Irregular Bottom Research Articles

Seismic wave propagation in coupled fluid and porous media: A finite element approach

AbstractWe present a numerical method to simulate seismic wave propagation in coupled fluid and porous media. We developed a numerical finite element–based algorithm to approximate solutions to viscoacoustic and Biot's equations, considering the open pore conditions at the interfaces between both media. The algorithm architecture allows to simulate arbitrary distributions of viscoacoustic and poroelastic regions, facilitating the modelling of heterogeneous systems involving complex geometries. The algorithm includes a double parallelization scheme whose efficiency in terms of computing time and memory requirements was tested for different core distributions and mesh sizes. We validate our proposal by performing a comparison between its results and those obtained with a well‐known freely available code. We test its capabilities by studying two different scenarios with geophysical interest: a lake with an irregular bottom and a fractured porous medium.

Dynamics and a Hydraulic-Soil Mechanical Model for Pockmarks in a Mud-draped Lake: Lake Sünnet (NW Anatolia)

The scarcity of bathymetric studies in most Turkish lakes does not allow the documentation and the potential causes of lake bottom irregularities. In this study, relatively high-resolution bathymetric data from Lake Sünnet (NW Anatolia) revealed five deep (5.7 to 9.2m) and narrow (10 to 20m) depressions located along the boundary between the lake bottom and the steep lake margins. Analysis of lake level data belonging to dry seasons hints no leakage through these depressions. However, the negative conical shape and weakly developed levees around the holes suggest an upward episodic groundwater discharge for which direct evidence has been absent up to date. A combined hydraulic and soil mechanical model successfully explains the pockmark activity due to the flow of water through conduits in karstic carbonate bedrock. According to sedimentation rates and average depth of pockmarks in Lake Sünnet, and available regional paleoclimate studies, the onset of pockmark activity might coincide with the transition from the Near East Aridification Phase to the humid Beyşehir Occupation Phase around 300 BCE in SW and NW Anatolia.

Shallow water modeling of wave–structure interaction over irregular bottom

This paper describes the results from a numerical simulation of long surface waves interaction with fixed and partially immersed structure located over irregular bottom. The topic is connected with risk of critical wave impact on structures placed in the coastal waters of seas and oceans. The wave–structure interaction is simulated within the framework of a hierarchy of mathematical models, including the model of potential flows of an ideal fluid, a fully nonlinear dispersive and dispersionless shallow water models. The numerical algorithm for the dispersive model is described in detail. The obtained results show that rectangular cutout in the structure bottom reduces the amplitude of the reflected wave and increases that of the transmitted one; the basin bottom irregularity plays the most important role when located directly under the body. The protrusion behind the body may slightly decrease the wave force, and it significantly increases the force at other locations. Generally, the results obtained by the dispersive model correspond well with those of potential model, while the dispersionless model often significantly overestimates the wave force and amplitude of the reflected wave.

Value of pseudopod sign on high‐frequency ultrasound in predicting the pathological invasion of extramammary Paget's disease lesions

Vertical invasion of extramammary Paget's disease (EMPD) is associated with poor prognosis. The usual vertical invasion route is directly downward or along the skin appendages. High-frequency ultrasound (HFUS) can be used to measure the EMPD lesion thickness, and visualize the pseudopod extensions due to skin appendage involvement. It is a non-invasive method for evaluating the extent of vertical invasion in EMPD. To investigate the value of HFUS in predicting the extent of vertical invasion in EMPD. In this retrospective study, 85 patients with EMPD were divided into two groups based on the pathology: invasive EMPD (iEMPD) group (n = 13) and in situ EMPD group (n = 72). The clinical and HFUS features of both the groups were analysed. The different types of pseudopodia morphology on HFUS were as follows: no pseudopodia, irregular bottom, small sphere, short strip, long strip, vase shape and nodular convex. These were further stratified into low-risk and high-risk levels. The clinical features were comparable between the two groups (P > 0.05). There were significant differences between the two groups in the HFUS features (lesion thickness, lesion shape, bottom shape, layer involvement, pseudopodia morphology and colour Doppler blood flow signal; all P < 0.05). The distribution of the pseudopodia morphology types in the in situ EMPD and iEMPD groups was as follows: no pseudopodia, 30/72 and 0/13; irregular bottom, 5/72 and 0/13; small sphere, 5/72 and 0/13; short strip, 21/72 and 0/13; long strip, 8/72 and 3/13; vase shape, 3/72 and 3/13; and nodular convex, 0/72 and 7/13 (P < 0.05 for all). The sensitivity and specificity of high-risk pseudopodia in identifying iEMPD were 100% and 84.7%, respectively. High-frequency ultrasound provides morphological information regarding EMPD lesions. Risk stratification for pseudopodia can help to distinguish between iEMPD and in situ EMPD lesions.

