NL2021354A - 2-D Seismic Travel Time Calculation Method Based on Virtual Source Wavefront Construction - Google Patents

2-D Seismic Travel Time Calculation Method Based on Virtual Source Wavefront Construction Download PDF

Info

Publication number
NL2021354A
NL2021354A NL2021354A NL2021354A NL2021354A NL 2021354 A NL2021354 A NL 2021354A NL 2021354 A NL2021354 A NL 2021354A NL 2021354 A NL2021354 A NL 2021354A NL 2021354 A NL2021354 A NL 2021354A
Authority
NL
Netherlands
Prior art keywords
wavefront
travel time
seismic
calculation
rays
Prior art date
Application number
NL2021354A
Other languages
Dutch (nl)
Other versions
NL2021354B1 (en
Inventor
Sun Hui
Original Assignee
Chengdu Qitai Zhilian Information Tech Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Chengdu Qitai Zhilian Information Tech Co Ltd filed Critical Chengdu Qitai Zhilian Information Tech Co Ltd
Publication of NL2021354A publication Critical patent/NL2021354A/en
Application granted granted Critical
Publication of NL2021354B1 publication Critical patent/NL2021354B1/en

Links

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
    • G01V1/30—Analysis
    • G01V1/303—Analysis for determining velocity profiles or travel times
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
    • G01V1/30—Analysis
    • G01V1/303—Analysis for determining velocity profiles or travel times
    • G01V1/305—Travel times
    • G01V20/00—
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V2210/00—Details of seismic processing or analysis
    • G01V2210/10—Aspects of acoustic signal generation or detection
    • G01V2210/12—Signal generation
    • G01V2210/125—Virtual source
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V2210/00—Details of seismic processing or analysis
    • G01V2210/50—Corrections or adjustments related to wave propagation
    • G01V2210/57—Trace interpolation or extrapolation, e.g. for virtual receiver; Anti-aliasing for missing receivers
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V2210/00—Details of seismic processing or analysis
    • G01V2210/60—Analysis
    • G01V2210/62—Physical property of subsurface
    • G01V2210/622—Velocity, density or impedance
    • G01V2210/6222—Velocity; travel time
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V2210/00—Details of seismic processing or analysis
    • G01V2210/60—Analysis
    • G01V2210/67—Wave propagation modeling
    • G01V2210/671—Raytracing

Abstract

The invention discloses a 2-D seismic travel time calculation method based on virtual source wavefront construction. The seismic travel time calculation method comprises the following steps of reading in relevant parameters and a velocity model; tracing rays in different directions from a seismic source by using a Runge-Kutta method, and inserting new rays during ray tracing according to relevant judgement conditions in the ray tracing process; dividing a calculation space into a plurality of wavefront quadrilaterals through discrete points on adjacent rays and adjacent wave front surfaces; finding grid points in the wavefront quadrilaterals; calculating the travel time of the grid point in each of the wavefront quadrilaterals by a virtual source method; and completing the calculation of the travel time of the grid points in all wavefront quadrilaterals. Through adoption of the virtual source method, during calculation of the travel time of the grid points in the wavefront quadrilaterals of the invention, the calculation precision of the travel time of the grid points is improved, and a high-precision seismic travel time calculation method based on wavefront construction is realized.

