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.     

Ekman motion in shallow open sea in the presence of time-harmonic variation of water depth

The time variation of the wind-induced flow in a homogeneous unbounded sea region has been analytically investigated. The time-dependent Ekman solution in a homogeneous, shallow open sea has been further extended by taking into account the time variation in water depth which might be caused by either tidal motion or change in the mixed layer thickness. The solution approach taken in this study is based on the Galerkin-eigenfunction method originally developed by Heaps [1972. On the numerical solution of three-dimensional hydrodynamical equations for tides and storm surges. Memoires de la Societe Royale des Sciences de Liege Serie 6(2), 143–180]. A series of calculations have been made with emphasis on the influence of the time variation in water depth upon the build-up of Ekman spirals in the presence of oscillatory variations in water depth. It has been found that two oscillations contribute to the wind drift current, the inertial oscillation and the depth-variation-induced oscillation; the inertial oscillation decays with time, but the depth-variation-induced oscillation remains undamped despite the presence of bottom friction. The presence of time-harmonic variation produces peculiar forms of hodograph with a curled or circular pattern according to the angular frequency of the water depth variation.     

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.     

Evolution of the eastern margin of Korea: Constraints on the opening of the East Sea (Japan Sea)

We interpreted marine seismic profiles in conjunction with swath bathymetric and magnetic data to investigate rifting to breakup processes at the eastern Korean margin that led to the separation of the southwestern Japan Arc. The eastern Korean margin is rimmed by fundamental elements of rift architecture comprising a seaward succession of a rift basin and an uplifted rift flank passing into the slope, typical of a passive continental margin. In the northern part, rifting occurred in the Korea Plateau that is a continental fragment extended and partially segmented from the Korean Peninsula. Two distinguished rift basins (Onnuri and Bandal Basins) in the Korea Plateau are bounded by major synthetic and smaller antithetic faults, creating wide and considerably symmetric profiles. The large-offset border fault zones of these basins have convex dip slopes and demonstrate a zig-zag arrangement along strike. In contrast, the southern margin is engraved along its length with a single narrow rift basin (Hupo Basin) that is an elongated asymmetric half-graben. Analysis of rift fault patterns suggests that rifting at the Korean margin was primarily controlled by normal faulting resulting from extension rather than strike-slip deformation. Two extension directions for rifting are recognized: the Onnuri and Hupo Basins were rifted in the east-west direction; the Bandal Basin in the east–west and northwest–southeast directions, suggesting two rift stages. We interpret that the east–west direction represents initial rifting at the inner margin; while the Japan Basin widened, rifting propagated southeastward repeatedly from the Japan Basin toward the Korean margin but could not penetrate the strong continental lithosphere of the Korean Shield and changed the direction to the south, resulting in east–west extension to create the rift basins at the Korean margin. The northwest–southeast direction probably represents the direction of rifting orthogonal to the inferred line of breakup along the base of the slope of the Korea Plateau; after breakup the southwestern Japan Arc separated in the southeast direction, indicating a response to tensional tectonics associated with the subduction of the Pacific Plate in the northwest direction. No significant volcanism was involved in initial rifting. In contrast, the inception of sea floor spreading documents a pronounced volcanic phase which appears to reflect asthenospheric upwelling as well as rift-induced convection particularly in the narrow southern margin. We suggest that structural and igneous evolution of the Korean margin, although it is in a back-arc setting, can be explained by the processes occurring at the passive continental margin with magmatism influenced by asthenospheric upwelling.     

Distinct sedimentary processes reflected in the isotopic signatures of dolomitic concretions in the Miocene Pohang Basin (southwestern East Sea)

