Computational aspects of finite-frequency traveltime inversion kernels

Finite-frequency traveltime inversion offers higher accuracy for velocity model building than ray-based traveltime inversion. The adjoint force is the key to computation of inversion kernels. Starting at the definition of inversion kernels for the acoustic wave equation, we derive the explicit formula for the spectral distribution density function used in the adjoint force computation. Two formulations are provided for the computation of adjoint forces for receiver-side extrapolation, frequency-domain representation and time-domain representation. The accuracy of finite-frequency traveltime inversion kernels is benchmarked with the analytical solutions for homogeneous isotropic media. We use wavefront construction to compute the first Fresnel zones for kernel conditioning. Based on dynamic ray tracing, we design a processing procedure guided by synthetic data tests to extract the desired events for wavefield backward extrapolation from the data. Unlike ray-based velocity tomography, finite-frequency inversion can resolve the velocity structures comparable with the size of Fresnel zones as we demonstrate on a marine salt model using ocean bottom node acquisition geometry. Despite the fact that the inversion kernels are based on Born approximation, velocities with errors up to 20% can be well resolved. For practical purposes, a simple formulation is given for the determination of the shot spacing. The proposed workflow for finite-frequency inversion is efficient and converges only in very few iterations.

Experimental Study on GNSS-R to Detect Effective Reflector Height

<p>GNSS provides high accurate point positioning for several geodetic facilities. To achieve that, data obtained from the GNSS should be eliminated from the major error sources through modeling, filtering and differential techniques. Multipath, which is one of the major error sources, is caused by reflecting surfaces around the receiver. In multipath theory, a signal transmitted from a satellite uses more than one path to arrive at the GNSS antenna. Here, the signal may be reflected from the surface around where the receiver is set. The reflected and direct signals, which interfere with each other at the phase center of the GNSS antenna, are recorded simultaneously. The ground reflected signal has an additional path, which enables to estimate the vertical distance between reflected surface of the signal and phase center of the GNSS antenna. Several studies have been conducted to estimate the reflector height to extract environmental variables, such as snow depth, vegetation height etc.</p><p>This study aims to control the quality of the signal-to-noise ratio (SNR) data to retrieve the effective reflector height and accuracy assessment of it. A field test was performed on top of a building, where surface of the roof is quite flat at Yildiz Technical University Campus in 2019. The dimensions of roof’s building are approximately 12 m x 75 m. About seven hours GNSS observations during six days (DoY: 211, 212, 213, 214, 215, 217) were collected with a GNSS receiver (CHC i80) considering GPS-only observations for L<sub>1</sub> frequency at a sampling rate of 1-Hz, mounted on a tripod. The height of the tripod from horizontal ground surface to receiver antenna reference point was arranged to 1.700 m and a decrement of 10 cm in every two days was implemented. The daily in-situ measurements were used to validate the estimated reflector heights. The powers of the frequencies on SNR series have been investigated under different elevation mask variations to obtain the effect of the noisy frequencies that can affect the estimations.  Accordingly, the first-Fresnel zones of signals are determined to identify the border and location of the potential candidate reflected signals. Here, the correlation coefficient calculated from estimated reflector heights and in-situ measurements is computed as 0.9346 for a totally 46 estimations. The daily mean values of estimated reflector heights and root mean square errors with respect to DoYs given are determined as 1.727 m ± 3.0 cm, 1.738 m ± 4.0 cm, 1.586 m ± 3.3 cm, 1.582 m ± 3.6 cm, 1.498 m ± 4.1 cm and 1.489 m ± 4.8 cm. Moreover, the model efficiency, computed from the differences between the 6-day estimated reflector heights and in-situ measurements was estimated to figure out how the model fits the field observation. Then, the accuracy of the model was determined as 2.2 cm. Finally, it can be concluded that the outcomes of this experimental study show that the studies related to the SNR data evaluations may be used for depth/height estimations with high correlation results.</p><p><strong>Keywords:</strong> GNSS, SNR, multipath, Fresnel zones, effective reflector height, elevation mask</p>

FIRST RESULTSOF THESEISMICTOMOGRAPHICGEOTRAVERSE "VINNYTSIA – TAGANROG" RESEARCH

Methodological aspects and results of studying of the stratigraphic section of the upper mantle along the seismic tomographic geotraverse "Vinnytsia – Taganrog" are considered in the article. To localize mantle anomalies associated with changes in the composition, density of the substrate, temperature, etc., an analysis of the curves of the first and second velocity gradients was used to search for the inflection points of the vp curve. A velocity curve was obtained by constructing a seismotomographic model using the Taylor approximation method. Before the curvature analysis, a smoothing procedure was carried out in accordance with the wavelength. This procedure is important for screening false anomalies, the size of which is responsible for Fresnel zones, since the resolution of the seismic wave has the dimension of the Fresnel zones. According to this technique, the curves of the first and second velocity gradients vp were calculated for the upper mantle under the main tectonic structures of the Ukrainian Shield along the "Vinnytsia – Taganrog" geotraverse. The profile crosses the Podol, Bug megablocks, Golovanev suture zone, Ingul megablock, Kryvyy-Rig-Kremenchug suture zone, Middle-Dnipro megablock, Orekhovo-Pavlograd suture zone and Azov megablock. According to the results, the most significant features of the mantle structure were identified in the depth interval of 50–750 km. A transregional tectonic zone was distinguished (between points 30.0E, 49N and 32.0E, 48.25N), over which the Golovan suture zone (GSZ) and the eastern part of the Bug-Ros megablock and the western part of Ingul, where significant violations of the common mantle border of 660 km are observed – a border between the upper and middle mantle. Under the Podol megablock, this border is located at a depth of 550–560 km. Under GSZ it rises to 450–460 km, and to the east of the suture zone it drops sharply to 660-670 km, where it takes a subhorizontal position. A sharp jump to marks of 450–460 km shows the global breakdown zone and the nature of the contact between different geodynamic mantle regions under the modern platform.

Imaging 3-D faults using diffractions with modified dip-angle gathers

SUMMARY Accurate identification of the locations and orientations of small-scale faults plays an important role in seismic interpretation. We have developed a 3-D migration scheme that can image small-scale faults using diffractions in time. This provides a resolution beyond the classical Rayleigh limit of half a wavelength in detecting faults. The scheme images weak diffractions by building a modified dip-angle gather, which is obtained by replacing the two dip angles dimensions of the conventional 2-D dip-angle gather with tangents of the dip angles. We build the modified 2-D dip-angle gathers by calculating the tangents of dip angles following 3-D prestack time migration (PSTM). In the resulting modified 2-D dip-angle gathers, the Fresnel zone related to the specular reflection exhibits an ellipse. Comparing with the conventional 2-D dip-angle gather, diffraction event related a fault exhibits a straight cylinder shape with phase-reversal across a line related the orientation of the fault. As a result, we can not only mute the Fresnel zones related to reflections, correct phase for edge diffractions and obtain the image of faults, but also detect the orientations of 3-D faults using the modified dip-angle gathers. Like the conventional dip-angle gathers, the modified dip-angle gathers can also be used to image diffractions resulting from other sources. 3-D Field data tests demonstrate the validity of the proposed diffraction imaging scheme.