APPLICATION OF LWD ACOUSTIC DISPERSIVE DATA PROCESSING FOR HIGH-QUALITY SHEAR SLOWNESS LOGS IN SLOW FORMATIONS

For conventional acoustic monopole sources in a logging-while-drilling (LWD) or wireline environment, shear slowness logs can be hard to obtain, particularly in slow formations where direct refracted shear-wave arrivals are often absent. For LWD dipole sources, formation flexural waves are often coupled with the lowest order of tool flexural waves, so the flexural mode does not approach shear wave slowness at low frequencies. A dispersion correction is required to extract shear slowness from LWD dipole data. Instead, a quadrupole firing, which generates screw waves, is considered the best LWD excitation mode for shear measurement. A fundamental feature of screw waves in an LWD environment is that their non-leaky cutoff frequency slowness is the formation shear slowness. However, slowness data near the cutoff frequency of LWD screw waves are often influenced by noise or the presence of other modes because of low excitation amplitude. To overcome these LWD data processing challenges, we propose a data-driven processing method that uses all useful dispersion responses of existing modes in the frequency domain. The process first generates a differential phase frequency-slowness coherence map and extracts the slowness dispersion vs. frequency. Then, it computes the slowness density log, referring to the intensity of the dispersion response along the slowness axis. Next, an edge-detection method is applied to capture the edge of the first peak associated with shear slowness on the slowness density map. To refine the shear slowness answer, this initial estimate of shear slowness serves as the input to another algorithm that minimizes the misfit between the screw slowness vector and a simplified screw dispersion model. The simplified screw dispersion model consists of a pre-computed base library of theoretical screw dispersion curves and two data-driven parameters. The two data-driven parameters are used by the measured data to stretch the base dispersion model in the frequency and slowness axes, respectively, to account for errors generated by alteration, anisotropy, or other parameters not included in the forward modeling. The method can also be applied to flexural waves, where the initial guess of shear slowness is picked from the slowness density map of flexural waves after dispersion-correction processing. This paper shows a case study of borehole flexural and screw waves processing in soft formations. A modified differential-phase frequency-semblance (MDPFS) approach is applied to extract the mode waves' full-frequency dispersion response from measured waveforms. The data-driven shear slowness processing is applied to the dispersion response. Both dipole flexural waves and quadrupole screw waves are processed. A combination of slowness density log from the flexural or screw wave slowness and the dispersion-corrected slowness is used as a QC metric of the final estimated shear. Results show that flexural and screw dispersions are well measured by the LWD sonic tool, even if the shear slowness is as large as 500 s/ft. Shear slowness extracted from flexural waves and screw waves match well with each other and with wireline shear slowness logs, demonstrating that the processing is reliable and robust.

Visualizing the Seismic Wavefield with AlpArray

<p>The AlpArray Seismic Network (AASN) is a large-scale multidisciplinary seismic network in Europe that consists of over 600 3-component (3C) broadband stations with mean inter-station distance of 30-40km. This dense array allows the recording of the seismic wave propagation of distant earthquakes at a resolution of typical body and surface waves.</p><p>By animating the spatially-dense seismic recordings of the AASN, we can visualize seismic waves propagating across the European Alps as a function of space and time. Our 3C ground motion animations illustrate the full spatial-temporal evolution of global body and surface waves and demonstrates how a dense array allows the transformation from translation measurements at single stations to spatial gradients of the wavefield at the surface, capturing both small- and large-scale wave propagation phenomena. The addition of travel-time estimation, ray path illustration, and array-specific information such as slowness vector of incoming waves facilitate identification of seismic phases and their arrival-angle deviations. We will highlight some interesting observations of different seismic wave types in the animations of a few example teleseismic events during the course of the AASN between 2016-2019. Application for future research and education will also be discussed.</p>

Slowness vector vs ray direction in polar anisotropic media

Summary The inverse problem of finding the slowness vector from a known ray direction in general anisotropic elastic media is a challenging task, needed in many wave/ray-based methods, in particular, solving two-point ray bending problems. The conventional resolving equation set for general (triclinic) anisotropy consists of two fifth-degree polynomials and a sixth-degree polynomial, resulting in a single physical solution for quasi-compressional (qP) waves and up to 18 physical solutions for quasi-shear waves (qS). For polar anisotropy (transverse isotropy with a tilted symmetry axis), the resolving equations are formulated for the slowness vectors of the coupled qP and qSV waves (quasi-shear waves polarized in the axial symmetry plane), and independently for the decoupled pure shear waves polarized in the normal (to the axis) isotropic plane (SH). The novelty of our approach is the introduction of the geometric constraint that holds for any wave mode in polar anisotropic media: The three vectors—the slowness, ray velocity and medium symmetry axis—are coplanar. Thus, the slowness vector (to be found) can be presented as a linear combination of two unit-length vectors: the polar axis and the ray velocity directions, with two unknown scalar coefficients. The axial energy propagation is considered as a limit case. The problem is formulated as a set of two polynomial equations describing: a) the collinearity of the slowness-related Hamiltonian gradient and the ray velocity direction (third-order polynomial equation), and b) the vanishing Hamiltonian (fourth-order polynomial equation). Such a system has up to twelve real and complex-conjugate solutions, which appear in pairs of the opposite slowness directions. The common additional constraint, that the angle between the slowness and ray directions does not exceed ${90^{\rm{o}}}$, cuts off one half of the solutions. We rearrange the two bivariate polynomial equations and the above-mentioned constraint as a single univariate polynomial equation of degree six for qP and qSV waves, where the unknown parameter is the phase angle between the slowness vector and the medium symmetry axis. The slowness magnitude is then computed from the quadratic Christoffel equation, with a clear separation of compressional and shear roots. The final set of slowness solutions consists of a unique real solution for qP wave and one or three real solutions for qSV (due to possible triplications). The indication for a qSV triplication is a negative discriminant of the sixth-order polynomial equation, and this discriminant is computed and analyzed directly in the ray-angle domain. The roots of the governing univariate sixth-order polynomial are computed as eigenvalues of its companion matrix. The slowness of the SH wave is obtained from a separate equation with a unique analytic solution. We first present the resolving equation using the stiffness components, and then show its equivalent forms with the well-known parameterizations: Thomsen, Alkhalifah and ‘weak-anisotropy’. For the Thomsen and Alkhalifah forms, we also consider the (essentially simplified) acoustic approximation for qP waves governed by the quartic polynomials. The proposed method is coordinate-free and can be applied directly in the global Cartesian frame. Numerical examples demonstrate the advantages of the method.

