Comparison of waveform inversion, part 1: conventional wavefield vs logarithmic wavefield

This is the first in a series of three papers focused on using variants of a logarithmic objective function approach to full waveform inversion. In this article, we investigate waveform inversion using full logarithmic principles and compare the results with the conventional least squares approach. We demonstrate theoretically that logarithmic inversion is computational similar to the conventional method in the sense that it uses exactly the same back‐propagation technology as used in least‐squares inversion. In the sense that it produces better results for each of three numerical examples, we conclude that logarithmic inversion is also more robust. We argue that a major reason for the inherent robustness is the fact that the logarithmic approach produces a natural scaling of the amplitude of the residual wavefield by the amplitude of the modelled wavefield that tends to stabilize the computations and consequently improve the final result. We claim that any superiority of the logarithmic inversion is based on the fact that it tends to be tomographic in the early stage of the inversion and more dependent on amplitude differences in the latter stages.     

Comparison of waveform inversion, part 3: amplitude approach

In the second paper of this three part series, we studied the case of conventional and logarithmic phase‐only approaches to full‐waveform inversion. Here, we concentrate on deriving amplitude‐only approaches for both conventional‐ and logarithmic‐based methods. We define two amplitude‐only objective functions by simply assuming that the phase of the modelled wavefield is equal to that of the observed wavefield. We do this for both the conventional least‐squares approach and the logarithmic approach of Shin and Min. We show that these functions can be optimized using the same reverse‐time propagation algorithm of the full conventional methodology. Although the residuals in this case are not really residual wavefields, they can both be considered and utilized in that sense. In contrast to the case for our phase‐only algorithms, we show through numerical tests that the conventional amplitude‐only inversion is better than the logarithmic method.     

Urban effect on the formation of the Moskva River environmental state (historical aspect)

Results of long-term monitoring of water quality parameters of the Moskva River section within the limits of the city are generalized. The dynamics in quality parameters of the water entering the city wastewater treatment plants, purified effluents of the treatment plants, and river water is analyzed. A relationship between the concentration of organic matter in the river water at the exit from the city and WWTP capacity is demonstrated. Periods of unfavorable environmental state of the river in terms of oxygen regime are singled out based on oxygen regime dynamics. Variations in the river self-purification process are shown. It is stated that purified effluents of the WWTP are a component of the city hydrological system.     

Dynamics of the radiation belt formed by solar protons during magnetic storms

Experimental proofs of the existence of the formation and destruction mechanisms of solar proton belts in the inner magnetosphere at a rapid change in the penetration boundary of solar protons are presented. An analysis of the measurements of solar protons and alpha-particles on board the Coronas-F low-altitude polar satellite during the magnetic storms in October–November 2003 is performed. During this period, formation and destruction of the belts of solar cosmic rays was observed several times. The compression of the magnetosphere during a storm makes possible the direct penetration of solar protons deep into the inner magnetosphere. The proton trajectories outside the penetration boundary are open, and the preliminary captured particles can easily leave the magnetosphere. During the recovery of the magnetospheric configuration, when the penetration boundary goes away from the Earth, the solar protons and alpha-particles with relatively low velocity of the magnetic drift remain stably captured, whereas the particles of higher energies follow the motion of the penetration boundary. That is why the energy range of the captured protons is limited from above in contrast to the effect of injection during ineffective SC in the low-energy region.     

Improved amplitude preservation for prestack depth migration by inverse scattering theory

A prestack reverse time-migration image is not properly scaled with increasing depth. The main reason for the image being unscaled is the geometric spreading of the wavefield arising during the back-propagation of the measured data and the generation of the forward-modelled wavefields. This unscaled image can be enhanced by multiplying the inverse of the approximate Hessian appearing in the Gauss–Newton optimization technique. However, since the approximate Hessian is usually too expensive to compute for the general geological model, it can be used only for the simple background velocity model.We show that the pseudo-Hessian matrix can be used as a substitute for the approximate Hessian to enhance the faint images appearing at a later time in the 2D prestack reverse time-migration sections. We can construct the pseudo-Hessian matrix using the forward-modelled wavefields (which are used as virtual sources in the reverse time migration), by exploiting the uncorrelated structure of the forward-modelled wavefields and the impulse response function for the estimated diagonal of the approximate Hessian. Although it is also impossible to calculate directly the inverse of the pseudo-Hessian, when using the reciprocal of the pseudo-Hessian we can easily obtain the inverse of the pseudo-Hessian. As examples supporting our assertion, we present the results obtained by applying our method to 2D synthetic and real data collected on the Korean continental shelf.     

Evaluation of density in layer compaction using SASW method

SASW test, which is non-intrusive and rapid in the field application, was used to evaluate the layer density in the roller compaction without performing the complicated inversion process. The concept of normalized shear wave velocity was introduced to minimize the effect of confinement in the density evaluation. SASW test was performed to determine the shear wave velocity of the layer, and the free–free resonant column (FF–RC) test was adopted to determine the correlation between the normalized shear wave velocity and density of the site, which is almost unique independent of confinement. Testing and data reduction procedures of both tests were briefly discussed and an evaluation procedure of the field density was proposed by effectively combining in-situ shear wave velocity determined by the SASW test with the correlation between the normalized shear wave velocity and the density determined by the FF–RC test. Finally, the feasibility of the proposed method was verified by performing a field case study at Hoengsung road construction site. Field densities determined by the proposed method matched well with those determined by sand cone tests, showing the potential of applying the proposed method in the field density evaluation.     

A correlation between the distributions of pulsars and emission measures in the galaxy

A correlation has been detected between the volume density of pulsars and the density of interstellar ionized gas on scales of more than 500 pc in Galactic longitude and 200 pc in Galactic latitude. On smaller scales, the correlation is present only for pulsars with ages less than 60000 years, which are located predominantly near supernova remnants and H II regions. This all indicates that pulsars are born in regions with high concentrations of interstellar gas. The minimum emission measures observed in the directions toward pulsars are inversely proportional to the pulsar ages. It is concluded that the ionized gas in the vicinities of a number of pulsars was formed during supernova explosions, and corresponds to Strömgren zones. The ionization of the gas in these zones requires a radiation energy on the order of 10⁵⁰–10⁵¹ erg.     

A magnetized disk around an O star in W75N. A VLBI map of the OH maser

W75N is a star-forming region containing ultracompact H II regions as well as OH, H₂O, and methanol masers. The VLBA maps obtained show that the masers are located in a thin disk rotating around an O star, which is the exciting star for the ultracompact H II region VLA1. A separate group of maser spots is associated with the ultracompact H II region VLA2. The radial velocity of the maser spots varies across the disk from 3.7 to 10.9 km/s. The disk diameter is 4000 AU. The maser spots revolve in Keplerian orbits around the O9 star.