Group Velocity Measurement

Size: px
Start display at page:

Download "Group Velocity Measurement"

Transcription

1 Group Velocity Measurement Distance Travelled (8.3) Group Velocity Time It Took

2 Group Velocity Measurement Distance Travelled (8.3) Group Velocity Time It Took station Earthquake t time d distance earthquake

3 Group Velocity Measurement Distance Travelled (8.3) Group Velocity Time It Took station Earthquake t = 238 s time d = 1000 km distance earthquake

4 Group Velocity Measurement Distance Travelled (8.3) Group Velocity Time It Took station Earthquake t = 238 s time d = 1000 km distance earthquake Need to know exact location and timing of an earthquake

5 Group Velocity Measurement Distance Travelled (8.3) Group Velocity Time It Took Location of stations are well known Earthquake t 1 = 238 s time d = 200 km station 1 station 2 t 2 = 285 s earthquake

6 Group Velocity Dispersion Dispersion: dependence of wave speed on frequency Filter seismograms Measure group velocity Plot group velocity vs. frequency

7 Group Velocity Dispersion Dispersion: dependence of wave speed on frequency Filter seismograms Measure group velocity Plot group velocity vs. frequency Use single, well-dispersed surface wave arrival

8 Group Velocity Dispersion Dispersion: dependence of wave speed on frequency Filter seismograms Measure group velocity Plot group velocity vs. frequency more accurate Use single, well-dispersed surface wave arrival less accurate

9 Group Velocity Dispersion Dispersion: dependence of wave speed on frequency Use single, well-dispersed surface wave arrival station d distance earthquake Earthquake: Mexico Station: CCM, Cathedral Cave, Missouri Distance: 22.4 degrees Component: Vertical

10 Group Velocity Dispersion Dispersion: dependence of wave speed on frequency Use single, well-dispersed surface wave arrival station Well-dispersed Rayleigh wave d distance earthquake Earthquake: Mexico Station: CCM, Cathedral Cave, Missouri Distance: 22.4 degrees Component: vertical

11 Group Velocity Dispersion Dispersion: dependence of wave speed on frequency Use single, well-dispersed surface wave arrival T/2 = s time = s Earthquake: Mexico Station: CCM, Cathedral Cave, Missouri Distance: 22.4 degrees Component: vertical

12 Group Velocity Dispersion Dispersion: dependence of wave speed on frequency Use single, well-dispersed surface wave arrival Period = T = 55.7 s Group Velocity (km/s) T/2 = s Period (seconds) time = s Earthquake: Mexico Station: CCM, Cathedral Cave, Missouri Distance: 22.4 degrees Component: vertical

13 Group Velocity Dispersion Dispersion: dependence of wave speed on frequency Use single, well-dispersed surface wave arrival Period = T = 42.8 s Group Velocity (km/s) T/2 = 21.4 s Period (seconds) time = s Earthquake: Mexico Station: CCM, Cathedral Cave, Missouri Distance: 22.4 degrees Component: vertical

14 Group Velocity Dispersion Dispersion: dependence of wave speed on frequency Use single, well-dispersed surface wave arrival Period = T = 38.5 s Group Velocity (km/s) T/2 = s Period (seconds) time = s Earthquake: Mexico Station: CCM, Cathedral Cave, Missouri Distance: 22.4 degrees Component: vertical

15 Group Velocity Dispersion Dispersion: dependence of wave speed on frequency Use single, well-dispersed surface wave arrival Group Velocity (km/s) Period (seconds) Earthquake: Mexico Station: CCM, Cathedral Cave, Missouri Distance: 22.4 degrees Component: vertical

16 Group vs. Phase Velocities Illustration from

17 Phase Velocity Measurement Phase Velocity: speed at which phase travels station Earthquake time d earthquake distance We need to know the initial phase of the wave generated by the earthquake single station method not reliable

18 Phase Velocity Measurement Phase Velocity: speed at which phase travels d station 2 station 1 time earthquake Cycle ambiguity

19 Phase Velocity Measurement Phase Velocity: speed at which phase travels d station 2 station 1 t time earthquake

20 Phase Velocity Dispersion Dispersion: dependence of wave speed on frequency Filter seismograms Measure phase velocity Plot phase velocity vs. frequency

21 Phase Velocity Dispersion Dispersion: dependence of wave speed on frequency Filter seismograms Measure phase velocity Plot phase velocity vs. frequency Shearer (1999)

22 Phase Velocity Dispersion Dispersion: dependence of wave speed on frequency Filter seismograms Measure phase velocity Plot phase velocity vs. frequency Shearer (1999) Rayleigh Wave Sensitivity to Depth Radius Period

23 Phase Velocity Dispersion Dispersion: dependence of wave speed on frequency Filter seismograms Measure phase velocity Plot phase velocity vs. frequency Implication for mantle velocity structure? Shearer (1999) Rayleigh Wave Sensitivity to Depth Radius Period

24 Global Surface Waves November 3, 2002 Denali, Alaska Earthquake ANTO VHZ Filtered between 3 and 8 mhz

25 Global Surface Waves November 3, 2002 Denali, Alaska Earthquake ANTO VHZ Filtered between 3 and 8 mhz

26 Global Surface Waves November 3, 2002 Denali, Alaska Earthquake ANTO VHZ Filtered between 3 and 8 mhz

27 Global Surface Waves November 3, 2002 Denali, Alaska Earthquake ANTO VHZ Filtered between 3 and 8 mhz

28 Global Surface Waves November 3, 2002 Denali, Alaska Earthquake ANTO VHZ Filtered between 3 and 8 mhz

29 Global Surface Waves November 3, 2002 Denali, Alaska Earthquake ANTO VHZ Filtered between 3 and 8 mhz

30 Global Surface Waves November 3, 2002 Denali, Alaska Earthquake ANTO VHZ ANTO VHE Filtered between 3 and 8 mhz

31

32 Standing Waves Standing Wave: Stationary wave generated by constructive/destructive interference of two waves travelling in opposite directions Standing waves or normal modes of the Earth

33 Standing Waves Standing Wave: Stationary wave generated by constructive/destructive interference of two waves travelling in opposite directions 1-D, fixed ends m = 0 m = 1 m = 2 Standing waves constitute basis functions. Sines and Cosines Fourier Transform: combination of sines and cosines describe any 1-D function Index gives the number of nodes.