Effective and efficient approaches for calculating seismic ray velocity and attenuation in viscoelastic anisotropic media

In viscoelastic anisotropic media, the elastic moduli, slowness vector, phase, and ray velocity are all complex-valued quantities in the frequency domain. Solving the complex eikonal equation becomes computationally complex and time-consuming. We have developed two approximate methods to effectively calculate the ray velocity vector, attenuation, and quality factor in viscoelastic transversely isotropic media with a vertical symmetry axis (VTI) and in orthorhombic (ORT) anisotropy. The first method is based on the perturbation theory (PER) under the assumption of a homogeneous complex ray vector, which is obtained by applying the elastic background and viscoelastic perturbations to the real and imaginary components of the modulus tensor, respectively. The perturbations of the slowness vectors of the three wave modes (qP, qSV, and qSH) are determined through the vanishing Hamiltonian function. The second method is derived by applying a real slowness direction (RSD) to the inhomogeneous complex slowness vector and then approximately calculating the complex ray velocity vector with the condition of the homogeneous complex vector. The numerical results verify that the two approaches can produce accurate ray velocity vector, attenuation, and quality factors of the qP-wave in viscoelastic VTI and ORT media. The RSD method can yield high accuracies of ray velocity for the qSV- and qSH-wave in viscoelastic VTI models even at triplication of the qSV wavefronts, as well as qS1 and qS2 in a weak ORT medium ([Formula: see text] > 20), except for near the cusp of the qS1 wavefronts (errors approximately 6%) where the PER has more than 10% error.

Consistent seismic event location and subsurface parameters inversion through slope tomography: a variable-projection approach

SUMMARY We revisit the hypocentre–velocity problem, which is of interest in different fields as for example microseismics and seismology. We develop a formulation based on kinematic migration of two picked kinematic attributes in the 2-D case, the traveltime and the slope (horizontal component of the slowness vector), from which we are able to retrieve the location and subsequently the origin time correction and the subsurface parameters mainly velocity. We show how, through a variable projection, the optimization problem boils down to a physically consistent and parsimonious form where the location estimation is projected into the subsurface parameter problem. We present in this study a proof of concept validated by a toy test in two dimensions and a synthetic case study on the Marmousi model. The method presented in this study is extendible to three dimensions by incorporating the crossline slope or the backazimuth as a supplementary attribute.

Complete phenomenon of reflection at the plane boundary of a dissipative anisotropic elastic medium

SUMMARY A complex slowness vector governs the 3-D propagation of harmonic plane waves in a dissipative elastic medium with general anisotropy. In any sagittal plane, this dual vector is specified with phase direction, propagation velocity and coefficients for attenuation. A generalized reflection phenomenon is illustrated for incidence of inhomogeneous waves at the stress free boundary of the medium. Each reflected wave at the boundary is characterized by its propagation direction, propagation velocity, inhomogeneity, amplitude ratio, phase shift and energy flux. These propagation characteristics are exhibited graphically for a numerical example of anisotropic viscoelastic medium.

Slowness vector estimation over large-aperture sparse arrays with the Continuous Wavelet Transform (CWT): application to Ocean Bottom Seismometers

SUMMARY This work presents a new methodology designed to estimate the slowness vector in large-aperture sparse Ocean Bottom Seismometer (OBS) arrays. The Continuous Wavelet Transform (CWT) is used to convert the original incoherent traces that span a large array, into coherent impulse functions adapted to the array aperture. Subsequently, these impulse functions are beamformed in the frequency domain to estimate the slowness vector. We compare the performance of this new method with that of an alternative solution, based on the Short-/Long-Term Average algorithm and with a method based on the trace envelope, with the ability to derive a very fast detection and slowness vector estimation of seismic signal arrivals. The new array methodology has been applied to data from an OBS deployment with an aperture of 80 km and an interstation distance of about 40 km, in the vicinity of Cape Saint Vincent (SW Iberia). A set of 17 regional earthquakes with magnitudes 2 < mbLg < 5, has been selected to test the capabilities of detecting and locating regional seismic events with the Cape Saint Vincent OBS Array. We have found that there is a good agreement between the epicentral locations obtained previously by direct search methods and those calculated using the slowness vector estimations resulting from application of the CWT technique. We show that the proposed CWT method can detect seismic signals and estimate the slowness vector from regional earthquakes with high accuracy and robustness under low signal-to-noise ratio conditions. Differences in epicentral distances applying direct search methods and the CWT technique are between 1 and 21 km with an average value of 12 km. The backazimuth differences range from 1° to 7° with an average of 1.5° for the Pwave and ranging from 1° to 10° with an average of 3° for the Swave.