A more deterministic version of Harris - Spitzer's “Random constant velocity” model for infinite systems of particles

1975 ◽  
pp. 157-168 ◽  
Author(s):  
W. Szatzschneider
Keyword(s):  
Constant Velocity ◽  
Velocity Model ◽  
Infinite Systems

Marchenko multiple elimination and full wavefield migration in a resonant pinch-out model

Geophysics ◽  
2021 ◽  
pp. 1-59
Author(s):  
Evert Slob ◽  
Lele Zhang ◽  
Eric Verschuur
Keyword(s):  
Constant Velocity ◽  
Local Minimum ◽  
Velocity Model ◽  
Dominant Frequency ◽  
Data Sampling ◽  
Multiple Reflections ◽  
Linear Inversion ◽  
Acoustic Reflection ◽  
Reflection Data ◽  
Multiple Elimination

Marchenko multiple elimination schemes are able to attenuate all internal multiple reflections in acoustic reflection data. These can be implemented with and without compensation for two-way transmission effects in the resulting primary reflection dataset. The methods are fully automated and run without human intervention, but require the data to be properly sampled and pre-processed. Even when several primary reflections are invisible in the data because they are masked by overlapping primaries, such as in the resonant wedge model, all missing primary reflections are restored and recovered with the proper amplitudes. Investigating the amplitudes in the primary reflections after multiple elimination with and without compensation for transmission effects shows that transmission effects are properly accounted for in a constant velocity model. When the layer thickness is one quarter of the wavelength at the dominant frequency of the source wavelet, the methods cease to work properly. Full wavefield migration relies on a velocity model and runs a non-linear inversion to obtain a reflectivity model which results in the migration image. The primary reflections that are masked by interference with multiples in the resonant wedge model, are not recovered. In this case, minimizing the data misfit function leads to the incorrect reflector model even though the data fit is optimal. This method has much lower demands on data sampling than the multiple elimination schemes, but is prone to get stuck in a local minimum even when the correct velocity model is available. A hybrid method that exploits the strengths of each of these methods could be worth investigating.

scholarly journals A Fast Ray-tracing Method for Locating Mining-Induced Seismicity by Considering Underground Voids

2020 ◽  
Vol 10 (19) ◽  
pp. 6763
Author(s):  
Pingan Peng ◽  
Yuanjian Jiang ◽  
Liguan Wang ◽  
Zhengxiang He ◽  
Siyu Tu
Keyword(s):  
Travel Time ◽  
Ray Tracing ◽  
Induced Seismicity ◽  
Constant Velocity ◽  
Velocity Model ◽  
Surface Model ◽  
Location Accuracy ◽  
Ray Tracing Method ◽  
Mining Induced Seismicity ◽  
Tracing Method

The accurate localization of mining-induced seismicity is crucial to underground mines. However, the constant velocity model is used by traditional location methods without considering the great difference in wave velocity between rock mass and underground voids. In this paper, to improve the microseismicity location accuracy in mines, we present a fast ray-tracing method to calculate the ray path and travel time from source to receiver considering underground voids. First, we divide the microseismic monitoring area into two categories of mediums—voids and non-voids—using a flexible triangular patch to model the surface model of voids, which can accurately describe any complicated three-dimensional (3D) shape. Second, the nodes are divided into two categories. The first category of the nodes is the vertex of the model, and the second category of the nodes is arranged at a certain step length on each edge of the 3D surface model to improve the accuracy of ray tracing. Finally, the set of adjacent nodes of each node is calculated, and then we obtain the shortest travel time from the source to the receiver based on the Dijkstra algorithm. The performance of the proposed method is tested by numerical simulation. Results show that the proposed method is faster and more accurate than the traditional ray-tracing methods. Besides, the proposed ray-tracing method is applied to the microseismic source localization in the Huangtupo Copper and Zinc Mine. The location accuracy is significantly improved compared with the traditional method using the constant velocity model and the FMM-based location method.

Fast acoustic velocity tomography of focusing operators

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. R121-R131 ◽  
Author(s):  
Hu Jin ◽  
George A. McMechan
Keyword(s):  
Constant Velocity ◽  
Null Space ◽  
Focal Point ◽  
Grid Point ◽  
Synthetic Data ◽  
Velocity Model ◽  
The Stability ◽  
Starting Model ◽  
Velocity Tomography ◽  
Focus Point

A 2D velocity model was estimated by tomographic imaging of overlapping focusing operators that contain one-way traveltimes, from common-focus points to receivers in an aperture along the earth’s surface. The stability and efficiency of convergence and the quality of the resulting models were improved by a sequence of ideas. We used a hybrid parameterization that has an underlying grid, upon which is superimposed a flexible, pseudolayer model. We first solved for the low-wavenumber parts of the model (approximating it as constant-velocity pseudo layers), then we allowed intermediate wavenumbers (allowing the layers to have linear velocity gradients), and finally did unconstrained iterations to add the highest wavenumber details. Layer boundaries were implicitly defined by focus points that align along virtual marker (reflector) horizons. Each focus point sampled an area bounded by the first and last rays in the data aperture at the surface; this reduced the amount of computation and the size of the effective null space of the solution. Model updates were performed simultaneously for the velocities and the local focus point positions in two steps; local estimates were performed independently by amplitude semblance for each focusing operator within its area of dependence, followed by a tomographic weighting of the local estimates into a global solution for each grid point, subject to the constraints of the parameterization used at that iteration. The system of tomographic equations was solved by simultaneous iterative reconstruction, which is equivalent to a least-squares solution, but it does not involve a matrix inversion. The algorithm was successfully applied to synthetic data for a salt dome model using a constant-velocity starting model; after a total of 25 iterations, the velocity error was [Formula: see text] and the final mean focal point position error was [Formula: see text] wavelength.