34 Basis Functions 1-D Sines and Cosines Fourier Transform: combination of sines and cosines describe any 1-D function 2-D (Spherical Surface) What are the standing waves or basis functions we can use to describe any 2-D functions on a sphere?

35 Basis Functions 2-D (Spherical Surface) Longitude: Sines/Cosines Index: angular order m Latitude: Legendre Functions Index: angular degree l and order m m = 0 m = 0 l = 0 m = 1 Rule: -l m l m = 1 l = 1 m = 2 m = 2 l = 2 m = 3 m = Longitude (degrees) l = 3 Latitude (degrees)

36 Basis Functions 2-D (Spherical Surface) Longitude: Sines/Cosines Index: angular order m Latitude: Legendre Functions Index: angular degree l and order m m = 0 m = 0 l = 0 m = 1 Rule: -l m l m = 1 l = 1 m = 2 m = 2 l = 2 m = 3 m = Longitude (degrees) l = 3 Latitude (degrees)

37 Spherical Harmonics m = 0 m = 1 m = 0 l = 1 l = 0 m = 2 l = 2 m = 3 l = 3 m = 4 l = 4

38 Basis Functions 3-D (Sphere) Spherical Surface: Spherical Harmonics Indices: angular degree l and order m Radius: Bessel Functions (homogeneous sphere) Index: number of zero crossings n Radius n = 0 n = 1 n = 2 n = 3

39 Basis Functions 1-D Sines and Cosines Fourier Transform: combination of sines and cosines describe any 1-D function 2-D (Spherical Surface) Longitude: Sines and Cosines Index: angular order m Latitude: Legendre Polynomials Index: angular degree l and order m Spherical Harmonic Transform: combination of spherical harmonics describe any function on a spherical surface Rule: -l m l 3-D (Sphere) Spherical Surface: Spherical Harmonics Indices: angular degree l and order m Radius: Bessel Functions (homogenous sphere) Index: number of zero crossings n Normal Modes: combination of the Earth s normal modes describe any motion

40 Normal Mode Nomenclature Earth: Sphere Spherical Harmonics and radial function to describe standing waves Need three indices: n = radius; l = latitude; m = longitude Type of Motion Toroidal pure shear, denote by T SH waves, Love waves Spheroidal Combination of shear and change in shape denote by S SV waves, Rayleigh waves

41 Characteristic Frequency Each mode has its characteristic frequency and decay constant. Degeneracy If Earth is Spherically symmetric Isotropic Non-rotating Laterally homogeneous then i.e., modes with same overtone number n, and angular degree l same characteristic frequency regardless of angular order m Mode names are often denoted and

42 Attenuation amount of energy dissipated quality factor Q initial energy e -wt/2q amplitude time

43 Seismograms Combination of normal modes can describe ANY motion on spherical Earth Seismogram observed at a station from a given earthquake Constants determined by earthquake source mechanism, and station/hypocentral locations. Fourier Transform

44 Earth s Free Oscillations (Spheroidal Mode)

45 Earth s Free Oscillations (Toroidal Mode)

46 Normal-Mode Central Frequency

47 Normal-Mode Central Frequency

48 Synthetic Seismograms Combination of normal modes can describe ANY motion on spherical Earth Generate synthetic seismograms Seismogram observed at a station from a given earthquake Constants determined by earthquake source mechanism, and station/hypocentral locations.

49 Synthetic Seismograms Combination of normal modes can describe ANY motion on spherical Earth Generate synthetic seismograms November 3, 2002 Denali, Alaska Earthquake ANTO VHZ observed ANTO VHZ synthetic Filtered between 3 and 8 mhz

50 Synthetic Seismograms Combination of normal modes can describe ANY motion on spherical Earth Generate synthetic seismograms November 3, 2002 Denali, Alaska Earthquake observed ANTO VHZ observed synthetic ANTO VHZ synthetic Filtered between 3 and 8 mhz

51 Normal-Mode Splitting 0 S 2

52 Earth s Free Oscillations ( 0 T 2 Receiver Strips) Frequency (mhz)

53 Earth s Free Oscillations (Spheroidal-Toroidal Coupling)

1. Explain how Doppler direction is identified with FMCW radar. Fig Block diagram of FM-CW radar. f b (up) = f r - f d. f b (down) = f r + f d

1. Explain how Doppler direction is identified with FMCW radar. Fig Block diagram of FM-CW radar. f b (up) = f r - f d. f b (down) = f r + f d 1. Explain how Doppler direction is identified with FMCW radar. A block diagram illustrating the principle of the FM-CW radar is shown in Fig. 4.1.1 A portion of the transmitter signal acts as the reference

More information

Module 2 WAVE PROPAGATION (Lectures 7 to 9)

Module 2 WAVE PROPAGATION (Lectures 7 to 9) Module 2 WAVE PROPAGATION (Lectures 7 to 9) Lecture 9 Topics 2.4 WAVES IN A LAYERED BODY 2.4.1 One-dimensional case: material boundary in an infinite rod 2.4.2 Three dimensional case: inclined waves 2.5

More information

We calculate the median of individual (observed) seismic spectra over 3-hour time slots.

We calculate the median of individual (observed) seismic spectra over 3-hour time slots. Methods Seismic data preparation We calculate the median of individual (observed) seismic spectra over 3-hour time slots. Earthquake and instrument glitches are easily identified as short pulses and are

More information

CHAPTER 11 TEST REVIEW -- MARKSCHEME

CHAPTER 11 TEST REVIEW -- MARKSCHEME AP PHYSICS Name: Period: Date: 50 Multiple Choice 45 Single Response 5 Multi-Response Free Response 3 Short Free Response 2 Long Free Response MULTIPLE CHOICE DEVIL PHYSICS BADDEST CLASS ON CAMPUS AP EXAM

More information

A mechanical wave is a disturbance which propagates through a medium with little or no net displacement of the particles of the medium.