Dolomitic concretions in diatomaceous hemipelagic sediments of the Miocene Pohang Basin in the southwestern East Sea (Sea of Japan) preserve distinct signals of two independent sedimentary processes, which controlled the extents of isotopic compositions. Variable δ¹⁸O (−9.1‰ to +0.7‰) and high δ¹³C (+3.1‰ to +17.9‰) values suggest that the concretions formed in the methanogenic zone with alteration of the residual mid-Miocene seawater by volcanogenic sediments. Remarkable δ¹⁸O and δ¹³C values show a strong linear relationship, indicating that distinctly independent depositional processes operated during the formation of the concretions. The degree of methanogenesis was enhanced during rapid hemipelagic sedimentation of organic-rich particles, resulting in higher δ¹³C values, and the effect of volcaniclastics was diluted, maintaining the original properties of ambient mid-Miocene seawater. In contrast, lower δ¹⁸O and ⁸⁷Sr/⁸⁶Sr values characterize the effect of volcaniclastic sediments that were transported by intermittent gravity flows and interacted with mid-Miocene seawater. The input of volcaniclastic sediment probably degraded the role of methanogenesis by lowering the contents of organic matter and thereby decreased the δ¹³C values within the concretions. Isotopic signals recorded within the concretions highlight understanding of the depositional environment and evolution of the pore-water chemistry.     

Radiatively driven mass accretion on to galactic nuclei by circumnuclear starbursts

We examine the physical processes of radiatively driven mass accretion on to galactic nuclei, owing to intensive radiation from circumnuclear starbursts. The radiation from a starburst not only causes the inner gas disc to contract via radition flux force, but also extracts angular momentum owing to relativistic radiation drag, thereby inducing an avalanche of the surface layer of the disc. To analyse such a mechanism, the radiation–hydrodynamical equations are solved, including the effects of the radiation drag force as well as the radiation flux force. As a result, it is found that the mass accretion rate owing to the radiative avalanche is given by M ˙ ( r )= η ( L _*/ c ²)( r / R )² (Δ R / R )(1 −  e ^−τ) at radius r , where the efficiency η ranges from 0.2 up to 1, L _* and R are respectively the bolometric luminosity and the radius of the starburst ring, Δ R is the extent of the emission regions, and τ is the face-on optical depth of the disc. In an optically thick regime, the rate depends upon neither the optical depth nor the surface mass density distribution of the disc. The present radiatively driven mass accretion may provide a physical mechanism which enables mass accretion from 100-pc scales down to ∼ parsec scales, and it may eventually be linked to advection-dominated viscous accretion on to a massive black hole. The radiation–hydrodynamical and self-gravitational instabilities of the disc are briefly discussed. In particular, the radiative acceleration possibly builds up a dusty wall, which 'shades' the nucleus in edge-on views. This provides another version of the model for the formation of an obscuring torus.     

Delineation of spatial redox zones using discriminant analysis and geochemical modelling in arsenic‐affected alluvial aquifers

This study characterized the redox conditions in arsenic‐affected groundwater aquifers of the Lanyang plain, Taiwan. Discriminant analysis was adopted to delineate three redox zones (oxidative, transitional and reductive zones) in different aquifers and yielded 92·3% correctness on groundwater quality data. Arsenic is mainly distributed in the reductive zone, and arsenic distribution in the shallow aquifer is mainly affected by surface activities. According to PHREEQC modelling results, possible mechanisms for arsenic release to groundwater in Lanyang plain are explored. Arsenic released to groundwater in the oxidative zone (zone 1) is primarily caused by the oxidations of arsenic‐bearing pyrite minerals, and arsenate is the predominant species. While the reductive dissolution of Fe‐oxides are responsible for the high arsenic concentration found in the transitional and reductive zones (zones 2 and 3), arsenite is the predominant species. The reduction potential of groundwater rises as the depths and zones increase. Some sulphates may be reduced to form sulphide ions, which then react with arsenic to form arseno‐sulphide deposits (such as realgar, orpiment) and then slightly lower groundwater arsenic concentrations. A conceptual diagram which summarized the possible release processes of arsenic in different redox zones along groundwater flow in Lanyang plain is postulated. Arsenic‐bearing pyrite and arsenopyrite (FeAsS) are oxidized as they are exposed to the infiltrated oxygenated rainwater, releasing soluble arsenate Fe(II) and SO₄^2? into zone 1. The dissolution of arsenic‐rich Fe‐oxides due to the onset of reducing conditions in zones 2 and 3 is responsible for the mobility of arsenic and likely to be the primary mechanism of arsenic release to groundwater in the Lanyang plain Copyright © 2007 John Wiley & Sons, Ltd.