Abstract: A method for estimating resistivity and dielectric constant values of a multi-layer subterranean formation acquiring electromagnetic propagation measurements of the subterranean formation and processing the measurements via inversion to compute the resistivity and dielectric constant values. A one-dimensional formation model is utilized including a plurality of formation layers in which each of the formation layers includes a resistivity value and a dielectric constant value.

Abstract: Properties of a geological formation, such as dielectric constant and conductivity, may be determined by a propagation well log data acquired by a propagation well logging tool based at least in part on a relative longitudinal position of two or more receivers of the propagation well logging tool. In some embodiments, the relative longitudinal position of the at least two receivers is based at least in part on a first distance between a first receiver of the at least two receivers and a transmitter of the propagation well logging tool and a second distance between a second receiver of the at least two receivers and the transmitter.

Abstract: Methods and systems are provided that use resistivity log data to estimate water saturation of formation rock and/or other useful formation parameters (such as CEC) in a manner that accounts for one or more electrically conductive mineral components contained in the formation rock.

Abstract: Properties of a geological formation, such as vertical resistivity values, horizontal resistivity values, dip, and azimuth may be determined by inverting electromagnetic (EM) well log data based at least in part on an anisotropic formation model and a cost function. The cost function may include a data misfit term, a smoothness term, and an entropy term. In some embodiments, one or more of the data misfit term, the smoothness term, and the entropy term may be represented as functions of vertical conductivity and horizontal conductivity. The cost function may include one or more regularization parameters that are based at least in part on the data misfit term. Further, the cost function may include one or more relaxation factors that are based at least in part on a ratio of the Hessians of the smoothness term and the data misfit term.

Abstract: The highly valuable properties of resistivity and dielectric constant of a geological formation may be determined using an induction measurement, even for a geological formation with bed boundary or dipping effects, using a one-dimensional (1D) formation model. Induction measurements may be obtained in a wellbore through the geological formation using one or more downhole tools. One or more processors may be used to perform an inversion to estimate resistivity and dielectric constant values of the geological formation. The inversion may be performed using the induction measurements and a one-dimensional model that includes a number of geological layers.

Abstract: A formation characterization system can include a processor; memory accessibly by the processor; instructions stored in the memory and executable by the processor to instruct the system to: acquire induction measurements in a borehole in a formation using an induction tool; determine dielectric properties of the formation using the induction measurements; and generate a log that characterizes particles in the formation based on the dielectric properties.

Abstract: Properties of a geological formation, such as vertical resistivity values, horizontal resistivity values, dip, and azimuth may be determined by inverting electromagnetic (EM) well log data based at least in part on an anisotropic formation model and a cost function. The cost function may include a data misfit term, a smoothness term, and an entropy term. In some embodiments, one or more of the data misfit term, the smoothness term, and the entropy term may be represented as functions of vertical conductivity and horizontal conductivity. The cost function may include one or more regularization parameters that are based at least in part on the data misfit term. Further, the cost function may include one or more relaxation factors that are based at least in part on a ratio of the Hessians of the smoothness term and the data misfit term.

Abstract: The highly valuable properties of resistivity and dielectric constant of a geological formation may be determined using an induction measurement, even for a geological formation with bed boundary or dipping effects, using a one-dimensional (1D) formation model. Induction measurements may be obtained in a wellbore through the geological formation using one or more downhole tools. One or more processors may be used to perform an inversion to estimate resistivity and dielectric constant values of the geological formation. The inversion may be performed using the induction measurements and a one-dimensional model that includes a number of geological layers.

Abstract: Identifying the dielectric constant and/or the electrical resistivity of part of a geological formation may reveal useful characteristics of the geological formation. This disclosure provides methods, systems, and machine-readable media to determine dielectric constant or electrical resistivity, or both, using contraction mapping. Specifically, contraction mapping may be used with a function of wavenumber k to iteratively solve for values of dielectric constant and electrical resistivity until convergence is achieved. This may allow for convergence to a solution without computing partial derivatives and/or with fewer iterations than previous techniques.

Abstract: A method for determining resistivity of subsurface formations includes generating an initial model of the formations from multiaxial electromagnetic transimpedance measurements, the model comprising values of vertical resistivity, horizontal resistivity, crossbed dip, crossbed azimuth, and bedding dip and azimuth. Expected measurements generated from the initial model measurements are decomposed into ordinary and extraordinary components. The actual tool measurements are compared to the summation of the expected decomposed measurement components. The initial model is adjusted, the expected decomposed components are recalculated and the foregoing are repeated until the difference between the actual tool measurements and the summation of the expected decomposed components falls below a selected threshold.