A mechanical wave is a disturbance which propagates through a medium with little or no net displacement of the particles of the medium. Waves and Sound Mechanical Wave A mechanical wave is a disturbance which propagates through a medium with little or no net displacement of the particles of the medium. Water Waves Wave Pulse People Wave

More information

QC TX Network. Introduction. R. B. Herrmann, Saint Louis University

QC TX Network. Introduction. R. B. Herrmann, Saint Louis University QC TX Network R. B. Herrmann, Saint Louis University Introduction The purpose of this report is to review the metadata of the TX network. The reason for this study is that regional moment tensor inversion

More information

Magnitude & Intensity

Magnitude & Intensity Magnitude & Intensity Lecture 7 Seismometer, Magnitude & Intensity Vibrations: Simple Harmonic Motion Simplest vibrating system: 2 u( x) 2 + ω u( x) = 0 2 t x Displacement u ω is the angular frequency,

More information

3/23/2015. Chapter 11 Oscillations and Waves. Contents of Chapter 11. Contents of Chapter Simple Harmonic Motion Spring Oscillations

3/23/2015. Chapter 11 Oscillations and Waves. Contents of Chapter 11. Contents of Chapter Simple Harmonic Motion Spring Oscillations Lecture PowerPoints Chapter 11 Physics: Principles with Applications, 7 th edition Giancoli Chapter 11 and Waves This work is protected by United States copyright laws and is provided solely for the use

More information

Appendix 3-B: The AJ-Disk 1-D Large Signal Code (A. Jensen)

Appendix 3-B: The AJ-Disk 1-D Large Signal Code (A. Jensen) Introduction & User s Guide Appendix 3-B: The AJ-Disk 1-D Large Signal Code (A. Jensen) The following is an introduction and user s tutorial for AJ Disk. Each step necessary to open AJ Disk and simulate

More information

EDDIE: Spectral Seismology

EDDIE: Spectral Seismology EDDIE: Spectral Seismology This module was initially developed by Soule, D. S., M. Weirathmuller, G. Kroeger, and R. Darner Gougis. 20 March 2017. EDDIE: Spectral Seismology. EDDIE Module 10, Version 1.

More information

Chapter 3, Part 4: Intro to the Trigonometric Functions

Chapter 3, Part 4: Intro to the Trigonometric Functions Haberman MTH Section I: The Trigonometric Functions Chapter, Part : Intro to the Trigonometric Functions Recall that the sine and cosine function represent the coordinates of points in the circumference

More information

The aim is to understand the power spectrum for non-white noise and non-coherent oscillations.

The aim is to understand the power spectrum for non-white noise and non-coherent oscillations. In the present lecture I will first discuss issues related to non-white noise sources and noncoherent oscillations (oscillations that are not described as a simple harmonic oscillator). The aim is to understand

More information

5.3 Trigonometric Graphs. Copyright Cengage Learning. All rights reserved.

5.3 Trigonometric Graphs. Copyright Cengage Learning. All rights reserved. 5.3 Trigonometric Graphs Copyright Cengage Learning. All rights reserved. Objectives Graphs of Sine and Cosine Graphs of Transformations of Sine and Cosine Using Graphing Devices to Graph Trigonometric

More information

http://www.math.utah.edu/~palais/sine.html http://www.ies.co.jp/math/java/trig/index.html http://www.analyzemath.com/function/periodic.html http://math.usask.ca/maclean/sincosslider/sincosslider.html http://www.analyzemath.com/unitcircle/unitcircle.html

More information

EDDIE: Spectral Seismology Instructors Manual

EDDIE: Spectral Seismology Instructors Manual EDDIE: Spectral Seismology Instructors Manual This module was initially developed by Soule, D. S., M. Weirathmuller, G. Kroeger, and R. Darner Gougis. 20 March 2017. EDDIE: Spectral Seismology. EDDIE Module

More information

OSCILLATIONS and WAVES

OSCILLATIONS and WAVES OSCILLATIONS and WAVES Oscillations Oscillations are vibrations which repeat themselves. EXAMPLE: Oscillations can be driven externally, like a pendulum in a gravitational field EXAMPLE: Oscillations can

More information

HF-Radar Network Near-Real Time Ocean Surface Current Mapping

HF-Radar Network Near-Real Time Ocean Surface Current Mapping HF-Radar Network Near-Real Time Ocean Surface Current Mapping The HF-Radar Network (HFRNet) acquires surface ocean radial velocities measured by HF-Radar through a distributed network and processes the

More information

Waves Q1. MockTime.com. (c) speed of propagation = 5 (d) period π/15 Ans: (c)

Waves Q1. MockTime.com. (c) speed of propagation = 5 (d) period π/15 Ans: (c) Waves Q1. (a) v = 5 cm (b) λ = 18 cm (c) a = 0.04 cm (d) f = 50 Hz Q2. The velocity of sound in any gas depends upon [1988] (a) wavelength of sound only (b) density and elasticity of gas (c) intensity

More information

Signals and Systems Lecture 9 Communication Systems Frequency-Division Multiplexing and Frequency Modulation (FM)

Signals and Systems Lecture 9 Communication Systems Frequency-Division Multiplexing and Frequency Modulation (FM) Signals and Systems Lecture 9 Communication Systems Frequency-Division Multiplexing and Frequency Modulation (FM) April 11, 2008 Today s Topics 1. Frequency-division multiplexing 2. Frequency modulation

More information

UNIT Explain the radiation from two-wire. Ans: Radiation from Two wire

UNIT Explain the radiation from two-wire. Ans:   Radiation from Two wire UNIT 1 1. Explain the radiation from two-wire. Radiation from Two wire Figure1.1.1 shows a voltage source connected two-wire transmission line which is further connected to an antenna. An electric field