Nonstandard Liouville tori and caustics in asymptotics in the form of Airy and Bessel functions for 2D standing coastal waves

The spectral problem − ⟨ ∇ , D ( x ) ∇ ψ ⟩ = λ ψ -\langle \nabla ,D(x)\nabla \psi \rangle = \lambda \psi in a bounded two-dimensional domain Ω \Omega is considered, where D ( x ) D(x) is a smooth function positive inside the domain and zero on the boundary whose gradient is different from zero on the boundary. This problem arises in the study of long waves trapped by the shore and by bottom irregularities. For its asymptotic solutions as λ → ∞ \lambda \rightarrow \infty , explicit formulas are given when D ( x ) D(x) has a special form that guarantees the complete integrability of the Hamiltonian system corresponding to the Hamiltonian H ( x , p ) = D ( x ) p 2 H(x,p)=D(x)p^2 . Since the problem is degenerate, the relevant Liouville tori are not in the standard phase space T ∗ Ω T^*\Omega , but in the “extended” phase space Φ ⊃ T ∗ Ω \mathbf {\Phi }\supset T^*\Omega , while their restrictions to T ∗ Ω T^*\Omega are not compact and “go to infinity” with respect to momenta near the boundary of Ω \Omega . As a result, nonstandard caustics emerge, formed by the boundary or its part, near which asymptotic eigenfunctions are expressed in terms of a Bessel function of composite argument. Standard caustics (within the domain) may also appear, which yield Airy functions in the asymptotics.

Devising a procedure to calculate and analyze parameters for passing the flood and breakthrough wave taking into consideration the topographical and hydraulic riverbed irregularities

It has been established that the most likely period of breakthrough wave occurrence is the time of spring flooding or heavy rain when water-head facilities are subjected to significant loads that lead to the collapse of their individual elements or the entire structure. In addition, the possibility of man-made accidents that can occur at any time cannot be ruled out. It has been proven that breakthrough wave formation depends on the nature of the destruction or the overflow through a water-head facility. For the study reported in this paper, a model of the kinematics of riverbed and breakthrough flows was used, which is based on the equations of flow, washout, and transport of sediments that are averaged for the depths of the stream. The differential equations describing the nonstationary flow averaged for depth are solved using the numerical grid system FST2DH (2D Depth-averaged Flow and Sediment Transport Model), which implements a finite-element method on the plan of a riverbed's topographic region. These tools are publicly available, which allows their wide application to specific loads and boundary conditions of mathematical models. The construction of an estimation grid involving the setting of boundary conditions and the use of geoinformation system tools makes it possible to simulate the destruction of a culvert of the pressure circuit and obtain results for a specific case of an actual riverbed and a water-head facility. It has been established that there is a decrease in the speed of wave propagation along the profile, from 3 m/s to 1 m/s. The impact of bottom irregularities, the effect of floodplains, and the variety of bottom roughness have also been assessed, compared to the results of their calculation based on one-dimensional models given in the regulatory documents. Hydraulic calculations were carried out taking into consideration the related properties of the main layer of the floodplain, which consists of peat accumulations, and the heterogeneity of the depths and roughness of floodplain surfaces of soils. It has been established that there is almost no erosion of supports in the floodplain zone in this case. It was found that as the distance between the flow and breakthrough intersection increases, there is a decrease in the height of the head from 2.1 m to 1.25 m.