Description

TECHNICAL FIELD
The invention relates to the field of seismic travel time calculation, in particular to a 2-D seismic travel time calculation method based on wavefront construction.
BACKGROUND
The Journal of Jilin University (Earth Science Edition) disclosed, in the 2nd issue of 2008, a paper Ray-Tracing of Wavefront Construction by Bicubic Convolution Interpolation published by Han Fuxing et al. The paper introduced an io improved seismic travel time calculation method based on wavefront construction, that a bicubic convolution interpolation method was applied to grid point travel time calculation, so as to improve the calculation precision of seismic travel time and the calculation efficiency of the algorithm. Besides, the error analysis on the wavefront construction method based on a bicubic convolution interpolation algorithm was carried out through a homogenous medium, and the analysis results obtained good effects.
The Chinese Journal of Computational Physics disclosed, in the 2nd issue of 2008, a paper Application and Comparison of Different Interpolation Algorithms in Ray-Tracing of Wavefront Construction published by Han Fuxing et al. In the paper, the application effects of a nearest region interpolation method, a bilinear interpolation method, a piecewise interpolation method and a bicubic convolution interpolation method in ray tracing of wavefront construction were compared and analysed. The model calculation results reflected that the bicubic convolution interpolation method can obtain more accurate ray paths than the other three methods.
The Progress in Geophysics disclosed, in the 5th issue of 2009, a paper Study on Gird Point Positioning and Attribute Evaluation with the Method of Wavefront
Construction published by Han Fuxing et al. The paper introduced how to use a vector product method to judge the relative position relationship of a rectangle grid point and a nonregular wavefront quadrilateral, and provided a corresponding interpolation method for calculating the attribute information of the grid point according to position relationship of the grid point and the nonregular wavefront io quadrilateral. The provided method was verified through a homogeneous model and calculation examples, and good calculation results were obtained.
As can be seen from the above examples, conventional 2-D seismic travel time calculation methods based on wavefront construction can improve the calculation precision to a certain extent, but the propagation rule of seismic waves was not considered in the interpolation method, and the calculation precision improved was also limited.
SUMMARY
The invention aims to solve the technical problem of providing a seismic travel time calculation method based on virtual source wavefront construction. In consideration of the propagation rule of seismic waves in a medium, a virtual source calculation method is used to replace a conventional bicubic convolution interpolation method in the process of calculating the travel time of grid points in wavefront quadrilaterals, and the calculation precision and the stability of the seismic travel time calculation method based on wavefront construction are improved.
In order to solve the technical problem, the adopted technical scheme lies in that a high-precision seismic travel time calculation method based on wavefront construction comprises the following steps:
step 1: reading in relevant parameter files and a velocity model, wherein the parameter files comprise the grid point number, grid spacing, source location, tracing step length, ray angle range, and ray sampling interval of the velocity model; io step 2: tracing rays, and inserting new rays during the tracing to ensure the coverage of the rays, wherein the essence of ray tracing is to solve a kinematics ray tracing equation group by using a Runge-Kutta method, as shown in the formula below:
dx, — = ^gp! ατ ^Pl = JL( 1Ί _ v-· 5v dr ©GJ © wherein y represents the location component, p, represents the slowness component, τ represents the seismic travel time, and v represents the seismic velocity;
step 3: dividing a calculation space into a plurality of wavefront quadrilaterals by calculating the spatial position information of discrete points on the acquired rays;
step 4: judging the position relationship of the grid point and the wavefront quadrilateral by a vector product method, and determining the grid point contained in the wavefront quadrilateral;
step 5: calculating the locations of virtual sources corresponding to the points through the relevant information of vertices of the wavefront quadrilateral, and calculating the seismic travel time of the grid points contained in the wavefront quadrilateral based on the locations of the virtual sources; and step 6: completing the travel time calculations of all grid points and outputting the final travel time calculation results.