More information

Lecture # 7 Coordinate systems and georeferencing

Lecture # 7 Coordinate systems and georeferencing Lecture # 7 Coordinate systems and georeferencing Coordinate Systems Coordinate reference on a plane Coordinate reference on a sphere Coordinate reference on a plane Coordinates are a convenient way of

More information

RADIOMETRIC TRACKING. Space Navigation

RADIOMETRIC TRACKING. Space Navigation RADIOMETRIC TRACKING Space Navigation Space Navigation Elements SC orbit determination Knowledge and prediction of SC position & velocity SC flight path control Firing the attitude control thrusters to

More information

Use of Lamb Waves High Modes in Weld Testing

Use of Lamb Waves High Modes in Weld Testing Use of Lamb Waves High Modes in Weld Testing Eduardo MORENO 1, Roberto OTERO 2, Bernaitz ARREGI 1, Nekane GALARZA 1 Benjamín RUBIO 1 1 Fundación Tecnalia R&I, Basque Country, Spain Phone: +34 671 767 083,

More information

From Last Time Wave Properties. Description of a Wave. Water waves? Water waves occur on the surface. They are a kind of transverse wave.

From Last Time Wave Properties. Description of a Wave. Water waves? Water waves occur on the surface. They are a kind of transverse wave. From Last Time Wave Properties Amplitude is the maximum displacement from the equilibrium position Wavelength,, is the distance between two successive points that behave identically Period: time required

More information

SODAR- sonic detecting and ranging

SODAR- sonic detecting and ranging Active Remote Sensing of the PBL Immersed vs. remote sensors Active vs. passive sensors RADAR- radio detection and ranging WSR-88D TDWR wind profiler SODAR- sonic detecting and ranging minisodar RASS RADAR

More information

In Phase. Out of Phase

In Phase. Out of Phase Superposition Interference Waves ADD: Constructive Interference. Waves SUBTRACT: Destructive Interference. In Phase Out of Phase Superposition Traveling waves move through each other, interfere, and keep

More information

Coda Waveform Correlations

Coda Waveform Correlations Chapter 5 Coda Waveform Correlations 5.1 Cross-Correlation of Seismic Coda 5.1.1 Introduction In the previous section, the generation of the surface wave component of the Green s function by the correlation

More information

Filtering and Data Cutoff in FSI Retrievals

Filtering and Data Cutoff in FSI Retrievals Filtering and Data Cutoff in FSI Retrievals C. Marquardt, Y. Andres, L. Butenko, A. von Engeln, A. Foresi, E. Heredia, R. Notarpietro, Y. Yoon Outline RO basics FSI-type retrievals Spherical asymmetry,

More information

Broadband Signal Enhancement of Seismic Array Data: Application to Long-period Surface Waves and High-frequency Wavefields

Broadband Signal Enhancement of Seismic Array Data: Application to Long-period Surface Waves and High-frequency Wavefields Broadband Signal Enhancement of Seismic Array Data: Application to Long-period Surface Waves and High-frequency Wavefields Frank Vernon and Robert Mellors IGPP, UCSD La Jolla, California David Thomson

More information

SuperDARN (Super Dual Auroral Radar Network)

SuperDARN (Super Dual Auroral Radar Network) SuperDARN (Super Dual Auroral Radar Network) What is it? How does it work? Judy Stephenson Sanae HF radar data manager, UKZN Ionospheric radars Incoherent Scatter radars AMISR Arecibo Observatory Sondrestrom

More information

GEOMETRIC RECTIFICATION OF EUROPEAN HISTORICAL ARCHIVES OF LANDSAT 1-3 MSS IMAGERY

GEOMETRIC RECTIFICATION OF EUROPEAN HISTORICAL ARCHIVES OF LANDSAT 1-3 MSS IMAGERY GEOMETRIC RECTIFICATION OF EUROPEAN HISTORICAL ARCHIVES OF LANDSAT -3 MSS IMAGERY Torbjörn Westin Satellus AB P.O.Box 427, SE-74 Solna, Sweden tw@ssc.se KEYWORDS: Landsat, MSS, rectification, orbital model

More information

StandingWaves_P2 [41 marks]

StandingWaves_P2 [41 marks] StandingWaves_P2 [41 marks] A loudspeaker emits sound towards the open end of a pipe. The other end is closed. A standing wave is formed in the pipe. The diagram represents the displacement of molecules

More information

Retrieving Focal Mechanism of Earthquakes Using the CAP Method

Retrieving Focal Mechanism of Earthquakes Using the CAP Method Retrieving Focal Mechanism of Earthquakes Using the CAP Method Hongfeng Yang April 11, 2013 1 Introduction Waveforms recorded at a seismic station, W (t), compose of three components: W (t) = S(t) G(t)

More information

THE SINUSOIDAL WAVEFORM

THE SINUSOIDAL WAVEFORM Chapter 11 THE SINUSOIDAL WAVEFORM The sinusoidal waveform or sine wave is the fundamental type of alternating current (ac) and alternating voltage. It is also referred to as a sinusoidal wave or, simply,

More information

t =1 Transmitter #2 Figure 1-1 One Way Ranging Schematic

t =1 Transmitter #2 Figure 1-1 One Way Ranging Schematic 1.0 Introduction OpenSource GPS is open source software that runs a GPS receiver based on the Zarlink GP2015 / GP2021 front end and digital processing chipset. It is a fully functional GPS receiver which

More information

PHYS102 Previous Exam Problems. Sound Waves. If the speed of sound in air is not given in the problem, take it as 343 m/s.

PHYS102 Previous Exam Problems. Sound Waves. If the speed of sound in air is not given in the problem, take it as 343 m/s. PHYS102 Previous Exam Problems CHAPTER 17 Sound Waves Sound waves Interference of sound waves Intensity & level Resonance in tubes Doppler effect If the speed of sound in air is not given in the problem,

More information

AP Physics B (Princeton 15 & Giancoli 11 & 12) Waves and Sound

AP Physics B (Princeton 15 & Giancoli 11 & 12) Waves and Sound AP Physics B (Princeton 15 & Giancoli 11 & 12) Waves and Sound Preview What are the two categories of waves with regard to mode of travel? Mechanical Electromagnetic Which type of wave requires a medium?

