# 3D Grid-based Tomography

## Update subsurface velocity and anisotropic material parameters along a predefined coarse grid.

**GeoDepth**™ Tomography supports both grid-based and model-based methods that can be used according to the problem to be solved. For example, Gulf of Mexico sediments affected by long period compaction are normally parameterized by a Cartesian grid.

### VELOCITY VOLUME UPDATES

3D grid tomography updates velocity volumes and (optionally) volumes of the anisotropic parameters ε and δ. The updates are calculated on a spatial grid which is generally coarser than the velocity volume, and whose vertical dimension can vary with depth. The updates can be constrained to honor the structure. After calculations are completed, the updates are interpolated to the size of velocity and anisotropic parameter grids. The interpolated updates are added to the current volumes to produce new volumes of velocities and anisotropic parameters, again taking into account the geological structure.

3D grid tomography can use well markers in the form of mis-tie maps as an additional constraint on the updated subsurface model.

Paradigm grid-based tomography supports Ocean Bottom Cable acquisitions.

### 3D REFRACTION TOMOGRAPHY FOR ACCURATE SHALLOW VELOCITY MODELING

Visualization of velocity logs on top of updated velocity cross sections following refraction tomography shows good correlation between the two.

3D refraction tomography is a new technology designed to estimate the shallow velocity model. The shallow subsurface section has a significant effect on seismic wave propagation in the deeper sections and thus on the quality and resolution of the seismic image in general.

3D refraction tomography is a sophisticated and accurate way to build the shallow velocity model. It uses refracted waves and first arrival travel times and is based on a tomographic inversion engine that enables a detailed estimation of the shallow velocity model by finding a model that minimizes the difference between actual travel times and simulated travel times calculated by refraction ray tracing. This tomography used is grid-based, in which the velocity model is estimated at every grid cell. Input includes first arrival travel times and an initial 3D near surface model.

The output velocity model can be used in various workflows, including:

- Directly in the prestack migration, bypassing the classic static shifts and greatly contributing to the accuracy of the migrated results
- As an initial model for a joint reflection-refraction tomography workflow to build a more accurate subsurface model
- To QC input data geometry: a large travel time difference between the measured and simulated time may indicated problems in the shot-receiver geometries.

### JOINT REFRACTION-REFLECTION TOMOGRAPHY BUILDS CONSISTENT VELOCITY MODELS FOR BOTH SHALLOW AND DEEP PARTS

Joint reflection-refraction tomography combines the new refraction tomography with our well-known reflection tomography into one workflow, to enable consistent construction of the velocity model in both the shallow and deep sections. This strategy increases accuracy and resolution in the velocity model and can result in much-improved migrated images.

One proposed workflow is as follows: First the shallow velocity model is defined by refraction tomography. Once established, the shallow velocity model is combined with an initial standard velocity model for a joint reflection-refraction tomographic process. At that stage the near-surface velocity-depth model derived from refraction tomography is more accurate and has high resolution, so it is left unchanged during the early iterations of the joint tomography and acts as a constraint for the reflection tomography process. In the later iteration, the joint tomography enables the update of both the shallow and deep velocities simultaneously. It uses reflection data and reflection ray tracing for the process. Another proposed workflow is to use both refraction and reflection tomography from the start to resolve the shallow and deep models simultaneously.

### INTEGRATING VSP DATA REDUCES UNCERTAINTY IN THE MODEL BUILDING PROCESS, RESULTING IN FEWER ITERATIONS AND QUICKER DELIVERY OF THE FINAL MODEL.

Incorporating VSP data into the tomographic inversion process can yield very accurate results, especially when updating anisotropic parameters. The information in VSP seismic data is superior to that of reflection seismic data, as it avoids the ambiguity of depth vs. velocity. Grid-based Tomography now supports first arrival VSP data, which can be used alone or together with regular reflection seismic data (CIG's). Grid-based Tomography uses point-to-point ray tracing to converge from the receivers in the borehole to the surface acquisition.

### WELL TIE TOMOGRAPHY

Tying the horizons interpreted on the seismic image to well markers plays a critical role in the velocity model building workflow, especially in the presence of anisotropy. The aim is to find a velocity model that yields flat gathers after depth migration, and ties to the well markers. Subsurface velocities cannot be uniquely determined by the surface recorded seismic data alone; in such cases, it’s possible to find a velocity that will flatten the gathers but not tie to the wells. Well information is used to reduce this ambiguity and generate a geologically plausible velocity model.

Mis-ties between seismic horizons and well markers are calculated and used as input to well tie tomography to update the velocity/anisotropic parameters, resulting in a velocity model that minimizes the input mis-ties.