Compared with the prior art, the seismic travel time calculation method disclosed by the invention has the beneficial effects that in consideration of the io propagation rule of the seismic waves in the medium, the travel time of the grid points in the wavefront quadrilaterals is calculated by a virtual source method, the calculation precision of the grid point travel time is improved, and the calculation precision of the seismic travel time method based on wavefront construction is improved.
BRIEF DESCRIPTION OF DRAWINGS
Fig. 1 is a flow chart of a seismic travel time calculation method based on virtual source wavefront construction of the invention.
Fig. 2 is a schematic diagram of calculation region division.
Fig. 3 is a schematic diagram of virtual source seismic travel time calculation, 20 A, B, C and D are four vertexes of a wavefront quadrilateral, Oa, Ob, Oc and Od are the locations of virtual sources corresponding to A, B, C and D, and R is a grid point in the wavefront quadrilateral ABCD.
Fig. 4 is the relative error of travel time in a conventional wavefront construction method in a homogeneous medium.
Fig. 5 is the relative error of the seismic travel time calculation method based on virtual source wavefront construction in the homogeneous medium.
DETAILED DESCRIPTION
The invention is described in details below with reference to the accompanying drawings and specific embodiments.
Fig. 1 is the flow chart of the seismic travel time calculation method based on virtual source wavefront construction. The realization flow of the method of the invention is specially shown in the figure as follows: io 1) reading in relevant parameter files and a velocity model, wherein the parameter files comprise the grid point number, grid spacing, source location, tracing step length, ray angle range, and ray sampling interval of the velocity model;
2) tracing rays, and inserting new rays during the tracing to ensure the coverage of the rays, wherein the ray emission angle range is -80° to +80°, the sampling interval is 3° to 6°, the ray tracing step length is 2ms to 6ms, the essence of ray tracing is to solve a kinematics ray tracing equation group by using a Runge-Kutta method, as shown in the formula below:
dx, ατ _ a f1Ί _ v-»5v d t ex, y v J dx.
wherein y represents the location component, p, represents the slowness component, τ represents the seismic travel time, and v represents the seismic velocity;
3) dividing a calculation space into a plurality of wavefront quadrilaterals with the four points on adjacent rays and adjacent wave front surfaces as the vertices of each of the wavefront quadrilaterals, by calculating the spatial position information of discrete points on the acquired rays (as shown in Fig. 2);
4) firstly, roughly screening a grid point that can be positioned in the coverage 5 area of each of the wavefront quadrilaterals through the positions of the vertices of the wavefront quadrilateral, then judging the position relationship of the grid point and the wavefront quadrilateral by a vector product method, and detennining the grid point contained in the wavefront quadrilateral;
5) calculating the locations of virtual sources corresponding to the vertices io through the information such as the ray directions of the vertices of the wavefront quadrilateral, the seismic travel time, and the seismic velocity, as shown in Fig. 3: supposing that the four vertices of a wavefront quadrilateral are A, B, C and D respectively, and R is a grid point in the wavefront quadrilateral, wherein after the locations of the virtual sources Oa, Ob, Oc and Od corresponding to A, B, C, and D are calculated through relevant information, the expression of seismic travel time at point R is:
(|OaR| + |ObR| + |OcR| + |OdR|) Tr= 4*Vr |OaR|, |ObR|, |OcR| and |OdR| respectively represent the distance from Oa , Ob , Oc and Od to point R, and Vr represents the seismic velocity at point R;
and
6) completing the travel time calculations of all grid points and outputting the final travel time calculation results.
The calculation precision of the method disclosed by the invention is analysed and verified below by a homogeneous model.
Fig. 4 and Fig. 5 are absolute errors of a conventional wavefront construction method and a virtual source wavefront construction method in a homogeneous medium model respectively. The number of horizontal grid points of the homogeneous medium model is 761, the number of vertical grid points is 777, the horizontal grid spacing and the vertical grid spacing are 10m, the speed is 1000m/s, and a seismic source is positioned at 3800m. As can be seen from the figures, compared with the conventional wavefront construction method, the calculation precision of the seismic travel time calculation method based on virtual source io wavefront construction is greatly improved.
The travel time of the grid points in the wavefront quadrilaterals of the invention is calculated by the virtual source method, the calculation precision of the travel time of the grid points in the wavefront quadrilaterals is improved, and a high-precision seismic travel time calculation method based on wavefront construction is realized.