More information

Ultrasound Physics and Instrumentation, 5e Chapter 7: Level 1 Quiz Answers. 1) Which of the following is stated in the introduction of the chapter?

Ultrasound Physics and Instrumentation, 5e Chapter 7: Level 1 Quiz Answers. 1) Which of the following is stated in the introduction of the chapter? Ultrasound Physics and Instrumentation, 5e Chapter 7: Level 1 Quiz Answers 1) Which of the following is stated in the introduction of the chapter? a) Because of the importance of Doppler, this chapter

More information

Definition of Sound. Sound. Vibration. Period - Frequency. Waveform. Parameters. SPA Lundeen

Definition of Sound. Sound. Vibration. Period - Frequency. Waveform. Parameters. SPA Lundeen Definition of Sound Sound Psychologist's = that which is heard Physicist's = a propagated disturbance in the density of an elastic medium Vibrator serves as the sound source Medium = air 2 Vibration Periodic

More information

Waves ADD: Constructive Interference. Waves SUBTRACT: Destructive Interference. In Phase. Out of Phase

Waves ADD: Constructive Interference. Waves SUBTRACT: Destructive Interference. In Phase. Out of Phase Superposition Interference Interference Waves ADD: Constructive Interference. Waves SUBTRACT: Destructive Interference. In Phase Out of Phase Superposition Traveling waves move through each other, interfere,

More information

13-2 Angles of Rotation

13-2 Angles of Rotation 13-2 Angles of Rotation Objectives Draw angles in standard position. Determine the values of the trigonometric functions for an angle in standard position. Vocabulary standard position initial side terminal

More information

RADIOMETRIC TRACKING. Space Navigation

RADIOMETRIC TRACKING. Space Navigation RADIOMETRIC TRACKING Space Navigation October 24, 2016 D. Kanipe Space Navigation Elements SC orbit determination Knowledge and prediction of SC position & velocity SC flight path control Firing the attitude

More information

Professor Emeritus, University of Tokyo, Tokyo, Japan Phone: ;

Professor Emeritus, University of Tokyo, Tokyo, Japan Phone: ; 17th World Conference on Nondestructive Testing, 25-28 Oct 2008, Shanghai, China New Ultrasonic Guided Wave Testing using Remote Excitation of Trapped Energy Mode Morio ONOE 1, Kenji OKA 2 and Takanobu

More information

Chapter 4 Trigonometric Functions

Chapter 4 Trigonometric Functions Chapter 4 Trigonometric Functions Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Section 8 Radian and Degree Measure Trigonometric Functions: The Unit Circle Right Triangle Trigonometry

More information

Communication Engineering Prof. Surendra Prasad Department of Electrical Engineering Indian Institute of Technology, Delhi

Communication Engineering Prof. Surendra Prasad Department of Electrical Engineering Indian Institute of Technology, Delhi Communication Engineering Prof. Surendra Prasad Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 16 Angle Modulation (Contd.) We will continue our discussion on Angle

More information

Northing (km)

Northing (km) Imaging lateral heterogeneity at Coronation Field with surface waves Matthew M. Haney, Boise State University, and Huub Douma, ION Geophysical/GXT Imaging Solutions SUMMARY A longstanding problem in land

More information

Bakiss Hiyana binti Abu Bakar JKE, POLISAS BHAB

Bakiss Hiyana binti Abu Bakar JKE, POLISAS BHAB 1 Bakiss Hiyana binti Abu Bakar JKE, POLISAS 1. Explain AC circuit concept and their analysis using AC circuit law. 2. Apply the knowledge of AC circuit in solving problem related to AC electrical circuit.

More information

Interference & Superposition. Creating Complex Wave Forms

Interference & Superposition. Creating Complex Wave Forms Interference & Superposition Creating Complex Wave Forms Waves & Interference I. Definitions and Types II. Parameters and Equations III. Sound IV. Graphs of Waves V. Interference - superposition - standing

More information

Precalculus Lesson 9.2 Graphs of Polar Equations Mrs. Snow, Instructor

Precalculus Lesson 9.2 Graphs of Polar Equations Mrs. Snow, Instructor Precalculus Lesson 9.2 Graphs of Polar Equations Mrs. Snow, Instructor As we studied last section points may be described in polar form or rectangular form. Likewise an equation may be written using either

More information

From Last Time Wave Properties. Description of a Wave. Question. Examples. More types of waves. Seismic waves

From Last Time Wave Properties. Description of a Wave. Question. Examples. More types of waves. Seismic waves From Last Time Wave Properties Amplitude is the maximum displacement of string above the equilibrium position Wavelength, λ, is the distance between two successive points that behave identically Period:

More information

SUMMARY. ) f s Shock wave Sonic boom UNIT. Waves transmit energy. Sound is a longitudinal mechanical wave. KEY CONCEPTS CHAPTER SUMMARY

SUMMARY. ) f s Shock wave Sonic boom UNIT. Waves transmit energy. Sound is a longitudinal mechanical wave. KEY CONCEPTS CHAPTER SUMMARY UNIT D SUMMARY KEY CONCEPTS CHAPTER SUMMARY 9 Waves transmit energy. Crest, trough, amplitude, wavelength Longitudinal and transverse waves Cycle Period, frequency f 1_ T Universal wave equation v fλ Wave

More information

Fundamentals of Radio Interferometry

Fundamentals of Radio Interferometry Fundamentals of Radio Interferometry Rick Perley, NRAO/Socorro 15 th Synthesis Imaging School Socorro, NM 01 09 June, 2016 Topics The Need for Interferometry Some Basics: Antennas as E-field Converters

More information

WAVES. Chapter Fifteen MCQ I

WAVES. Chapter Fifteen MCQ I Chapter Fifteen WAVES MCQ I 15.1 Water waves produced by a motor boat sailing in water are (a) neither longitudinal nor transverse. (b) both longitudinal and transverse. (c) only longitudinal. (d) only

More information

EE 442 Homework #3 Solutions (Spring 2016 Due February 13, 2017 ) Print out homework and do work on the printed pages.

