Questions & explanations
1. What is a common problem in reverse-time migration and how can we reduce it?
A common problem in reverse-time migration (RTM) is low-frequency noise, sometimes called 'backscattering' artifacts. This noise appears as smooth, long-wavelength energy in the image, especially near strong reflectors. It happens because the cross-correlation of forward and backward wavefields sums energy from all angles, including unwanted backscattered energy. To reduce this noise, we apply a Laplace filter after imaging, which removes the low-wavenumber components. Another method is to use a source-wavefield reconstruction with a directional damping term. Also, using a smooth velocity model helps minimize strong scattering. Even with these steps, some noise may remain, requiring careful parameter tuning.
2. How does full-waveform inversion update the model iteratively?
Full-waveform inversion (FWI) works in a loop. First, it computes synthetic data from the current velocity model using the wave equation. Then it calculates the difference (residual) between synthetic and real data. Next, it back-propagates this residual through the model to compute a gradient, which shows how to change the velocity at each point to reduce the residual. The model is then updated by a small step in the direction of the negative gradient. This loop repeats for many iterations, each time making the synthetic data match the real data better. The step size and update direction are chosen carefully to ensure convergence. After many iterations, the model resolves fine details of the subsurface.
3. How does pre-stack inversion estimate P-wave and S-wave impedances?
Pre-stack inversion works on angle gathers (or offset gathers). It uses the fact that the reflection amplitude changes with angle, and this change is related to P-wave impedance, S-wave impedance, and density. The inversion typically uses the Fatti approximation of the Zoeppritz equations, which expresses reflectivity as a sum of three terms: one for P-impedance, one for S-impedance, and one for density. By inverting the amplitudes at different angles simultaneously, we solve for these three properties. Usually, the density term is less reliable and may be fixed. The result is a 3D volume of P-impedance, S-impedance, and sometimes Vp/Vs ratio, which help identify lithology and fluids.
4. How is full-waveform inversion different from traveltime tomography?
Traveltime tomography uses only the arrival times of first breaks or reflections to build a velocity model. It ignores the waveform shape, so it gives a smooth, low-resolution model. Full-waveform inversion (FWI) uses the entire recorded waveform, including amplitude and phase, so it can resolve much finer details. FWI can image small features like thin layers and velocity variations that tomography misses. However, FWI requires a very good starting model to avoid cycle-skipping, while tomography is more robust and works with a rough initial guess. FWI also needs more computing power and clean data. The two methods are often combined: tomography builds the starting model for FWI.
5. How does reverse-time migration differ from one-way wave-equation migration?
One-way wave-equation migration only propagates waves in one direction, typically downward, so it cannot handle waves that turn or reflect from steep slopes. Reverse-time migration (RTM) uses the full two-way wave equation, propagating waves in all directions. This allows RTM to image overturned structures and salt overhangs that one-way methods miss. The trade-off is that RTM requires much more computer memory and time because it must store or recompute the forward wavefield. Also, RTM produces low-frequency artifacts that need special filtering, while one-way methods have fewer noise issues. In short, RTM is more accurate for complex geology but is slower and more expensive.
6. How does reverse-time migration handle turning waves and multiple arrivals?
Reverse-time migration (RTM) uses the two-way wave equation, which naturally allows waves to travel in any direction. When a wave turns (e.g., around a salt body), RTM can follow that path because it does not assume a one-way downward direction. Multiple arrivals—when a wave reaches the same point by different paths—are also handled correctly because RTM cross-correlates the source and receiver wavefields at each image point. This sums contributions from all paths, giving a clearer image of complex structures. One-way methods would miss these arrivals or require special correction. That is why RTM is preferred for areas with strong velocity contrasts and complicated geology.
7. What assumption does post-stack inversion make about the seismic data?
Post-stack inversion assumes that the stacked seismic trace is equivalent to a normal-incidence (zero-offset) reflection. This means it ignores the amplitude variation with angle and treats all reflections as coming from the same angle. In reality, the stack is a sum over a range of angles, so the assumption is only valid if the subsurface is isotropic and the reflectivity does not change much with angle. Post-stack inversion also assumes a convolutional model where the seismic trace is the convolution of a reflectivity series with a wavelet. These assumptions limit the accuracy, especially when the angle-dependent response is significant, such as in the presence of fluids.
8. How does amplitude vs offset (AVO) analysis help distinguish gas sands from brine sands?
Amplitude vs offset (AVO) analysis looks at how the seismic reflection amplitude changes as the distance (offset) between source and receiver increases. Gas sands often show a strong increase in amplitude with offset, while brine sands may show little change or a decrease. This happens because gas changes the rock's elastic properties, especially Poisson's ratio. By plotting amplitude versus angle of incidence, we can classify the AVO response. Different fluid types produce different AVO classes: for example, a gas sand often gives a class III AVO (negative intercept and gradient). AVO analysis is a quick way to identify potential hydrocarbon reservoirs from seismic data.
9. What is the 4D difference attribute and what does it show?
The 4D difference attribute is simply the subtraction of the baseline seismic volume (first survey) from the monitor seismic volume (later survey). The result is a volume of amplitude changes. Positive and negative differences indicate where the seismic response has changed. These changes can correspond to fluid substitution (e.g., oil replaced by water), pressure variation, or gas coming out of solution. The difference attribute is often displayed as a map or cross-section, with bright spots showing areas of high change. It is the primary tool for interpreting reservoir dynamics. Calibration with well production data is essential to understand what the changes mean.
10. What are the common AVO classes (I, II, III) and how do they differ?
AVO classes describe how the reflection amplitude changes with offset for a given interface. Class I has a positive intercept (high impedance) that decreases with offset. Class II has a near-zero intercept that may become positive or negative with offset. Class III has a negative intercept (low impedance) that becomes more negative with offset (amplitude increasing). Class I is typical for tight sands or carbonates, Class II for moderate impedance contrasts, and Class III for gas sands. There is also Class IV, which has a negative intercept but amplitude decreases with offset. Each class relates to different rock properties, particularly Poisson's ratio and density.
11. How do we choose between deterministic and stochastic inversion?
Deterministic inversion produces a single, smooth model that best fits the seismic data in a least-squares sense. It is fast and gives a unique solution, but it loses high-frequency details and uncertainty. Stochastic inversion generates many possible models (realizations) that all honor the seismic data and well statistics. It captures a range of uncertainties and can produce high-resolution details. The choice depends on the goal: if you need a quick average model, use deterministic; if you need to assess risk or model thin layers, use stochastic. Stochastic inversion is more computationally expensive but useful for reservoir modeling. Often both are run together.
12. How does full-waveform inversion use observed seismic data to build a velocity model?
Full-waveform inversion (FWI) starts with an initial velocity model and simulates synthetic seismic data using the wave equation. It compares the synthetic data to the real observed data and measures the difference (residual). Then it updates the velocity model in a way that reduces this difference, using a mathematical method called gradient descent. This process is repeated many times, with each iteration improving the model. FWI tries to match the full waveforms, not just arrival times, so it can build high-resolution models. It works well for areas with good data coverage and low noise. The final model has fine details of the subsurface, like layers and faults.