DEVELOPMENT OF A METHOD FOR MAPPING THE BOTTOM OF SHALLOW RESERVOIRS BY LASER BATHYMETRY

The article is devoted to the development of methods for mapping the bottom of shallow reservoirs by laser bathymetry. It is noted that the main factors influencing the depth of laser bathymetric studies are the correct choice of the emitter wavelength, turbidity of sea water, especially in coastal zones and undulation of the sea surface. The problem of developing a method for mapping the bottom relief of shallow-water reservoirs is formulated and solved. A laser installed on board the aircraft is used as an emitter. It is noted that one of the main problems in laser bathymetry is the issue of modeling the seabed. While the surface of various reservoirs is currently modeled by various continuous functions, such as Hermite polynomials, B-splines, etc., modeling of reflection from the bottom of a reservoir is mainly limited to a diffuse model, i.e. The bottom is considered as a Lambert reflector Based on the geometric representation of the course of optical rays in laser bathymetry and the analysis of known measurement results, a step model of the bottom of the reservoir is proposed, the height and width of the steps of which vary widely. Based on the wellknown method of mapping the bottom of a shallow reservoir from one point, as well as the proposed step model of the bottom of the reservoir, a method for mapping the relief of the bottom irregularity has been developed, according to which measurements are carried out at two spatial points, with respect to which the difference in the depth of the reservoir should be determined. At the same time, measurements are carried out using a laser beam of constant power and at constant nadir angles, model studies have shown that the measurement error of the proposed method is within ±4.5%.

Monitoring and analysis of ground movement from multi-seam mining

Two surface deep-hole extensometers , each consisting of 11 anchors, were installed above a longwall panel operated approximately 70 m underneath a previously mined seam to investigate ground movement behaviour. The active longwall was 400 m wide and obliquely orientated with the previously mined longwalls. One instrument hole was drilled through the central part of an old goaf, and the other was drilled through the edge of the old goaf near a remnant pillar, representing two distinct mining regions. The interburden strata between the two worked seams at the two monitoring locations were found to undergo similar goafing processes of delamination , re-compaction and consolidation; however, the strata above the upper mined seam behaved differently. The strata above the central part of the goaf underwent re-compaction whereas the strata near the remnant pillar experienced significant shear displacement. Such strata deformation behaviour resulted in an irregular bottom of the subsidence profile over the active longwall goaf. Based on the observed average strain, the caved and highly fractured zones were estimated to be approximately 4 and 18 times the mining thickness, respectively. Possible failure scenarios of the instrument boreholes and the associated extensometer wire movement were also analysed; it is estimated that approximately 37–67% of the total monitored displacement was attributed to the shear movement of strata around the boreholes. The monitoring results were informative to optimising goaf gas drainage system by identifying gas emission sources, characterising fracture connection in the surrounding strata and assessing failure scenarios of vertical goaf wells. • Overburden movement above a multi-seam longwall was monitored with extensometers. • Longwall caving dynamics and parameters were quantified from the monitored data. • Strata above the previously mined goaf further recompacted. • 37–67% of total extensometer reading was attributed to strata lateral movement. • Gas emission sources and flow pathways were characterised from strata movement behaviour.

