##### Wave-equation migration Q analysis

* by Yi Shen*

**Downloads**

- Thesis pdf

**Table of contents**

- Chapter 1: Introduction
- Chapter 2: Wave-equation migration Q analysis
- Chapter 3: Rock physics constrained WEMQA
- Chapter 4: Multi-parameter inversion of velocity and Q using wave-equation migration analysis
- Chapter 5: Field data application
- Chapter 6: Conclusions
- Appendix A: Spectral ratio method for migrated events
- Appendix B: Image perturbation
- Appendix C: Wave-equation Q tomographic operator
- Bibliography

**Abstract**

Quantitative estimates of quality factor Q are useful for a variety of applications, ranging from seismic-acquisition design, to seismic processing, amplitude analysis, and reservoir characterization. In my thesis, I mainly target to the attenuation caused by gas clouds/pockets, which is a notoriously challenging problem for reservoir identification and interpretation. The goal of my thesis is to understand and quantify the attenuation effects to create an accurate laterally- and vertically- varying attenuation model. Such estimates will be used to improve the image quality and provide greater confidence for hydrocarbon exploration.

Q model building, which is traditionally done in the data space using ray-based tomography, is a challenging problem due to issues like spectral interference, low signal-to-noise ratio, diffraction, and complex subsurface structure. I present an inversion based method, wave-equation migration Q analysis, to produce reliable Q models with two major features. First, this method will be performed in the image- space to stack out noise, focus and simplify events, and provide a direct link between the model perturbation and the image perturbation. Second, this method uses wave- equation-based Q tomography to handle the complex wave propagation. I develop both the Q migration and the Q tomographic operator using frequency-domain and time-domain visco-acoustic wave equations. Its numerical synthetic examples show that it works well for models with Q anomalies.

To improve the resolution of the Q model estimated by wave-equation migration Q analysis, I add a regularization term to the objective function based on the provided compressional velocity model. I derive an approximate closed-form solution relating the compressional velocity to compressional quality factor using rock physics model- ing. This solution is validated using well data in which the elastic properties were measured and Q was derived numerically. I apply this relation between velocity and Q to both synthetic and field seismic data, which produced an improved Q estimated model. I show that this improved Q model leads to a better seismic migration image.

Such developed methods require highly accurate velocity models. Therefore, I also develop a multi-parameter inversion of velocity and Q models using wave-equation migration analysis. This method poses the estimation problem as an optimization problem that seeks optimum velocity and Q models by minimizing user-defined image residuals. The numerical tests on a modified SEAM model with two gas clouds demonstrate the benefit of using such multi-parameter inversion, when the existing velocity and Q models are inaccurate. The results show that this inversion method is able to retrieve both velocity and Q models, and to correct and compensate the distorted migrated image caused by inaccurate velocity and Q models. I apply this joint inversion of velocity and Q models to the 3D Dolphin’s multi-client field data acquired in the North Sea, which have attenuation and velocity problems due to shallow subsurface gas chimneys and channels that are correlated with strong attenuation and low-interval velocity. The updated velocity shows low velocity regions around the gas and channel features. The inverted Q model detects the shape and location of the gas and channel areas, which align with Dolphin’s interpretation. Consequently, the migration with the updated velocity model and the estimated Q anomalies flattens the events in the subsurface angle gathers, enhances the damped amplitudes and the frequency content of the migrated events, corrects the distorted phase of the migrated events and makes them more coherent.

**Reproducibility and source codes**

This thesis has been tested for reproducibility. The source codes are made available for download. The scripts for field data applications are available for download.

** Programs for Q migration compensation and Q tomography**

Download here.

**Defense**

Defense presentation