Downhole measurement systems and methods include deploying a bottomhole assembly having a multipole transmitter into a formation and transmitting acoustic signals into the formation. The multipole transmitter is of order n ≥ 2. Acoustic signals are received at respective receivers that are circumferentially aligned with the multipole transmitter, and are axially offset from the multipole transmitter, and axially offset from each other. The order of the first and second multipole receivers are equal to the order of the multipole transmitter. A controller is used to obtain first and second acoustic multipole data from the first and second multipole receivers at one or more azimuthal angles of a rotation of the bottomhole assembly in a formation during a drilling operation. Acoustic azimuthal anisotropy of the formation is determined from the first acoustic multipole data and the second acoustic multipole data.

A method for modelling and migrating seismic data, that includes using an acoustic wave equation and a spatial distribution of one or more earth-model parameters. The acoustic wave equation is modified by including at least one secondary source term, and based on a seismic acquisition configuration, either calculating the seismic signals that would be detected from the modelled wavefield or migrating observed seismic signals or migrating residual signals as part of an inversion.

A method for estimating all five transversely-isotropic (TI)-elastic constants using borehole sonic data obtained from at least one subterranean borehole in a transversely isotropic formation. In an embodiment, the method includes: solving for a quasi-compressional qP-wave velocity V.sub.qP using inversion algorithms based on exact solutions of the Kelvin-Christoffel equations for plane wave velocities in arbitrarily anisotropic formations, where the five TI-elastic constants may include C.sub.11, C.sub.13, C.sub.33, C.sub.55, and C.sub.66.

A method, including: obtaining Earth models including velocity, anisotropy, and attenuation reconstructing a source wavefield using the Earth models; reconstructing a receiver wavefield using the Earth models, wherein the reconstructing the source wavefield and the receiver wavefield each include applying an attenuation operator that increases an amplitude of down-going wavefields within an attenuation body and that decreases an amplitude of up-going wavefields within the attenuation body; applying an imaging condition to the source wavefield and receiver wavefield for a plurality of shots; and generating a subsurface image by stacking images for the plurality of shots.

A method of obtaining an equivalent tool model includes obtaining a set of known well data, in which the known well data includes sensor data measured by a logging tool and an actual dispersion response, and the logging tool has an actual tool size. The method also includes obtaining one or more well parameters from the known well data, and inputting the one or more well parameters and a model tool size into a rigid tool model. The method further includes obtaining an estimated dispersion response from the rigid tool model, and fitting the estimated dispersion response to the actual dispersion response by adjusting the model tool size.

Systems and methods for modeling dispersion curves are disclosed. The method includes obtaining an acoustic dataset along a well that accesses a hydrocarbon reservoir. The method further includes determining a set of depth windows along the well and determining a first subset of dispersion curves for a first subset of depth windows using a dispersion model. The method still further includes initializing a second subset of dispersion curves for a second subset of depth windows using a nearest neighbor search of the first subset of dispersion curves. The method still further includes determining slowness-frequency pairs for the second subset of depth windows using the acoustic dataset and updating the second subset of dispersion curves using a recursive scanning method. The method still further includes characterizing rock properties near the well based, at least in part, on the first subset of dispersion curves and the second subset of dispersion curves.

Methods and systems for determining a drilling-induced rock damage map are disclosed. The method includes obtaining a sonic dataset, including sonic waveforms recorded at a plurality of source-receiver separations for a plurality of source positions along an axis of a wellbore. The method further includes determining a log of a first metric using the sonic dataset and determining a map of a second metric using the sonic dataset. The method still further includes determining the drilling-induced rock damage map based, at least in part, on the log of the first metric and the map of the second metric.

A method and system for estimating a full elastic tensor. The method may comprise taking a measurement for compressional wave sonic data and cross-dipole shear data with a sonic logging tool at a first location as cross-dipole data, processing the compressional wave sonic data to produce a compressional wave slowness (P), and processing the cross-dipole shear data to produce a fast horizontal polarized shear wave slowness (SH) and a slow quazi-vertical shear wave slowness (qSV) as a function of depth. The method may further comprise setting an initial guess for at least five constants of the full elastic tensor for Vertical Transversely Isotropy (VTI) symmetry, determining a modeled slowness surfaces from the full elastic tensor, and comparing the modeled slowness surfaces with measured values of the P, the SH, and the qSV. The method may be performed by a system comprising a sonic logging tool and an information handling system.

In some embodiments, an apparatus and a system, as well as a method and an article, may operate to generate a parent population, wherein each member of the parent population includes a set of model parameters describing a layer model of the geological formation; to execute a perturbation algorithm to generate subsequent child populations, from the parent population, until a termination criterion is met; to provide a plurality of solutions based on at least one member of the parent population and on at least one member of each child population; and to control a drilling operation based on a revised layer model that has been generated based on a selected one of the plurality of solutions. Additional apparatus, systems, and methods are disclosed.

Disclosed are systems and methods for numerically simulating seismic-wave propagation in tilted transversely isotropic (TTI) media, using an adaptive Lebedev staggered grid. In various embodiments, the adaptive grid includes multiple horizontal zones having different associated grid spacings, which may be determined based on a vertical wave-velocity model. The numerical simulation may involve iteratively solving a set of finite-difference equations including finite-difference coefficients that vary spatially depending on the grid spacing. Additional embodiments and features are described.