EE 442 Homework #3 Solutions (Spring 2016 Due February 13, 2017 ) Print out homework and do work on the printed pages. NAME Solutions EE 44 Homework #3 Solutions (Spring 06 Due February 3, 07 ) Print out homework and do work on the printed pages. Textbook: B. P. Lathi & Zhi Ding, Modern Digital and Analog Communication

More information

Datasheet DS USGS NEIC-data: OT 11:56: N 23.55E h = 10km mb = 5.8

Datasheet DS USGS NEIC-data: OT 11:56: N 23.55E h = 10km mb = 5.8 Topic compiled by Version Additional seismogram examples within the distance range 13-100 Klaus Klinge (formerly Federal Institute for Geosciences and Natural Resources, 30655 Hannover, Germany); E-mail:

More information

Short Notes Characterization of a Continuous, Very Narrowband Seismic Signal near 2.08 Hz

Short Notes Characterization of a Continuous, Very Narrowband Seismic Signal near 2.08 Hz Bulletin of the Seismological Society of America, 91, 6, pp. 1910 1916, December 2001 Short Notes Characterization of a Continuous, Very Narrowband Seismic Signal near 2.08 Hz by Kelly H. Liu and Stephen

More information

CHAPTER 8 ANTENNAS 1

CHAPTER 8 ANTENNAS 1 CHAPTER 8 ANTENNAS 1 2 Antennas A good antenna works A bad antenna is a waste of time & money Antenna systems can be very inexpensive and simple They can also be very expensive 3 Antenna Considerations

More information

(3) A traveling wave transfers, but it does not transfer.

(3) A traveling wave transfers, but it does not transfer. AP PHYSICS TEST 9 Waves and Sound (1) Give a good physics definition of a wave. (2) Any wave has as its source. (3) A traveling wave transfers, but it does not transfer. (4) What is a mechanical wave?

More information

Here I briefly describe the daily seismicity analysis procedure: Table 1

Here I briefly describe the daily seismicity analysis procedure: Table 1 A: More on Daily Seismicity Analysis Here I briefly describe the daily seismicity analysis procedure: Table 1 The broadband continuous data set was acquired as hour-long files. For this purpose I wrote

More information

Audio Engineering Society. Convention Paper. Presented at the 113th Convention 2002 October 5 8 Los Angeles, California, USA

Audio Engineering Society. Convention Paper. Presented at the 113th Convention 2002 October 5 8 Los Angeles, California, USA Audio Engineering Society Convention Paper Presented at the 113th Convention 2002 October 5 8 Los Angeles, California, USA This convention paper has been reproduced from the author's advance manuscript,

More information

Green s Function Extraction from Ambient Seismic Field: Analysis of Seasonal Variations

Green s Function Extraction from Ambient Seismic Field: Analysis of Seasonal Variations Green s Function Extraction from Ambient Seismic Field: Analysis of Seasonal Variations Sutton Chiorini 1 Supervisor: Kazuki Koketsu 2 Supporter: Loïc Viens 2 1 University of Maryland, College Park, U.S.A,

More information

Experimental and Numerical Study of Topographic Site Effect on a Hill Near Tehran

Experimental and Numerical Study of Topographic Site Effect on a Hill Near Tehran Missouri University of Science and Technology Scholars' Mine International Conferences on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics 2010 - Fifth International Conference

More information

Sound is the human ear s perceived effect of pressure changes in the ambient air. Sound can be modeled as a function of time.

Sound is the human ear s perceived effect of pressure changes in the ambient air. Sound can be modeled as a function of time. 2. Physical sound 2.1 What is sound? Sound is the human ear s perceived effect of pressure changes in the ambient air. Sound can be modeled as a function of time. Figure 2.1: A 0.56-second audio clip of

More information

Waves and Sound Practice Test 43 points total Free- response part: [27 points]

Waves and Sound Practice Test 43 points total Free- response part: [27 points] Name Waves and Sound Practice Test 43 points total Free- response part: [27 points] 1. To demonstrate standing waves, one end of a string is attached to a tuning fork with frequency 120 Hz. The other end

More information

ACOUSTIC PROPAGATION IN 1D AND 3D PERIODIC MEDIA UNDER CONSTRAINTS

ACOUSTIC PROPAGATION IN 1D AND 3D PERIODIC MEDIA UNDER CONSTRAINTS ACOUSTIC PROPAGATION IN 1D AND 3D PERIODIC MEDIA UNDER CONSTRAINTS PACS REFERENCE : 43.2.Fn, 43.35.Gk, 43.35.Pt Julien Anfosso 1 ; Vincent Gibiat 2. 1 Laboratoire Ondes et Acoustique E.S.P.C.I., UMR 7587,

More information

Final Reg Wave and Sound Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Final Reg Wave and Sound Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Final Reg Wave and Sound Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) What is the frequency of a 2.5 m wave traveling at 1400 m/s? 1) 2)

More information

Spectrum Analysis: The FFT Display

Spectrum Analysis: The FFT Display Spectrum Analysis: The FFT Display Equipment: Capstone, voltage sensor 1 Introduction It is often useful to represent a function by a series expansion, such as a Taylor series. There are other series representations

More information

Set No.1. Code No: R

Set No.1. Code No: R Set No.1 IV B.Tech. I Semester Regular Examinations, November -2008 RADAR SYSTEMS ( Common to Electronics & Communication Engineering and Electronics & Telematics) Time: 3 hours Max Marks: 80 Answer any

More information

A Rayleigh wave back-projection method applied to the 2011 Tohoku earthquake

A Rayleigh wave back-projection method applied to the 2011 Tohoku earthquake A Rayleigh wave back-projection method applied to the 2011 Tohoku earthquake Daniel Roten, Hiroe Miyake, and Kazuki Koketsu (2012), GRL Earthquake of the Week - 27 January 2012 Roten, D., H. Miyake, and