Endoscopic Scoring System for T2 Invasion in Colorectal Cancer

Background and AimsThe depth of tumor invasion in colorectal cancer (CRC), especially T1b or T2, is crucial in treatment decision-making. However, their differences are not well-characterized. Thus, this study aimed to investigate the predictive endoscopic findings in tumor invasion of CRC. MethodsData from patients with T1b or T2 CRCs resected endoscopically or surgically were reviewed retrospectively. The patients were divided into 2 groups: T1b (n = 298) and T2 (n = 267) tumor invasion. A scoring system was established based on the endoscopic findings in each group, and the accuracy of the system was assessed using a receiver-operating-characteristic (ROC) curve analysis. ResultsT2 invasion was predicted by tumor size, irregular bottom of depression, existence of depression, expansion appearance, convergency of folds, and erosion or white coat. The risk scoring system was developed using the regression coefficient values of the above variables. The area under the ROC curve was 0.894 (95% confidence interval, 0.868-0921). Cases with a score ≥4 had a high risk of T2 (sensitivity, 84.5%; specificity, 78.9%). ConclusionOur scoring system was useful for the diagnosis of T1b and T2, and a score ≥4 could predict T2 invasion. Additional studies are warranted to confirm these results before our scoring system can be applied clinically.

Mine surveying technique and steel storage tank base deformation removal

Introduction. Vertical steel tanks are extensively used in oil fields to hold crude oil and other liquids. Their construction requires continuous surveying control. However, measurement procedures, data processing, and deviations and documentation correction are not universal and cannot be applied for tanks with a capacity of less than 3000 m3. Moreover, the process of correcting the detected bottom irregularities is poorly substantiated and intuitive. Research objective is to improve the as-built survey accuracy and reliability of the low-capacity steel tank bottom, substantiate the minimum height of its irregularities, increase the objectivity and productivity of measurement processing, develop an unambiguous method for time-predictable correction of bottom irregularities, and substantiate the optimal contents of its relief’s as-built scheme. Methods of research. Geometric leveling for the bottom profile survey failed to provide adequate accuracy and was therefore replaced by the method of trigonometric leveling. A method has been developed for determining the deviations of the existent tank bottom profile from the design position by means of algebraic actions with surfaces of a topographic order. The accuracy of determining the smallest height of bottom irregularities has been estimated under the tacheometric survey. A method has been proposed for controlling the correction of tank bottom irregularities based on evaluation calculations of bottom deformations by the finite element method. Research results. All the development results are exemplified by a specific production example. It was found that for a full completion of work, two iterations of tank bottom irregularities correction are enough. Methods of optimal design for the facility’s as-built schemes are presented. Conclusions. A simple, accurate, low-cost, productive, and time-predictable method of mine surveying, mathematical processing and correction of deviations in the tank bottom profile has been developed. This technique reduces the construction period and increases the operating time of the facility.

Influence of Bottom Irregularities on Caustic Beam Propagation in Oceanic Waveguides

Influence of Bottom Irregularities on Caustic Beam Propagation in Oceanic Waveguides

Linear stability analysis for flows over sinusoidal bottom topography

Abstract

Propagation and attenuation characteristics of Rayleigh waves in the irregular bottom of the ocean in porous half-spaces

The Rayleigh wave propagation in the irregular bottom of the ocean, which is the interface of a homogeneous non-viscous liquid layer overlaying a porous half-space, under the influence of different factors has been discussed. The mathematical model is established by formula derivation. The propagation and attenuation characteristics of Rayleigh waves in a liquid layer over a transverse isotropy liquid-saturated porous half-space with irregular interface were studied. In addition, the dispersion and attenuation equations of the phase velocity and the attenuation coefficient with respect to the wave number were derived by which the effects of different parameters were analyzed. It was found that the magnitude of phase velocity varies with respect to the corrugation degree of the interface. In addition, irrespective of the type of interface, initially the attenuation coefficient rapidly increases and after the maximum value, it becomes constant. Furthermore, it has been observed that the change of the permeability coefficient affects the Rayleigh wave attenuation for the low wave number. For the low wave number, smaller permeability coefficient results in larger phase velocity and smaller attenuation. Moreover, both the phase velocity and the attenuation coefficient will eventually approach constant value in the high wave number region, for all parameters.