Claims (1)

ConclusiesConclusions 1. Tweedimensionale seismische reistijdberekeningswerkwijze op basis van een virtuele bron met een golffrontconstructie, met het kenmerk, dat de volgendeA two-dimensional seismic travel time calculation method based on a virtual source with a wavefront construction, characterized in that the following 5 stappen worden omvat:5 steps are included: stap 1: lezen in relevante parameterbestanden en een snelheidsmodel, waarbij de parameterbestanden het rasterpuntnummer, rasterafstand, bronlocatie, traceringsstaplengte, straalhoekbereik en straalbemonsteringsinterval van het snelheidsmodel omvatten;step 1: reading into relevant parameter files and a speed model, wherein the parameter files include the raster point number, raster distance, source location, tracing step length, beam angle range, and beam sampling interval of the speed model; ïo stap 2: traceren van stralen en invoegen van nieuwe stralen tijdens het traceren om de dekking van de stralen te garanderen, waarbij de essentie van het traceren van de stralen is om een kinematische straaltracering-vergelijkingsgroep op te lossen met behulp van eenstep 2: tracing rays and inserting new rays during tracing to ensure coverage of the rays, the essence of tracing the rays is to solve a kinematic ray tracing comparison group using a Runge-Kutta-methode, zoals weergegeven in de onderstaande formule:Runge-Kutta method, as shown in the formula below: dxt 2 — = v gp, ατ ’ A = Af ik _v-A άτ öxt fv J cx, waarin xt de locatiecomponent weergeeft, p, de traagheidscomponent weergeeft, τ de seismische reistijd weergeeft en v de seismische snelheid 20 weergeeft;dx t 2 - = v gp, ατ 'A = Af i _ v -A άτ öx t fv J cx, where x t represents the location component, p, the inertia component, τ the seismic travel time and v the seismic speed 20 ; stap 3; verdelen van een berekeningsruimte in een aantal vierhoeken van het golffront door middel van het berekenen van de ruimtelijke locatie-informatie van discrete punten op de verworven stralen;step 3; dividing a calculation space into a plurality of quadrangles of the wavefront by calculating the spatial location information of discrete points on the acquired rays; stap 4: beoordelen van de locatiebetrekking van het rasterpunt en de 5 vierhoek van het golffront door middel van een vectorproductmethode, en het bepalen van het rasterpunt dat zich in de vierhoek van het golffront bevindt; stap 5; berekenen van de locaties van virtuele bronnen die overeenkomen met de punten door middel van de relevante informatie van hoekpunten van de vierhoek van het golffront, en berekenen van de seismische reistijd van de io rasterpunten die zijn opgenomen in de vierhoek van het golffront op basis van de locaties van de virtuele bronnen; en stap 6: voltooien van de reistijdberekeningen van alle rasterpunten en het uitvoeren van de resultaten van de uiteindelijke reistijdberekening.step 4: judging the location relation of the grid point and the quadrangle of the wavefront by means of a vector product method, and determining the grid point which is in the quadrangle of the wavefront; step 5; calculate the locations of virtual sources corresponding to the points through the relevant information of corner points of the quadrilateral of the wavefront, and calculate the seismic travel time of the io grid points that are included in the quadrangle of the wavefront based on the locations of the virtual sources; and step 6: completing the travel time calculations of all grid points and performing the results of the final travel time calculation. 15 2. Seismische reistijdberekeningswerkwijze gebaseerd op de virtuele tweedimensionale golffrontconstructiebron volgens conclusie 1, met het kenmerk, dat de bij de stap 5, wanneer de seismische reistijd van de rasterpunten die zijn opgenomen in de vierhoek van het golffront wordt berekend door middel van een virtuele bronmethode, vier hoekpunten van een2. Seismic travel time calculation method based on the virtual two-dimensional wavefront construction source according to claim 1, characterized in that in step 5, when the seismic travel time of the grid points included in the quadrangle of the wavefront is calculated by means of a virtual source method , four vertices of one 20 vierhoek van het golffront als respectievelijk A, B, C en D worden verondersteld, en R een rasterpunt in de vierhoek van het golffront is; en nadat de locaties van de virtuele bronnen Oa, Ob, Oc en Od die overeenkomen met A,Quadrilateral of the wavefront if A, B, C and D are assumed, respectively, and R is a grid point in the quadrangle of the wavefront; and after the locations of the virtual sources Oa, Ob, Oc and Od corresponding to A, B, C en D worden berekend door middel van relevante informatie, de uitdrukking van seismische reistijd op punt R is:B, C and D are calculated by means of relevant information, the expression of seismic travel time at point R is: (|OaR| + |ObR|+|OcR| + |OdR|) rR= 4*Vr ’ waarin |OAR|, |ObR|, |OcR| en |OdR| respectievelijk de afstand van OA, Ob, Oc en Od tot punt R weergeven, en VR de seismische snelheid in punt R weergeeft.(| OaR | + | ObR | + | OcR | + | OdR |) r R = 4 * Vr 'where | O A R |, | ObR |, | OcR | and | OdR | represent the distance from O A , Ob, Oc and Od to point R, respectively, and V R represents the seismic speed in point R. read in parameters and a velocity model i£Sread in parameters and a velocity model i £ S I divide a calculation space into a ί I plurality of quadrilaterals II divide a calculation space into a variety of quadrilaterals I J calculate the travd time of grid points) I I in the ctiadrilaterals I comolete calculation for all the quadrilaterals .YESJ calculate the travd time of grid points) I I in the ctiadrilaterals I comolete calculation for all the quadrilaterals .YES Output results^..Output results ^ ..
NL2021354A 2018-06-21 2018-07-19 2-D Seismic Travel Time Calculation Method Based on Virtual Source Wavefront Construction NL2021354B1 (en)