More information

To Estimate The Regional Ionospheric TEC From GEONET Observation

To Estimate The Regional Ionospheric TEC From GEONET Observation To Estimate The Regional Ionospheric TEC From GEONET Observation Jinsong Ping(Email: jsping@miz.nao.ac.jp) 1,2, Nobuyuki Kawano 2,3, Mamoru Sekido 4 1. Dept. Astronomy, Beijing Normal University, Haidian,

More information

Estimation of the Earth s Impulse Response: Deconvolution and Beyond. Gary Pavlis Indiana University Rick Aster New Mexico Tech

Estimation of the Earth s Impulse Response: Deconvolution and Beyond. Gary Pavlis Indiana University Rick Aster New Mexico Tech Estimation of the Earth s Impulse Response: Deconvolution and Beyond Gary Pavlis Indiana University Rick Aster New Mexico Tech Presentation for Imaging Science Workshop Washington University, November

More information

Standing waves. Consider a string with 2 waves of equal amplitude moving in opposite directions. or, if you prefer cos T

Standing waves. Consider a string with 2 waves of equal amplitude moving in opposite directions. or, if you prefer cos T Waves 2 1. Standing waves 2. Transverse waves in nature: electromagnetic radiation 3. Polarisation 4. Dispersion 5. Information transfer and wave packets 6. Group velocity 1 Standing waves Consider a string

More information

Algebra and Trig. I. The graph of

Algebra and Trig. I. The graph of Algebra and Trig. I 4.5 Graphs of Sine and Cosine Functions The graph of The graph of. The trigonometric functions can be graphed in a rectangular coordinate system by plotting points whose coordinates

More information

Multicomponent seismic polarization analysis

Multicomponent seismic polarization analysis Saul E. Guevara and Robert R. Stewart ABSTRACT In the 3-C seismic method, the plant orientation and polarity of geophones should be previously known to provide correct amplitude information. In principle

More information

Name: Lab Partner: Section:

Name: Lab Partner: Section: Chapter 11 Wave Phenomena Name: Lab Partner: Section: 11.1 Purpose Wave phenomena using sound waves will be explored in this experiment. Standing waves and beats will be examined. The speed of sound will

More information

MULTI-COMPONENT ACTIVE SOURCE RAYLEIGH WAVE ANALYSIS. Gabriel Gribler. A thesis. submitted in partial fulfillment

MULTI-COMPONENT ACTIVE SOURCE RAYLEIGH WAVE ANALYSIS. Gabriel Gribler. A thesis. submitted in partial fulfillment MULTI-COMPONENT ACTIVE SOURCE RAYLEIGH WAVE ANALYSIS by Gabriel Gribler A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Geophysics Boise State University

More information

Chapter 18. Superposition and Standing Waves

Chapter 18. Superposition and Standing Waves Chapter 18 Superposition and Standing Waves Particles & Waves Spread Out in Space: NONLOCAL Superposition: Waves add in space and show interference. Do not have mass or Momentum Waves transmit energy.

More information

RECOMMENDATION ITU-R S.1257

RECOMMENDATION ITU-R S.1257 Rec. ITU-R S.157 1 RECOMMENDATION ITU-R S.157 ANALYTICAL METHOD TO CALCULATE VISIBILITY STATISTICS FOR NON-GEOSTATIONARY SATELLITE ORBIT SATELLITES AS SEEN FROM A POINT ON THE EARTH S SURFACE (Questions

More information

# DEFINITIONS TERMS. 2) Electrical energy that has escaped into free space. Electromagnetic wave

# DEFINITIONS TERMS. 2) Electrical energy that has escaped into free space. Electromagnetic wave CHAPTER 14 ELECTROMAGNETIC WAVE PROPAGATION # DEFINITIONS TERMS 1) Propagation of electromagnetic waves often called radio-frequency (RF) propagation or simply radio propagation. Free-space 2) Electrical

More information

Periodic Error Correction in Heterodyne Interferometry

Periodic Error Correction in Heterodyne Interferometry Periodic Error Correction in Heterodyne Interferometry Tony L. Schmitz, Vasishta Ganguly, Janet Yun, and Russell Loughridge Abstract This paper describes periodic error in differentialpath interferometry

More information

Chapter 6: Periodic Functions

Chapter 6: Periodic Functions Chapter 6: Periodic Functions In the previous chapter, the trigonometric functions were introduced as ratios of sides of a right triangle, and related to points on a circle. We noticed how the x and y

More information

Chapter 17 Waves in Two and Three Dimensions

Chapter 17 Waves in Two and Three Dimensions Chapter 17 Waves in Two and Three Dimensions Slide 17-1 Chapter 17: Waves in Two and Three Dimensions Concepts Slide 17-2 Section 17.1: Wavefronts The figure shows cutaway views of a periodic surface wave

More information

ADAPTIVE CORRECTION FOR ACOUSTIC IMAGING IN DIFFICULT MATERIALS

ADAPTIVE CORRECTION FOR ACOUSTIC IMAGING IN DIFFICULT MATERIALS ADAPTIVE CORRECTION FOR ACOUSTIC IMAGING IN DIFFICULT MATERIALS I. J. Collison, S. D. Sharples, M. Clark and M. G. Somekh Applied Optics, Electrical and Electronic Engineering, University of Nottingham,

More information

III Satellite Ephemeris and Coordinates

III Satellite Ephemeris and Coordinates III Satellite Ephemeris and Coordinates Exercise III.1 Orbital Parameters Consider a satellite with the following orbital parameters orbit semi-major axis: A = 26559755m; orbit eccentricity: e = 0.017545;

More information

P34 Determination of 1-D Shear-Wave Velocity Profileusing the Refraction Microtremor Method

P34 Determination of 1-D Shear-Wave Velocity Profileusing the Refraction Microtremor Method P34 Determination of 1-D Shear-Wave Velocity Profileusing the Refraction Microtremor Method E. Baniasadi* (University of Tehran), M. A. Riahi (University of Tehran) & S. Chaychizadeh (University of Tehran)

More information

Goals. Introduction. To understand the use of root mean square (rms) voltages and currents.

