The effect of single-phase fluid saturation on the seismic bulk modulus of a rock is well understood; however, the behavior becomes more complex when multiple fluids are present. Several fluid mixing theories have been developed (e.g., Voigt, Reuss, and Hill) and each is valid in certain situations; however, in some scenarios it is unclear which theory to select, or indeed whether any are accurate. The critical wave propagation behavior depends on the manner that fluids are spatially distributed within the rock, compared to a seismic wavelength. We apply elastic finite-difference modeling to different rock-fluid distribution scenarios and replicate behavior described by various theoretical, empirical and lab data results. Significantly, our results compare well with observations from lab experiments, yet do not rely on poroelastic or squirt-flow models whose parameters are difficult to estimate in real reservoir settings. Our elastic scattering approach is less computationally expensive than poroelastic modeling and can be more easily applied to actual reservoir rock and fluid distributions. Our results provide us with a powerful new tool to analyze and predict the effects of multiple fluids and ‘patchy’ saturation on elastic moduli and seismic velocities. They also challenge assumptions about the controlling factors on saturated bulk moduli, suggesting they are more strongly affected by the spatial fluid distribution properties and wave scattering, than by pore-scale fluid flow effects.
Adjoint-state methods (ASMs) have proven successful for calculating the gradients of the functionals commonly found in geophysical inverse problems. The 3D image-domain formulation of the seismic velocity estimation problem uses imperfections in 3D migrated images to form an objective function, which is minimized using a combined ASM plus line-search approach. While image-domain methods are less sensitive than their data-domain counterparts because they are based largely on wavefield kinematics and not directly matching amplitudes, they are more robust to poorer starting models, which makes them attractive for the early stages of seismic velocity estimation. For time-lapse (4D) seismic scenarios, we show that the 3D ASM approach can be be extended to multiple datasets to offer high-quality estimates of production- and/or injection-induced subsurface change. We discuss two different penalty operators that lead to what we term absolute and relative inversion strategies. The absolute approach straightforwardly uses the difference of two independent 3D inversions to estimate a 4D slowness perturbation. The relative approach directly incorporates the baseline image into the penalty function to highlight where the baseline and monitor images are different and to mask where they are similar - even if reflectors are imperfectly focused. Both these techniques yield good 4D slowness estimates for synthetic data; however, we assert that the relative approach is more robust and preferable to the absolute strategy in the presence of 4D field noise because it represents a less-demanding inversion goal.
Wavefield tomography represents a family of velocity model building techniques based on seismic waveforms as the input and seismic wavefields as the information carrier. For wavefield tomography implemented in the image domain, the objective function is designed to optimize the coherency of reflections in extended common-image gathers. This function applies a penalty operator to the gathers, thus highlighting image inaccuracies due to the velocity model error. Uneven illumination is a common problem for complex geological regions, such as subsalt. Imbalanced illumination results in defocusing in common-image gathers regardless of the velocity model accuracy. This additional defocusing violates the wavefield tomography assumption stating that the migrated images are perfectly focused in the case of the correct model and degrades the model reconstruction. We address this problem by incorporating the illumination effects into the penalty operator such that only the defocusing due to model errors is used for model construction. This method improves the robustness and effectiveness of wavefield tomography applied in areas characterized by poor illumination. The Sigsbee synthetic example demonstrates that velocity models are more accurately reconstructed by our method using the illumination compensation, leading to more coherent and better focused subsurface images than those obtained by the conventional approach without illumination compensation.
Time-lapse analysis of 4D seismic data acquired at different stages of hydrocarbon production or fluid/gas injection has been very successful at capturing detailed reservoir changes (e.g., pressure, saturation, fluid flow). Conventionally, 4D seismic analysis is performed in the time-migrated domain assuming a fixed migration velocity model; however, this scenario is violated when the subsurface velocity is significantly altered by production/injection effects resulting in large time-shift anomalies and complex 4D wavefield coda. For these scenarios we argue that one should use a robust 4D analysis procedure involving iterative wave-equation prestack depth migration and time-lapse velocity analysis. We adapt 3D image-domain wave-equation migration velocity analysis (WEMVA) to such time-lapse scenarios to backproject discrepancies (residuals) in migrated baseline, monitor, and time-lapse images to estimate 4D velocity model perturbations. We highlight the differences between the 3D and 4D WEMVA inversion problems, and how we constrain 4D perturbation estimates to preferentially be updated within the reservoir zone. We demonstrate the benefits of various 4D WEMVA strategy in a set of synthetic experiments that involve estimating time-lapse model perturbations arising from a thin layer (<20m) of injected CO2 in a North Sea analogue reservoir.