Seismic constant‐velocity remigration

Geophysics ◽  
1997 ◽  
Vol 62 (2) ◽  
pp. 589-597 ◽  
Author(s):  
Jörg Schleicher ◽  
Peter Hubral ◽  
German Höcht ◽  
Frank Liptow
Keyword(s):  
Constant Velocity ◽  
Wave Equations ◽  
Single Point ◽  
Velocity Model ◽  
Migration Velocity ◽  
Body Waves ◽  
Reflection Point ◽  
Ray Trajectories ◽  
Zero Offset ◽  
Migration Velocities

When a seismic common midpoint (CMP) stack or zero‐offset (ZO) section is depth or time migrated with different (constant) migration velocities, different reflector images of the subsurface are obtained. If the migration velocity is changed continuously, the (kinematically) migrated image of a single point on the reflector, constructed for one particular seismic ZO reflection signal, moves along a circle at depth, which we call the Thales circle. It degenerates to a vertical line for a nondipping event. For all other dips, the dislocation as a function of migration velocity depends on the reflector dip. In particular for reflectors with dips larger than 45°, the reflection point moves upward for increasing velocity. The corresponding curves in a Time‐migrated section are parabolas. These formulas will provide the seismic interpreter with a better understanding of where a reflector image might move when the velocity model is changed. Moreover, in that case, the reflector image as a whole behaves to some extent like an ensemble of body waves, which we therefore call remigration image waves. In the same way as physical waves propagate as a function of time, these image waves propagate as a function of migration velocity. Different migrated images can thus be considered as snapshots of image waves at different instants of migration velocity. By some simple plane‐wave considerations, image‐wave equations can be derived that describe the propagation of image waves as a function of the migration velocity. The Thales circles and parabolas then turn out to be the characteristics or ray trajectories for these image‐wave equations.

scholarly journals Evaluating Mobility Management Models for Content Forwarding in Named Data Networking Environments

2019 ◽  
Vol 13 (04) ◽  
pp. 47
Author(s):  
Muhammed Zaharadeen Ahmed ◽  
Aisha Hassan Abdalla Hashim ◽  
Othman O. Khalifa ◽  
Abdulkadir H. Alkali ◽  
Nur Shahida Bt Midi ◽  
...  
Keyword(s):  
Mobility Management ◽  
Constant Velocity ◽  
Simulation Analysis ◽  
Velocity Model ◽  
Mobility Model ◽  
Named Data Networking ◽  
Management Models ◽  
Mobile Router ◽  
Distance Vector Algorithm ◽  
Data Networking

<span>Named Data Networking (NDN) performs its routing and forwarding decisions using name prefixes. This removes some of the issues affecting addresses in our traditional IP architecture such as limitation in address allocation and management, and even NAT translations etcetera. Another positivity of NDN is its ability to use the conventional routing like the link state and distance vector algorithm. In route announcement, NDN node broadcasts its name prefix which consists of the knowledge of the next communicating node. In this paper, we evaluate the performance of mobility management models used in forwarding NDN contents to a next hop. This makes it crucial to select an approach of mobility model that translates the nature of movement of the NDN mobile routers. A detailed analysis of the famous mobility model such as the Random Waypoint mobility and Constant Velocity were computed to determine the mobility rate of the NDN mobile router. Simulation analysis was carried out using ndnSIM 2.1 on Linux Version 16.1. we build and compile with modules and libraries in NS-3.29. The sample of movement of the mobile router is illustrated and our result present the viability of the Constant Velocity model as compared with the Random Way point.</span>

Exponential asymptotically bounded velocity model: Part II — Ray tracing

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. T67-T85 ◽  
Author(s):  
Igor Ravve ◽  
Zvi Koren
Keyword(s):  
Ray Tracing ◽  
Constant Velocity ◽  
Critical Angle ◽  
Velocity Model ◽  
Velocity Variation ◽  
Infinite Depth ◽  
Source Point ◽  
Shallow Zone ◽  
Takeoff Angle ◽  
2D And 3D

A ray-tracing procedure is derived for the new exponential asymptotically bounded (EAB) velocity model introduced in Part I of this paper. The model inherits the properties of a medium with linear-velocity variation in depth in the shallow zone and of a medium with constant velocity in the deep zone. Two types of rays departing from the source point on the earth’s surface exist in this model, depending on the takeoff angles. The rays of the first kind are symmetric arcs that return up to the earth’s surface and have a limited maximum depth of propagation. The rays of the second kind propagate down to infinite depth. In the shallow region, they are curved lines, but at large depth they become asymptotically straight. The form of the ray is governed by the takeoff angle at the source point, where a critical angle splits the two kinds of rays. This critical angle depends only on the ratio between the velocity at the source point and the asymptotic velocity of the EAB model. We derive the formulae required to calculate the two kinds of rays and solve the inverse problem of two-point ray tracing. Finally, we construct the 2D- and 3D-isochron surfaces for a finite offset.

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