Goals. Introduction. To understand the use of root mean square (rms) voltages and currents. Lab 10. AC Circuits Goals To show that AC voltages cannot generally be added without accounting for their phase relationships. That is, one must account for how they vary in time with respect to one another.

More information

Multi-Path Fading Channel

Multi-Path Fading Channel Instructor: Prof. Dr. Noor M. Khan Department of Electronic Engineering, Muhammad Ali Jinnah University, Islamabad Campus, Islamabad, PAKISTAN Ph: +9 (51) 111-878787, Ext. 19 (Office), 186 (Lab) Fax: +9

More information

Modulation. Digital Data Transmission. COMP476 Networked Computer Systems. Sine Waves vs. Square Waves. Fourier Series. Modulation

Modulation. Digital Data Transmission. COMP476 Networked Computer Systems. Sine Waves vs. Square Waves. Fourier Series. Modulation Digital Data Transmission Modulation Digital data is usually considered a series of binary digits. RS-232-C transmits data as square waves. COMP476 Networked Computer Systems Sine Waves vs. Square Waves

More information

EWGAE 2010 Vienna, 8th to 10th September

EWGAE 2010 Vienna, 8th to 10th September EWGAE 2010 Vienna, 8th to 10th September Frequencies and Amplitudes of AE Signals in a Plate as a Function of Source Rise Time M. A. HAMSTAD University of Denver, Department of Mechanical and Materials

More information

ANECHOIC CHAMBER DIAGNOSTIC IMAGING

ANECHOIC CHAMBER DIAGNOSTIC IMAGING ANECHOIC CHAMBER DIAGNOSTIC IMAGING Greg Hindman Dan Slater Nearfield Systems Incorporated 1330 E. 223rd St. #524 Carson, CA 90745 USA (310) 518-4277 Abstract Traditional techniques for evaluating the

More information

Part 1: Standing Waves - Measuring Wavelengths

Part 1: Standing Waves - Measuring Wavelengths Experiment 7 The Microwave experiment Aim: This experiment uses microwaves in order to demonstrate the formation of standing waves, verifying the wavelength λ of the microwaves as well as diffraction from

More information

Study of Standing Waves to Find Speed of Sound in Air

Study of Standing Waves to Find Speed of Sound in Air Study of Standing Waves to Find Speed of Sound in Air Purpose Using mobile devices as sound analyzer and sound generator to study standing waves and determine the speed of sound in air. Theory The velocity

More information

Dependence of radio wave anomalous attenuation in the ionosphere on properties of spatial spectrum of irregularities

Dependence of radio wave anomalous attenuation in the ionosphere on properties of spatial spectrum of irregularities Dependence of radio wave anomalous attenuation in the ionosphere on properties of spatial spectrum of irregularities N.A. Zabotin, G.A. Zhbankov and E.S. Kovalenko ostov State University, ostov-on-don,

More information

Quantitative Crack Depth Study in Homogeneous Plates Using Simulated Lamb Waves.

Quantitative Crack Depth Study in Homogeneous Plates Using Simulated Lamb Waves. More Info at Open Access Database www.ndt.net/?id=18675 Quantitative Crack Depth Study in Homogeneous Plates Using Simulated Lamb Waves. Mohammad. (. SOORGEE, Aghil. YOUSEF)-KOMA Nondestructive Testing

More information

1. Measure angle in degrees and radians 2. Find coterminal angles 3. Determine the arc length of a circle

1. Measure angle in degrees and radians 2. Find coterminal angles 3. Determine the arc length of a circle Pre- Calculus Mathematics 12 5.1 Trigonometric Functions Goal: 1. Measure angle in degrees and radians 2. Find coterminal angles 3. Determine the arc length of a circle Measuring Angles: Angles in Standard

More information

Some observations of data quality at global seismic stations

Some observations of data quality at global seismic stations Some observations of data quality at global seismic stations Meredith Nettles and Göran Ekström Global CMT Project Waveform Quality Center SITS, 2009/11/10 1. Data quality control using signals 1a. Sensor

More information

GENERAL GUIDELINES FOR APPLICATION OF THE EXTENDED SUBTRACTION METHOD IN SASSI SOIL-STRUCTURE INTERACTION ANALYSIS

GENERAL GUIDELINES FOR APPLICATION OF THE EXTENDED SUBTRACTION METHOD IN SASSI SOIL-STRUCTURE INTERACTION ANALYSIS Transactions, SMiRT-22 GENERAL GUIDELINES FOR APPLICATION OF THE EXTENDED SUBTRACTION METHOD IN SASSI SOIL-STRUCTURE INTERACTION ANALYSIS C. C. Chin 1, Nan Deng 2, and Farhang Ostadan 3 1 Senior Engineer,

More information

Chapter 2. The Fundamentals of Electronics: A Review

Chapter 2. The Fundamentals of Electronics: A Review Chapter 2 The Fundamentals of Electronics: A Review Topics Covered 2-1: Gain, Attenuation, and Decibels 2-2: Tuned Circuits 2-3: Filters 2-4: Fourier Theory 2-1: Gain, Attenuation, and Decibels Most circuits

More information

Leaky Guided Ultrasonic Waves in NDT

Leaky Guided Ultrasonic Waves in NDT University of London Imperial College of Science, Technology, and Medicine Mechanical Engineering Department Exhibition Road London SW7 2BX Leaky Guided Ultrasonic Waves in NDT by Brian Nicholas Pavlakovic

More information

AVO processing of walkaway VSP data at Ross Lake heavy oilfield, Saskatchewan

AVO processing of walkaway VSP data at Ross Lake heavy oilfield, Saskatchewan AVO processing of walkaway VSP data at Ross Lake heavy oilfield, Saskatchewan Zimin Zhang, Robert R. Stewart, and Don C. Lawton ABSTRACT The AVO processing and analysis of walkaway VSP data at Ross Lake

More information