A Well-Balanced Asymptotic Preserving Scheme for the Two-Dimensional Shallow Water Equations Over Irregular Bottom Topography

A Well-Balanced Asymptotic Preserving Scheme for the Two-Dimensional Shallow Water Equations Over Irregular Bottom Topography

Propagated Uncertainty Models Arising From Device, Environment, and Target for a Small Laser Spot Airborne LiDAR Bathymetry and its Verification in the South China Sea

This contribution identifies the uncertainty sources influencing the component uncertainties for an airborne LiDAR bathymetry (ALB) measurement and presents the models for various component uncertainties (arising from the device, environment, and target for ALBs). Since various instrumental and environmental factors introduce vertical and horizontal uncertainties in ALB data, these uncertainties should be first analyzed and then precisely modeled to ensure the accuracy of the measurements. For this purpose, ten different effects that influence the accuracy of ALB data are systematically analyzed and modeled for four aspects in this article: the device aspect (laser pointing deflection, trajectory uncertainty, and boresight/lever arm offset), environmental aspect (atmospheric limitation, refraction on the sea surface, refraction in water, scattering in water, and water level fluctuation), target aspect (irregular bottom), and other aspect (accuracy of coordinate transformation model). In addition, the effect of the laser spot size is also discussed. To verify the presented uncertainty models, an ALB survey was operated around Yuanzhi Island in the South China Sea. For a water depth of 10 m, the theoretical overall root-sum-squares (RSS) for ten different effects of an ALB system (approximately 34 cm calculated using the total vertical uncertainty (TVU) models) is generally in accordance with the actual performance of the ALB data (approximately 39 cm) performance. The difference is mainly attributed to the limited accuracy of the ground truth data, and the difference between the water depth and laser ranging is reasonable. In this process, the topography data in the same region captured by a shipborne multibeam echo sounder (MBES) were used as the ground truth. The results indicated that for the typical ALB system, the laser pointing uncertainty and refraction uncertainty on the sea surface are primary uncertainty sources and should be corrected in a higher priority to meet the seafloor topographic accuracy demand of the International Hydrographic Organization (IHO) Standards for Hydrographic Surveys (S-44). The proposed uncertainty models can be used not only to guide the actual measurement of an ALB system but also to provide the uncertainty correction reference for ALB data postprocessing.

A parallel second-order unstructured finite volume method for 3D free-surface flows using a σ coordinate

In this paper, we introduce a second-order time- and space-accurate technique, developed to solve in parallel free-surface flows in arbitrary three-dimensional geometries. The discretization is based on a second-order finite-volume technique on prisms elements, consisting of triangular grids on the horizontal and bounded by a free surface and an irregular bottom on the vertical. The equations are transformed vertically to the σ-coordinate system in order to obtain an accurate representation of top and bottom topography. The reconstruction of three presure/velocity decoupling methods using a Crank-Nicolson scheme formulation is proposed. The Momentum Interpolation Method (MIM) is combined with Local Extremum Diminishing (LED) second-order upstream scheme for convective terms is developed. The parallelization is designed by a block domain decomposition technique. The discretization results in non-symmetric variable-coefficient linear systems which are solved using a parallel multi-color Successive Over-Relaxation algorithm. Several test cases of surface wave motion are used to demonstrate the capabilities, numerical stability and performance of the model.

Crustal Deformations and Geomorphological Units of Arabian Plate Foreland Region, North and Northeast of Iraq

The crustal shortening in the foreland of Arabian Plate (the Taurus and Zagros Mountains system) in N and NE of Iraq is accommodated in two principal ways: folding and thrusting. The fold and thrust patterns have evolved as an expression of shortening which was approximately NE-SW directed and subparallel to the bedding. In this area, observations of deformations along different cross sections were made using balancing cross sections for the estimation of the total shortening on five cross sections. The authors showed that shortening deformations were irregular and non-identical, which date back to the same age and the same location. This suggests that defects in this region are not homogeneous due to irregular bottom of the sedimentary basin, fault system and the form of the collision zone between the Arabian Plate and Iranian Plate or between the Arabian Plate and the Anatolian Plate. According to these magnitudes, the foreland region of Arabian Plate is affected by inhomogeneous deformations that are related rather to where these structures were developed, than to when they were formed. This study demonstrates the significant influence of geologic factor (especially structure) in forming and developing geomorphological features with a structural origin. These features are associated with tectonic history of the study area, such as units of structural origin. Another features related to the denudational factors, like glacis and badland, in addition to the features of fluvial origin which are alluvial fans, terraces and flood plains.

