To accurately locate microearthquakes that are genetically related to hydraulic fracture stimulation, a thorough knowledge of the velocity structure between monitoring and fracturing treatment wells is essential. Very fast simulated annealing (VFSA) is implemented to invert for a flat-layered velocity model between wells using perforation or string-shot data. A two-point ray-tracing method is used to find the ray parameter [Formula: see text] for a ray traveling from a source to a receiver. The original traveltime-calculation formula is modified to account for the borehole source-receiver geometry. VFSA is used as a tool to optimize P- and S-wave velocities simultaneously. Unlike previous applications of VFSA, two improvements result from a new study: (1) both P- and S-wave arrival-time misfits are considered in a joint-objective function, and (2) P- and S-wave velocities are perturbed simultaneously during annealing. The inverted velocities follow the true values closely with a very small root-mean-square error, indicating the inverted model is close to the global minimum solution whose rms error should be zero for synthetic examples. Data noise contaminates inverted models, but not substantially in synthetic test results. A comparison of models inverted using VFSA and Occam’s inversion technique indicates that inverted models using VFSA are superior to those using Occam’s method in terms of velocity accuracy.

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The simulated annealing ͑SA͒ inversion technique has been successfully applied for solving various nonlinear geophysical problems. Following previous developments, we modified the SA inversion, yielding 1D shallow S-wave velocity profiles from high frequency fundamental-mode Rayleigh dispersion curves, and validated the inversion with blind tests. Unlike previous applications of SA, this study draws random numbers from a standard Gaussian distribution. The numbers simultaneously perturb both S-wave velocities and the layer thickness of models. The annealing temperature is gradually decreased following a polynomial-time cooling schedule. Phase velocities are calculated using the reflectivity-transmission coefficient method. The reliability of the model resulting from our implementation is evaluated by statistically calculating the expected values of model parameters and their covariance matrices. Blind tests on two field and 12 synthetic Rayleigh dispersion data sets show that our SA implementation works well for S-wave velocity inversion of dispersion curves from high-frequency fundamental-mode Rayleigh waves. Blind estimates of layer S-wave velocities fall within one standard deviation of the velocities of the original synthetic models in 78% of cases.

Theorectically, the perforation shot origin time T 0 affects the accuracy of the inverted velocity structure, and therefore the accuracy of subsequent microseismic event locations. The origin time can be obtained from perforation timing measurements or estimated from the picked arrival times. In order to investigate the role of origin time in velocity calibration, we designed two inversion procedures. In procedure A, T 0 is calculated during the Occam's inversion while T 0 is set to its true value in procedure B. A grid search locator is applied on both inverted models to produce two locations. We constructed three synthetic P-wave velocity models and add normally distributed random noise to the synthetic arrival times of all models. The noisy synthetic data are piped through procedure A to obtain location A and through procedure B to produce location B. Graphical analysis show that location A is closer to the true shot location than location B although both are close to each other. If we remove the data noise and repeat the test, location B is closer to the true shot than location A. It was observed that the inverted location A is better in terms of the distance from the true location if using noisy data and location B is better if using noise-free data. This indicates that uncertainties due to data noise cause our inconsistent observation and implies that perforation timing measurements are not necessary and may actually result in a less accurate velocity model.

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