Abstract: A method for logging a formation or sample includes obtaining a plurality of multiaxial conductivity measurements from the formation or sample. A horizontal resistivity measurement, a dip measurement and a dip azimuth measurement are derived from the plurality of multiaxial conductivity measurements. A sharp vertical resistivity measurement is derived from a subset of the plurality of multiaxial conductivity measurements.

Abstract: A method to determine at least one formation property of a subterranean formation includes providing a downhole electromagnetic logging tool having at least one transmitter array and one receiver array to acquire measurements in the formation. The method further includes performing a first inversion in response to the measurements, assuming dip or dip azimuth is constant in an inversion zone within the formation to obtain an inverted formation model. The method includes determining an n-th order partial derivative matrix of at least one of dip or dip azimuth, wherein n is greater than or equal to 1. The method includes performing a second inversion using the determined n-th order partial derivative matrix, wherein at least one of dip and dip azimuth are allowed to vary in the inversion zone, to obtain an updated formation model. The method includes determining the formation property using the updated formation model.

Abstract: A formation characterization system can include a processor; memory accessibly by the processor; instructions stored in the memory and executable by the processor to instruct the system to: acquire induction measurements in a borehole in a formation using an induction tool; determine dielectric properties of the formation using the induction measurements; and generate a log that characterizes particles in the formation based on the dielectric properties.

Abstract: A system and method discloses performing a fracture operation at a wellsite about a subterranean formation. The method involves, obtaining wellsite measurements by placing a downhole tool in a wellbore and using the downhole tool to acquire measurements of the subterranean formation, simulating the obtained wellsite measurements to determine formation parameters comprising conductivity tensors based on a formation model of the measured subterranean formation, validating the formation model by comparing the obtained wellsite measurements with the simulated wellsite measurements, generating fracture parameters and triaxiality indicators based on the validated formation model, and fracturing the subterranean formation based on the generated fracture parameters and triaxiality indicators.

Abstract: A system and method of performing a fracture operation at a wellsite about a subterranean formation is disclosed. The method involves, obtaining wellsite measurements by placing a downhole tool in a wellbore and using the downhole tool to acquire measurements of the subterranean formation, simulating the obtained wellsite measurements to determine formation parameters comprising conductivity tensors based on a formation model of the measured subterranean formation, validating the formation model by comparing the obtained wellsite measurements with the simulated wellsite measurements, generating fracture parameters and triaxiality indicators based on the validated formation model, and fracturing the subterranean formation based on the generated fracture parameters and triaxiality indicators.

Abstract: Identifying the dielectric constant and/or the electrical resistivity of part of a geological formation may reveal useful characteristics of the geological formation. This disclosure provides methods, systems, and machine-readable media to determine dielectric constant or electrical resistivity, or both, using contraction mapping. Specifically, contraction mapping may be used with a function of wavenumber k to iteratively solve for values of dielectric constant and electrical resistivity until convergence is achieved. This may allow for convergence to a solution without computing partial derivatives and/or with fewer iterations than previous techniques.

Abstract: A method to determine at least one formation property of a subterranean formation includes providing a downhole electromagnetic logging tool having at least one transmitter array and one receiver array and acquiring measurements in the formation using the transmitter and receiver arrays of the downhole electromagnetic logging tool. The method further includes performing a first inversion in response to the measurements, wherein at least one of dip or dip azimuth are assumed constant in an inversion zone within the formation to obtain an inverted formation model that comprises at least one of horizontal resistivity (Rh), vertical resistivity (Rv), dip, and dip azimuth. The method includes determining an n-th order partial derivative matrix of at least one of dip or dip azimuth, wherein n is greater than or equal to 1.

Abstract: A method for determining resistivity of subsurface formations includes generating an initial model of the formations from multiaxial electromagnetic transimpedance measurements, the model comprising values of vertical resistivity, horizontal resistivity, crossbed dip, crossbed azimuth, and bedding dip and azimuth. Expected measurements generated from the initial model measurements are decomposed into ordinary and extraordinary components. The actual tool measurements are compared to the summation of the expected decomposed measurement components. The initial model is adjusted, the expected decomposed components are recalculated and the foregoing are repeated until the difference between the actual tool measurements and the summation of the expected decomposed components falls below a selected threshold.

Abstract: A method for logging a formation or sample includes obtaining a plurality of multiaxial conductivity measurements from the formation or sample. A horizontal resistivity measurement, a dip measurement and a dip azimuth measurement are derived from the plurality of multiaxial conductivity measurements. A sharp vertical resistivity measurement is derived from a subset of the plurality of multiaxial conductivity measurements.