Modeling of Long-Range Reverberation Signal for Rough Bottom Consisting of Polygon Facets

To acquire a stable reverberation signal from an irregular ocean bottom, we derive the analytic surface integral of a scattered signal using Stokes’ theorem while approximating the bottom using a combination of polygon facets. In this approach, the delay difference in the elemental scattering area is considered, while the representative delay is used for the elemental scattering area in the standard reverberation model. Two different reverberation models are applied to a randomly generated rough bottom, which is composed of triangular facets. Their results are compared, and the scheme using analytic integration shows a converged reverberation signal, even with a large elemental scattering area, at the cost of an additional computational burden caused by a higher order approximation in the surface integral of the scattered signals.

Origin of buried, bottom current-related comet marks and associated submarine bedforms from a Paleogene continental margin, southeastern Brazil

Bottom current-related bedforms, such as depositional and erosive features, are useful indicators of oceanographic circulation and sedimentary balance conditions in both modern and ancient marine environments. The Eocene-Oligocene transition in northern Santos Basin is seismically expressed as a prominent, high-amplitude reflector (horizon H8.1) that truncates Eocene prograding clinoforms and records a major transgression in the basin associated to global and local environmental changes. This surface is punctuated by circular depressions, elongated depressions, mounds and conic features, which, based on seismic interpretation, are associated with the escape of gas on the paleoseafloor. Elongated negative features with a head and an erosive tail (comet marks) are associated with the erosive action of bottom currents that, when encounters an obstacle or bottom irregularity such as pockmarks, create a downflow, linear furrow (tail). The occurrence of carbonate mounds and mud volcanoes may affect the erosive power of the flow by deflecting and/or focusing undercurrents. In the study area, parallel to subparallel comet marks occur abundantly on the former outer shelf and upper slope, being up to 1.2km long, 200m wide, and 30m deep. These dimensions allow the classification of such bedforms as giant comet marks, which form as a result of erosion of the irregular sea floor by currents as fast as 0.6ms−1. The strong alignment of the comet tails indicates paleocurrents to the NE on the Oligocene outer shelf and upper slope. Conditions for comet mark formation include the development of pockmarks due to gas seeps, reworking of pockmarks by vigorous and long-lived bottom currents and low sediment supply during the Eocene-Oligocene transition, a period marked by the opening of the Drake Pass and the establishment of undercurrents through the connection of the Atlantic and the Pacific oceans. Bottom-current related bedforms on H8.1 in Santos Basin may thus be related to such paleoenvironmental changes. Although no pre-Quaternary comet marks have been reported before, their identification and mapping through 3D seismic data is a unique opportunity to assess paleoenvironmental conditions and paleo-circulation on continental margins.

Study of Rayleigh type surface wave in the initial stressed irregular bottom of ocean due to point source

Rayleigh type surface wave propagation in the irregular bottom of ocean model which is the interface of homogeneous liquid layer over laying an irregular boundary of homogeneous orthotropic half space under initial stresses has been discussed in this paper. Three different dispersion equations are obtained in the form of simple equation using and not using Perturbation technique. Some special cases have been considered. The effect of irregularity, initial stressed, point source, and depth of liquid layer on the propagation of Rayleigh waves has been analyzed and results of numerical discussion have been presented graphically for three different dispersion equations. Mainly the graphs are shown the variation of phase velocity with wave number in different cases.