown to produce high quality images, but it is considered too expensive for practical imaging. • Solution: combine multisource technique and least-squares migration (MLSM).**Multisource Migration Image**Motivation for Multisource • Problem: LSM is too slow Many (i.e. 20) times slower than standard migration • Solution: multisource phase-encoding technique Multisource Crosstalk • Multisource LSM • To: • Increase efficiency • Remove artifacts • Suppress crosstalk**Overview**• Chapter 2 : MLSM is implemented with Kirchhoff migration method and the performance is analysed with signal-to-noise ratio measurements. • Chapter 3: MLSM is implemented with reverse time migration and plane-wave encoding. • Chapter 4: A new method is proposed to migrate prism waves with reverse time migration.**Outline**Introduction and Overview Chapter 2: Multisource least-squares migration Chapter 3: Plane-wave least-squares reverse time migration Chapter 4: Prism wave reverse time migration Summary**Random Time Shift**Random source time shifts O(1/S) cost! Encoding Matrix Supergather Encoded supergather modeler**Multisource Migration**Given: Supergathermodeller shots are encoded in the supergather Define: Supergather migration )**Multisource Migration**) 1 Signal term S-1 noise terms SNR Repeat for all the shots SNR The signal-to-noise ratio of the migration image from one supergather is 1, when . If there are more supergathers SNR is the number of stacks.**Numerical Verification**Image of One supergather True Model Conventional Image 0 Z (km) 1.5 0 X (km) 5 0 X (km) 5**Numerical Verification**Image of Isupergathers True Model Conventional Image 0 Z (km) 1.5 0 X (km) 5 0 X (km) 5**Multisource LSM**One supergather, static encoding Iteration: 1 Iteration: 30 Iteration: 10 Iteration: 60 True Model 0 Z (km) 1.5 0 X (km) 5 0 X (km) 5**Multisource LSM**One supergather, dynamic encoding Iteration: 1 Iteration: 10 Iteration: 30 Iteration: 60 True Model 0 Z (km) 1.5 0 X (km) 5 0 X (km) 5**Static vs Dynamic**dynamic Static Iteration: 1 Iteration: 1 Iteration: 30 Iteration: 60 Iteration: 10 Iteration: 60 Iteration: 30 Iteration: 10 0 Z (km) 1.5 0 X (km) 5 0 X (km) 5**Chapter 2: Conclusions**• MLSM can produce high quality images efficiently. • LSM produces high quality image. • Multisource technique increases computational efficiency. • SNR analysis suggests that not too many iterations are needed.**Chapter 2: Limitations**• MLSM implemented with Kirchhoff migration can only reduce I/O cost. • need to be implemented with reverse time migration. • Random encoding method requires fixed spread acquisition geometry. • Plane-wave encoding.**Limitation of Random Encoding**• It is not applicable to marine streamer data. Fixed spread geometry (synthetic) Marine streamer geometry (observed) 6 traces 4 traces Mismatch between acquisition geometries will dominate the misfit.**Outline**Introduction and Overview Chapter 2: Multisource least-squares migration Chapter 3: Plane-wave least-squares reverse time migration Chapter 4: Prism wave reverse time migration Summary**Chapter 3: Plane-wave LSRTM**• Implemented with wave-equation based method • Significant computation saving. • Plane-wave encoding • Applicable to marine-streamer data. • Instead of inverting for one stacked image, image from each shot is separated. • Common image gathers are available. • Good convergence even with bulk velocity error.**Plane Wave Encoding**d(p,g,t)= p= Δt=pxs θ xs 0**Plane Wave Encoding**A common shot gather A supergather (p=0 μs/m) 0 Time (s) 12 0 X (km) 12 0 X (km) 12**Least-squares Migration with Prestack Image**• Equation: = m • Equations with stacked image: • Equations with prestatck image: = • Misfit: Solution:**Theory: Least-squares Migration**+ • Misfit: Penalty on image difference of nearby angles -d)-λ • Gradient:**Prestack Images**• Prestack image: X X stack p Z extract Z**The Marmousi2 Model**• Model size: 801 x 351 • Source freq: 20 hz • shots: 801 • geophones: 801 • Plane-wave gathers: 31 km/s 0 4.5 Z (km) 3.5 1.5 8 0 X (km)**Smooth Migration Velocity**0 Z (km) 3.5 Conventional RTM Image 0 Z (km) 3.5 0 X (km) 8**Plane-wave RTM image**0 Z (km) 3.5 Plane-wave LSRTM image (30 iterations) 0 Z (km) 3.5 0 X (km) 8**Common Image Gathers from RTM Image**0 Z (km) 3.5 Common Image Gathers from LSRTM Image 0 Z (km) 3.5 0 X (km) 8**RTM Image /w 5% Velocity Error**0 Z (km) 3.5 LSRTM Image /w 5% Velocity Error 0 Z (km) 3.5 0 X (km) 8**CIGs from RTM Image /w 5% Velocity Error**0 Z (km) 3.5 CIGs from LSRTM Image /w 5% Velocity Error 0 Z (km) 3.5 0 X (km) 8**Plane-wave LSRTM of 2D Marine Data**• Model size: 16 x 2.5 km • Source freq: 25 hz • Shots: 515 • Cable: 6km • Receivers: 480 km/s 0 2.1 Z (km) 2.5 1.5 16 0 X (km)**Workflow**Raw data Transform into CDP domain Apply Normal Moveout to flat reflections 2D spline interpolation Shift all the events back Transform into CRG domain Tau-p transform in CRG domain to generate plane waves**Conventional RTM (cost: 1)**0 Z (km) 2.5 Plane-wave RTM (cost: 0.2) 0 Z (km) 2.5 16 0 X (km)**Plane-wave LSRTM (cost: 12)**0 Z (km) 2.5 Plane-wave LSRTM /w One Angle per Iteration (cost: 0.4) 0 Z (km) 2.5 0 16 X (km)**Zoom Views**Conventional RTM Plane-wave LSRTM Plane-wave LSRTM (one angle) Plane-wave RTM**Zoom Views**Conventional RTM Plane-wave LSRTM Plane-wave LSRTM (one angle) Plane-wave RTM**Observed Data vs Predicted Data**(Plane Waves) Observed Data Predicted Data 0 Time (s) 3 0 X (km) 3.75 0 X (km) 3.75**Plane waves are fitted perfectly**Observed Data (Red lines) vs Predicted Data (Black lines) Amplitude 0 Time (s) 3**Chapter 3: Conclusions**• Plane-wave LSRTM can efficiently produce high quality images. • LSM produces high quality image. • Plane-wave encoding applicable to marine data. • Prestack image incorporated to produce common image gathers and enhance robustness.**Limitations**• Prestack images need to be stored during iterations. • Large memory cost.. • Plane wave encoding. • Regular sampling in shot axis is required (interpolation). • Sufficient amount of angles to reduce aliasing artifacts (i.e. 31).**Outline**Introduction and Overview Chapter 2: Multisource least-squares migration Chapter 3: Plane-wave least-squares reverse time migration Chapter 4: Prism wave reverse time migration Summary**Chapter 4: Introduction**• Problem: Vertical boundaries (salt flanks) are difficult to image because they are usually not illuminated by primary reflections. • Solution: Prism waves contain valuable information.**Conventional Method**• When the known boundaries are embedded in the velocity model, conventional RTM can migrate prism waves correctly.**Recorded Trace**0 2 Time (s)