- Vail 99 slides
- Ph. D. thesis: Tetrahedral based earth models, ray tracing in tetrahedral models and analytical migration velocity analysis.
- 3d analytic migration velocity analysis.
We have developed new algorithms based on Liu and Bleistein's
2.5-D analytic MVA approach. The new algorithms use the imaging
conditions to estimate the "normal depth" perturbation. Explicit
solutions are obtained, while they can be used iteratively for
more complicated models. Here are the new ideas, either geophysically
or mathematically:
- I develop a mathematical platform based on ray theory. This mathematical platform is used to understand the 3-D PSDM imaging;
- I examined and justified some existing algorithms in use in the industry;
- The reflector-normal misfits are introduced. I pointed out that, the vertical misfits, widely used in the industry, lose accuracy when dip increases;
- Velocity and depth estimation algorithms are developed in the study;
- Velocity and gradient estimation algorithms are derived;
- I proposed a new way for velocity and depth trade/off study;
- MVA with alternative acquisition parameters are studied. It is found that MVA vs. offset^2 is superior to MVA vs. offset; and further superior to MVA vs. azimuth. This is shown only for simple background model, but, I argue that it is also true for mildly varying background models;
- I studied reflector-normal misfits with respect to different acquisition parameters in the appendices.

- 3-D Synthetic data tests on the velocity and depth estimation and the velocity and gradient estimation;
- 3-D Mahogany data tests on the velocity and depth estimation and the velocity and gradient estimation.

- 3d Tetrahedral Model Builder (tetramod, done)
- Following Zhenyue's 2-D/2.5-D migration velocity analysis, we have started a new project--3-D migration velocity analysis. Such a 3-D application requires many important tools such as model builder, visualization, ray tracer, depth migration tool. For this purpose, first, I have developed a 3-D tetrahedral model builder called TETRAMOD. TETRAMOD defines a set of syntax, and fully takes advantage of the 2-D model building tools in Seismic Unix (a horizon can be defined with a set of 2-D models, for examples). To define a tetrahedral model, the model builder first uses parametric equations (representing x, y and z in parameters u and v) to represent horizons, followed by the triangulation of horizons and then makes tetrahedra by connecting the control points on the triangular horizons. It generates several tables, bookkeeps properties of control points, facets and tetrahedra, as well as the relationship among them, so that the ray tracer can load them before the ray tracing, other than calculate them on the fly, which can dramatically speed up the ray tracer. Some of these information are useful for 3-D visualization of the models as well. Models built by TETRAMOD can be viewed by the 3-D visualization tools such as VIEWER3. Ray tracing and migration have been carried out on these models.

- I have developed our in-house tetrahedral WF ray tracer. Capability
of the ray tracer include, but not limited to, automated maintenance
of ray density, multiple ray tracing, multivaluedness, and much
more. Applications include:
- Modeling: users can arbitrarily define a reflection sequence, all the ray paths will automatically follow the sequence;
- Traveltimes for migration: it generates traveltime tables in a way that Kirchhoff migration will not suffer from multivalued traveltimes and Beylkin determinant has a closed-form;
- Ray path calculation: this is the key to our tomographic velocity analysis. Again, the advantage is that we end up with an extremely sparse Jacobian matrix which makes the ray tracing/MVA damn efficient!

- 3-d model VIEWER ( viewer3)
It can display any combinations of the following:
- Model features: triangulated horizons; tetrahedral layers; solid layers and solid horizons.
- Ray tracing results: rays in white or color, color coded by the value of traveltimes;
- Wavefronts: wired or solid wavefronts.
- Surface traveltimes: the interpolated traveltimes on the surface (color coded by traveltimes).

- 3-d TRI-Plane cut viewer ( trip ) You define the 3 planes cutting the cube, so that you can look inside the cube.

- Freely distributed in Seismic Unix (release 30 and later)
- 3-D velocity and depth two-step velocity estimation (vplusz)
- 3-D velocity gradient estimation (vzest)
- n-D wavelet transform libraries (wtlib)
- 3-D tetrahedral model builder (tetramod)
- 3-D tetrahedral model viewer (viewer3)
- 3-D tri-plane data/model viewer (trip)
- 3-D grid converter (regrid3)
- 5-D/6-D dynamic memory allocation subroutines (*alloc5d* and *alloc6*)

- Proprietary to Consortium Project on Seismic Inverse
Methods for Complex Structures
- 2-D Multi-resolution analysis of images using Daubechies wavelet transforms (mrafxzwt)
- 3-D tetrahedral wavefront construction ray tracer (sutetraray)

- Tomographic Velocity Analysis (Summer 1996, Directed by Kay D. Wyatt)
- Event Identification (Summer 1997, Directed by Kay D. Wyatt)

- Wavefield Imaging
- Z. Meng, et al.: 3-D Hale-McClellan prestack depth migration with enhanced extrapolation operators, 70th SEG expanded abstracts, 2000.

- 3-D Prestack Depth Imaging and Migration Velocity Analysis
- Z. Meng and N. Bleistein: Wavefront Construction (WF) Ray Tracing in Tetrahedral Models -- Application to 3-D traveltime and ray path computations, CWP-251, 1997 ( also 67th SEG expanded abstracts, 1997)

- Wavelet: Traveltime Tomography
- Z. Meng and J. A. Scales: 2-D tomography in multi-resolution analysis model space, 66th SEG expanded abstracts, 1996
- Z. Meng and J. A. Scales: Multiresolution analysis with wavelet transform: An application to 2-D tomography, CWP-223, 1996

- Wavelets: Bleistein/Cohen Inversion Theory
- Wavelet: Full Waveform Inversion
- L. Yang and Z. Meng: One dimensional ladder inversion of wave equation by wavelet representation, Chinese Journal of Geophysics, Vol. 38, No. 4, pp. 551-559, 1995.

- Wavelet: Seismic Data Compression
- Z. Meng and L. Yang: Seismic data compression with wavelets (in Chinese), Oil Geophysical Prospecting, Vol. 30, 1995, No. 2.