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201810641651.7A CN108957538A (en) 2018-06-21 2018-06-21 A kind of virtual focus two dimension wavefront construction seimic travel time calculation method

Publications (2)

Publication Number Publication Date
NL2021354A true NL2021354A (en) 2018-08-14
NL2021354B1 NL2021354B1 (en) 2019-04-26

Family

ID=63141839

Family Applications (1)

Application Number Title Priority Date Filing Date
NL2021354A NL2021354B1 (en) 2018-06-21 2018-07-19 2-D Seismic Travel Time Calculation Method Based on Virtual Source Wavefront Construction

Country Status (5)

Country Link
CN (1) CN108957538A (en)
BE (1) BE1025828B1 (en)
LU (1) LU100878B1 (en)
NL (1) NL2021354B1 (en)
WO (1) WO2019242045A1 (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108957538A (en) * 2018-06-21 2018-12-07 成都启泰智联信息科技有限公司 A kind of virtual focus two dimension wavefront construction seimic travel time calculation method

Families Citing this family (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110660135A (en) * 2019-09-20 2020-01-07 西南石油大学 Method for realizing wavefront construction by utilizing triangular gridding rays
CN110568496B (en) * 2019-09-26 2021-02-09 核工业北京地质研究院 Ray tracing method under complex medium condition
CN111257939B (en) * 2020-03-26 2021-06-01 中国石油大学(北京) Time-lapse seismic virtual source bidirectional wave field reconstruction method and system
CN114924312B (en) * 2022-05-10 2024-03-12 吉林大学 Gaussian beam migration method and device based on wavefront initialization ray tracing technology

Family Cites Families (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6035256A (en) * 1997-08-22 2000-03-07 Western Atlas International, Inc. Method for extrapolating traveltimes across shadow zones
EP1423735B1 (en) * 2001-09-07 2010-08-18 Shell Internationale Research Maatschappij B.V. Seismic imaging a subsurface formation by means of virtual sources
US20170363759A1 (en) * 2016-06-17 2017-12-21 Cgg Services Sa System and method for seismic interferometry optimized data acquisition
CN105974470B (en) * 2016-07-04 2017-06-16 中国石油大学(华东) A kind of multi-component seismic data least square reverse-time migration imaging method and system
CN108072897A (en) * 2018-01-23 2018-05-25 西南交通大学 It is a kind of to mix computational methods when two-dimensionally seismic wave is walked
CN108957538A (en) * 2018-06-21 2018-12-07 成都启泰智联信息科技有限公司 A kind of virtual focus two dimension wavefront construction seimic travel time calculation method

