Obtaining hypocenters of microseismic events, a primary task in mining, geothermal, and hydraulic-fracturing applications of induced seismicity, requires a velocity model for computing those hypocenters. In our paper, relying on a notion that information provided by microseismic events themselves enables one to construct a velocity model and calculate the event hypocenters in that model, we derive exact analytic solutions to the joint velocity-estimation/event-location problem for downhole microseismic data acquired in homogeneous isotropic media. We show that traveltimes and polarization vectors of the direct P- and S-waves excited by a microseismic event and recorded by a string of receivers placed in one or two vertical wells not only uniquely constrain the event location and the medium velocities but also entail a straightforward analysis of the uncertainties of those estimates caused by the presence of noise in the data. Although the P- and S-wave velocities calculated analytically under the assumption of the medium homogeneity cannot fully absorb the complexity of heterogeneous subsurface models, they become the proper effective velocities for a given microseismic event, and the corresponding event location—which is no longer exact even for noise-free data—might serve as a useful initial guess for more sophisticated event-location techniques that account for the velocity heterogeneity.

Inelastic attenuation, quantified by [Formula: see text], the seismic quality factor, has considerable impact on surface seismic reflection data. A new method for interval [Formula: see text]-factor estimation using near-offset VSP data was based on an objective function minimization measuring the difference between cumulative [Formula: see text] estimates and those calculated through interval [Formula: see text]. To calculate interval [Formula: see text], we used all receiver pairs that provided reasonable [Formula: see text] values. To estimate [Formula: see text] between two receiver levels, we used the equation that links amplitudes at different levels and could provide more accurate [Formula: see text] values than the spectral-ratio method. To improve interval [Formula: see text] estimates, which rely on traveltimes, we used a high-accuracy approach in the frequency domain to determine time shifts. Application of this method to real data demonstrated reasonable correspondence between [Formula: see text] estimates and log data.

A B S T R A C TI introduce a new explicit form of vertical seismic profile (VSP) traveltime approximation for a 2D model with non-horizontal boundaries and anisotropic layers. The goal of the new approximation is to dramatically decrease the cost of time calculations by reducing the number of calculated rays in a complex multi-layered anisotropic model for VSP walkaway data with many sources. This traveltime approximation extends the generalized moveout approximation proposed by Fomel and Stovas. The new equation is designed for borehole seismic geometry where the receivers are placed in a well while the sources are on the surface. For this, the time-offset function is presented as a sum of odd and even functions. Coefficients in this approximation are determined by calculating the traveltime and its first-and second-order derivatives at five specific rays. Once these coefficients are determined, the traveltimes at other rays are calculated by this approximation. Testing this new approximation on a 2D anisotropic model with dipping boundaries shows its very high accuracy for offsets three times the reflector depths. The new approximation can be used for 2D anisotropic models with tilted symmetry axes for practical VSP geometry calculations. The new explicit approximation eliminates the need of massive ray tracing in a complicated velocity model for multi-source VSP surveys. This method is designed not for NMO correction but for replacing conventional ray tracing for time calculations.

Waves propagating across a vertical seismic profiling (VSP) array may be distinguished by their differing arrival times and linear-moveout velocities. Current methods typically assume that the waves propagate uniformly with an unvarying wavelet shape and amplitude. These assumptions break down in the presence of irregular spatial sampling, event truncations, wavelet variations, and noise. I present a new method that allows each event to independently vary in its amplitude and arrival time as it propagates across the array. The method uses an iterative global nonlinear optimization scheme that consists of several least-squares and two eigenvalue problems at each step. Events are stripped from the data one at a time. As stronger events are predicted and removed, weaker events then become visible and can be modeled in turn. As each new event is approximately modeled, the fit for all previously removed events is then revisited and updated. Iterations continue until no remaining coherent events can be distinguished. As VSP data sets are typically not large, the expense of this method is not a significant limitation. I demonstrate with a real-data example that this iterative approach can lead to a significantly better VSP wavefield separation than that which has been available when using conventional techniques.

Lateral velocity changes (velocity anomalies) in the overburden may cause significant oscillations in normal moveout velocities. Explicit analytical moveout formulas are presented and provide a direct explanation of these lateral fluctuations and other phenomena for a subsurface with gentle deep structures and shallow overburden anomalies. The analytical conditions for this have been derived for a depth‐velocity model with gentle structures with dips not exceeding 12°. The influence of lateral interval velocity changes and curvilinear overburden velocity boundaries can be estimated and analysed using these formulas. An analytical approach to normal moveout velocity analysis in a laterally inhomogeneous medium provides an understanding of the connection between lateral interval velocity changes and normal moveout velocities. In the presence of uncorrected shallow velocity anomalies, the difference between root‐mean‐square and stacking velocity can be arbitrarily large to the extent of reversing the normal moveout function around normal incidence traveltimes. The main reason for anomalous stacking velocity behaviour is non‐linear lateral variations in the shallow overburden interval velocities or the velocity boundaries. A special technique has been developed to determine and remove shallow velocity anomaly effects. This technique includes automatic continuous velocity picking, an inversion method for the determination of shallow velocity anomalies, improving the depth‐velocity model by an optimization approach to traveltime inversion (layered reflection tomography) and shallow velocity anomaly replacement. Model and field data examples are used to illustrate this technique.