Velocity Tomography Using Wave Equation Migration Time Lags
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Solution Overview
Problem
Direct measurement of residual depth errors (RDE) in complex imaging areas, such as sub-salt regions, is difficult due to the failure of ray tracing in complicated velocity models, and existing methods like Dix-like equations or computing derivatives are either inaccurate or computationally expensive.
Innovation Solution
Reconstructing RDE from time lags of wave equation migration, using a direct relation between RDE and time lags, and incorporating these into tomographic inversion workflows to update the velocity model, particularly in complex imaging areas where wave equation migration provides superior quality imaging.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If wave equation migration is used to generate offset or angle gathers in complex imaging areas, then imaging quality is improved, but computational cost becomes extremely expensive and impractical
Solution Approach 1:
The patent uses pre-computed Green's functions and time-lag measurements from wave equation migration as disposable intermediate results to estimate RDE, avoiding the need to perform full wave equation migration for gather generation. This approach uses cheap approximations (time-lag measurements) instead of expensive full migrations while still achieving the goal of RDE estimation in complex imaging areas.
2Measurement precision
If direct measurement of RDE is performed in complex imaging areas, then measurement accuracy is improved, but the measurement becomes difficult or impossible due to ray tracing failure
Solution Approach 1:
The patent introduces time-lag measurements as an intermediary quantity that can be obtained from wave equation migration results. Instead of directly measuring RDE from migrated gathers (which fails in complex areas), the method uses time-lags as a mediator to indirectly determine RDE through the relationship between time-lag and depth error, thereby overcoming the direct measurement difficulty.
3Productivity
If Dix-like equation approach is used to update velocity model, then computational efficiency is improved, but accuracy deteriorates due to 1D assumptions
Solution Approach 1:
The patent changes the fundamental parameter relationship used in velocity updates. Instead of using the Dix-like equation which assumes 1D layered media and relates velocity to root-mean-square velocity, the method uses the direct relationship between time-lag and residual depth error in the angle domain, allowing for more accurate velocity model updates in complex 3D imaging conditions while maintaining computational efficiency.
Data Source
AI summary
Velocity tomography using time lags of wave equation migration is disclosed. Seismic tomography is a technique for imaging the subsurface of the Earth with seismic waves by generated a migration velocity model from a multitude of observations using combinations of source and receiver locations. The migration velocity model may be updated in order to reduce depth differences of reflection events (also called residual depth errors (RDE)). Direct measurement of RDE may be difficult in certain complex subsurface areas. In such areas, the RDE may be reconstructed based on time lags of wave equation migration and then used to update the migration velocity model. In particular, the RDE may be directly reconstructed from the time lags of wave equation migration, such as based on a direct relation between RDE and the time lags.