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
FUXING HAN ET AL: "Positioning of grid points in wave front construction", APPLIED GEOPHYSICS, vol. 6, no. 3, 1 September 2009 (2009-09-01), Heidelberg, pages 248 - 258, XP055535404, ISSN: 1672-7975, DOI: 10.1007/s11770-009-0024-z *
K. CHAMBERS ET AL: "A practical implementation of wave front construction for 3-D isotropic media", GEOPHYSICAL JOURNAL INTERNATIONAL., vol. 173, no. 3, 1 June 2008 (2008-06-01), GB, pages 1030 - 1038, XP055535417, ISSN: 0956-540X, DOI: 10.1111/j.1365-246X.2008.03790.x *
V. VINJE ET AL: "Estimation of multivalued arrivals in 3D models using wavefront construction-Part I1", GEOPHYSICAL PROSPECTING, vol. 44, no. 5, 1 September 1996 (1996-09-01), pages 819 - 842, XP055085423, ISSN: 0016-8025, DOI: 10.1111/j.1365-2478.1996.tb00175.x *
VETLE VINJE ET AL: "Traveltime and amplitude estimation using wavefront construction", GEOPHYSICS, 1 August 1993 (1993-08-01), pages 1157 - 1166, XP055535413, Retrieved from the Internet <URL:https://library.seg.org/doi/pdf/10.1190/1.1443499> [retrieved on 20181217], DOI: 10.1190/1.1443499 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108957538A (en) * 2018-06-21 2018-12-07 成都启泰智联信息科技有限公司 A kind of virtual focus two dimension wavefront construction seimic travel time calculation method

Also Published As

Publication number Publication date
BE1025828B1 (en) 2019-07-25
LU100878B1 (en) 2019-12-30
WO2019242045A9 (en) 2021-02-18
WO2019242045A1 (en) 2019-12-26
BE1025828A1 (en) 2019-07-18
CN108957538A (en) 2018-12-07
NL2021354B1 (en) 2019-04-26

Similar Documents

Publication Publication Date Title
NL2021354B1 (en) 2-D Seismic Travel Time Calculation Method Based on Virtual Source Wavefront Construction
US11461964B2 (en) Satellite SAR artifact suppression for enhanced three-dimensional feature extraction, change detection, and visualizations
US7352369B2 (en) System and method for approximating an editable surface
Ward et al. Reducing Anisotropic BSDF Measurement to Common Practice.
CN110335301A (en) A kind of 3-D scanning method and device based on laser radar and structure light
Kada 3D building generalization based on half-space modeling
CN110208769B (en) Ray tracing method and system based on NURBS curved surface
CN104517318A (en) System and method for three-dimensional measurement simulation point selection
Maleika The influence of track configuration and multibeam echosounder parameters on the accuracy of seabed DTMs obtained in shallow water
CN109116413B (en) Imaging domain stereo chromatography velocity inversion method
CN109255837B (en) Construction method of efficient B-spline surface for laser radar point cloud data processing
Bradley et al. A complementary sensor approach to reverse engineering
He et al. Fast flux density distribution simulation of central receiver system on GPU
Telescope et al. Modeling in-ice radio propagation with parabolic equation methods
CA2883668A1 (en) System and method for analysis of designs of a seismic survey
NL2020684B1 (en) Mixed 2D seismic wave travel time calculation method
Fournier et al. Chebyshev polynomials for boxing and intersections of parametric curves and surfaces
EP4127457A1 (en) System and method for wind flow turbulence measurement by lidar in a complex terrain
Wu et al. An Accurate Error Measure for Adaptive Subdivision Surfaces.
JP2007327898A (en) Standard deviation calculation method and its program of sound field energy spread in gaussian ray bundle model
Jensen et al. Ray methods
Ozendi et al. Stochastic surface mesh reconstruction
Venuvinod et al. Reverse Engineering and CAD Modeling
Neklyudov et al. “Fat” Rays in Three Dimensional Media to Approximate a Broadband Signal Propagation
Yadav et al. CASA-Report 16-19 September 2016

Legal Events

Date Code Title Description
MM Lapsed because of non-payment of the annual fee

Effective date: 20210801