Static Correction
Seismic static correction is a crucial step in seismic data processing used to compensate for time delays caused by near-surface irregularities. These irregularities affect the travel time of seismic waves, introducing artificial time shifts in the recorded data, which can distort subsurface images and reduce the quality of stacking and migration.
Why is Static Correction Needed?
1. Near-surface layers (weathering zone) often have low velocity and varying thickness.
2. Seismic waves passing through these layers experience different delays at different source/receiver locations.
3. These delays are not related to subsurface structure, so they must be removed to properly align reflections.
Types of Static Corrections
1. Elevation Statics:
- Corrects for differences in source/receiver elevation.
- Applies a time shift based on a reference datum and assumed velocity.
2. Refraction (or Weathering) Statics:
- Corrects for variations in the thickness and velocity of the weathering layer.
- Often estimated using first arrival times.
3. Residual Statics:
- Fine-tunes time shifts after elevation and refraction statics.
- Optimizes alignment of reflection events across traces.
- Estimated using cross-correlation or stack-power maximization.
Elevation Static
Elevation statics are a fundamental part of seismic data processing, aiming to correct the travel times of seismic waves for variations in surface elevation. Since seismic waves travel at finite velocities, differences in the elevation of source and receiver points lead to differences in travel paths and thus differences in recorded travel times. If left uncorrected, these variations can misalign reflection events and degrade the quality of the seismic image.
The concept behind elevation statics is straightforward: we want to simulate the scenario where all shots and receivers are located on a flat, horizontal reference plane known as the datum. To do this, we calculate the extra or missing travel time that results from the actual elevation differences between the field locations and the datum. The replacement velocity—a constant velocity that represents the near-surface layer (often an average of the weathering layer or shallow soil)—is used to convert vertical elevation differences into time shifts.
Mathematically, the elevation static correction is computed by measuring the vertical distance from each source and receiver to the datum. If a source or receiver is above the datum, its travel path is shorter, and a positive correction (time delay) is applied. Conversely, if it is below the datum, its travel path is longer, and a negative correction (time advance) is applied. The static correction for each point is simply the elevation difference divided by the replacement velocity, usually expressed in time units (milliseconds).
Elevation statics are typically the first correction applied in a seismic processing workflow. They correct for the large-scale, predictable timing differences caused by topography but do not address velocity variations within the near-surface layers. For this reason, elevation statics are often combined with refraction statics or more advanced methods to handle the more detailed and complex velocity effects that arise from lateral variations in weathering thickness and velocity.
It is important to choose an appropriate replacement velocity when applying elevation statics. If the replacement velocity is too high or too low compared to the actual near-surface velocity, the static corrections will be inaccurate, and the data may not properly align. In some cases, the replacement velocity is estimated from uphole surveys, near-surface velocity models, or first-arrival analyses.
In summary, elevation statics serve as a geometric correction that flattens the acquisition surface to a common datum by compensating for elevation differences. They are a necessary step to ensure the initial alignment of seismic events, but they are typically not sufficient on their own. More detailed statics corrections, such as refraction statics, are usually required to correct for lateral velocity changes that elevation statics cannot resolve. Together, these corrections significantly enhance the coherence of reflection events and improve the final seismic image.
Refraction Tomography Static
Refraction tomography is an advanced method used in seismic processing to accurately model the near-surface velocity structure. It is particularly useful for computing static corrections in areas where the subsurface exhibits strong lateral and vertical velocity variations that simpler methods, such as the delay-time or Generalized Reciprocal Method (GRM), cannot adequately resolve.
The core idea of refraction tomography is to use first-arrival travel times to invert for a detailed two-dimensional velocity model. Initially, the near-surface is discretized into a grid of small rectangular cells, each assigned a slowness value (the reciprocal of velocity). Using the straight-ray approximation as a starting point, the travel path of seismic waves from sources to receivers is assumed to be linear segments through these cells. The lengths of these ray paths within each cell form the basis of a system of linear equations that relates the unknown slowness distribution to the observed travel times. This system is typically solved using damped least squares to provide a stable and smooth velocity model, preventing non-physical solutions caused by noise or insufficient ray coverage.
For more complex geological settings, straight-ray tomography may not be sufficient. Curved-ray tomography, which accounts for ray bending due to velocity gradients and interfaces, provides more accurate results in such cases. Curved rays can be computed using ray-bending algorithms, finite-difference eikonal solvers, or shortest-path methods. These approaches iteratively adjust the ray paths to minimize the difference between calculated and observed travel times while satisfying physical constraints like Snell’s Law. Forward modeling in these schemes often employs efficient eikonal solvers that can rapidly calculate travel times across large models, enabling more accurate imaging of complex near-surface structures.
Inverting the travel-time data to build the velocity model requires regularization techniques to stabilize the solution. This often includes damping to control the magnitude of slowness variations and smoothing constraints to suppress unrealistic sharp velocity changes. The inversion process can also incorporate lateral and vertical smoothness penalties to ensure that the final model is geologically reasonable and physically consistent.
Once the near-surface velocity model is obtained, static corrections are calculated by ray tracing from each shot and receiver position down to a common datum surface. The time it takes for a seismic wave to travel through the near-surface layers, as predicted by the tomography model, is used to determine the delay times. These delays are then compared to what would have been recorded if the near-surface were replaced by a uniform medium at a standard replacement velocity. The difference between these times forms the static correction, which is applied to the seismic data to align reflection events and improve image quality.
Overall, refraction tomography provides a powerful and detailed approach to resolving near-surface velocity variations and obtaining accurate static corrections, significantly enhancing the quality of seismic imaging in challenging environments.
Our Experience
Comparison of static correction methods for refraction tomography static and elevation static.
Easy concept in elevation static uses the elevation of sources and receivers and final datum and replacement velocity to obtain transit time from surface to datum.
Refraction tomography uses the picked first arrivals to obtain the delay times for weathering layers using inverse problem solution; then estimates the transit time from surface to datum.
Residual static corrections
Seismic residual static correction is a crucial processing step in reflection seismic data that corrects for small time shifts caused by near-surface irregularities that remain after elevation and refraction statics have been applied. These shifts can distort reflection events and degrade image quality, especially on stacked sections.
Residual statics are small, time-varying corrections applied to individual shot and receiver locations to align reflection events across traces—usually based on surface-consistent assumptions.
Why Is It Needed
- Near-surface conditions (e.g., weathering layers, topography, velocity variations) cause variable travel times.
- Elevation statics and refraction statics handle large-scale effects.
- Residual statics address remaining short-wavelength timing errors that still misalign reflections, especially at the CMP level.
How It Works (Conceptually)
1. Input: Common Midpoint (CMP) gathers or pre-stack data, after elevation and refraction statics.
- Cross-correlation or semblance analysis is used to:
- Measure the time misalignment of reflection events across traces.
- Estimate static shifts needed to align them.
2. Solve for Source and Receiver corrections assuming a surface-consistent model.
3. Apply corrections to each trace:
- Shift traces earlier or later in time (typically a few milliseconds)
Methods Used
- Cross-correlation of reflection events (most common)
- Stack power maximization
- Coherency (semblance) maximization
- Generalized linear inversion (GLI)
REAL DATA EXAMPLE
Comparison of static solution for three methods of max power optimization, cross correlation and GLI method.
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Application of Max power optimization (right panel) method on real data (left panel).
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