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See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/311308562 Lecture slides on "Very basic GPR" Presentation December 2016 DOI: 10.13140/RG.2.2.10693.45288 CITATIONS READS

  1. Basic equations and parameters • In the next slide the difference between the attenuation in three different materials is shown. • It is worthy to note that at GPR frequencies (50 MHz-1000 MHz) a significant difference between resistive and conductive materials occurs. Ampitude • every -6dB the A out =0.5Ain  dB 20log out 10 Amplitude in L. Sambuelli - Politecnico di Torino - DIATI - 31 2016

  2. Basic equations and parameters L. Sambuelli - Politecnico di Torino - DIATI - 32 2016

  3. Basic equations and parameters The EM energy, as long as propagates in a medium, disregarding the EM properties of r 1 r 2 the medium and the frequency, attenuates because it is spread over increasing semispherical surfaces. Then there is another attenuation: the geometrical one r (spherical divergence).    r E E 0 e This one too contributes to 0 r decrease the signal strength. L. Sambuelli - Politecnico di Torino - DIATI - 33 2016

  4. Basic equations and parameters • In the following two slides the effect of α and spherical divergence on a propagating pulse is shown; • The first one (35) shows what happens to the pulse as long as it travels away from the source at three depths in a medium with 100 0 Ω m ; • The second one (36) shows the Fourier spectra of the pulses. L. Sambuelli - Politecnico di Torino - DIATI - 34 2016

  5. Basic equations and parameters L. Sambuelli - Politecnico di Torino - DIATI - 35 2016

  6. Basic equations and parameters L. Sambuelli - Politecnico di Torino - DIATI - 36 2016

  7. Basic equations and parameters • In the following two slides the effect of α and spherical divergence on a propagating pulse is shown; • The first one (38) shows what happens to the pulse as long as it travels away from the source at three depths in a medium with 20 20 Ω m ; • The second one (39) shows the Fourier spectra of the pulses; • No Note th the di differences nces betw between th the tw two m o medi dia L. Sambuelli - Politecnico di Torino - DIATI - 37 2016

  8. Basic equations and parameters L. Sambuelli - Politecnico di Torino - DIATI - 38 2016

  9. Basic equations and parameters L. Sambuelli - Politecnico di Torino - DIATI - 39 2016

  10. Basic equations and parameters • In the next slide the difference between the wavelengths in three different materials is shown. • It is worthy to note that at GPR frequencies (50 MHz-1000 MHz) differences in material conductivities do not affect the main pulse wavelength (differences in relative permittivities 𝑑 𝜁 𝑠 ; λ = 𝑤 𝑑 affect more!! 𝑤 = 𝑔 → 𝜇 = 𝜁 𝑠 𝑔 ) L. Sambuelli - Politecnico di Torino - DIATI - 40 2016

  11. Basic equations and parameters L. Sambuelli - Politecnico di Torino - DIATI - 41 2016

  12. Basic equations and parameters L. Sambuelli - Politecnico di Torino - DIATI - 42 2016

  13. Basic reflection and patterns L. Sambuelli - Politecnico di Torino - DIATI - 43 2016

  14. Basic reflection and patterns • GPR pulse, as the other wave phenomena, are REFLECTED, REFRACTED, DIFFRACTED crossing media with different EM properties (  ,  ,  ). • GPR survey are mainly based on REFLECTION. • GPR pulse REFLECTION and REFRACTION occurs when the pulse impinges a surface separating two materials with different EM properties. L. Sambuelli - Politecnico di Torino - DIATI - 44 2016

  15. Basic reflection and patterns Reflec lection tion a) a) an and refraction action b) b) la laws ws: : an angles les        sin sin v    i i 2 a) 1 b) 1        sin sin v r t 2 1 H i H r i r   i r 1 H t 2  t t E orthogonal to page L. Sambuelli - Politecnico di Torino - DIATI - 45 2016

  16. Basic reflection and patterns Reflecti lection on a) a ) and refraction action b) la ) laws: s: amplitud litudes es  Z Z  a) REFLECTION COEFFICIENT: R= 2 1 E RE r i  Z Z 2 1 2 Z  b) TRANSMISSION COEFFICIENT: T= 2 E TE t i  Z Z 2 1 H i H r      20 T R 1 i r i 𝜘 𝑗 𝜘 𝑠   E E E t r i 1 H t 2 𝜘 𝑢 t E orthogonal to page L. Sambuelli - Politecnico di Torino - DIATI - 46 2016

  17. Basic reflection and patterns  i Z is a complex quantity:  Z    i     But for low-con conductiv ductivit ity materials 0 then Z    1 1       But being also r 0 c and 1 Z r      c 0 0 r 0 r     2  r 1 r 2 r 1 R and T=       r 1 r 2 r 1 r 2 L. Sambuelli - Politecnico di Torino - DIATI - 47 2016

  18. Basic reflection and patterns REFLECTOR PARALLEL TO THE GROUND SURFACE: In the radargram the reflected pulses are on a horizontal line which can be seen at a time 2 h  twt v 1 Onc nce e an an es estim imat ate e of the e vel eloci city ty of the e fir irst layer er is is avail ilable le the depth of the reflector can be calculated. The horizontal reflectors look horizontal on radargram. L. Sambuelli - Politecnico di Torino - DIATI - 48 2016

  19. Basic reflection and patterns TxRx TxRx TxRx TxRx TxRx h v1 v2 twt  2h/v1 L. Sambuelli - Politecnico di Torino - DIATI - 49 2016

  20. Basic reflection and patterns REFLECTOR INCLINED WITH RESPECT TO THE GROUND SURFACE: In the radargram the reflected pulses are on an inclined line which can be seen at times 2 h  twt x ( ) x    cos v 1 Once e an es estim imate e of the e vel eloci city ty of the e fir irst layer er is is avai ailab able le the depth of the reflector can annot not be calculated. The inclination of the reflector on radargram is “ wrong ”: it depends on reflector inclination, velocity AND depth L. Sambuelli - Politecnico di Torino - DIATI - 50 2016

  21. Basic reflection and patterns TxRx TxRx TxRx TxRx TxRx d h v1  v2 twt  2d/v1 L. Sambuelli - Politecnico di Torino - DIATI - 51 2016

  22. Basic reflection and patterns DIFFRACTION DUE TO A POINT-LIKE OBJECT In the radargram the diffracted pulses are on a hyperbola which can be seen at times   2   2 2 x x h  0 twt v 1 and it has: the slopes of its asymptotes equal to  2/v1 v1; the twt of its vertex equal to 2h/v1 v1 L. Sambuelli - Politecnico di Torino - DIATI - 52 2016

  23. Basic reflection and patterns TxRx TxRx TxRx TxRx TxRx h x v1 x 0 twt=2h/v1 Asymptote: slope=2/v1 L. Sambuelli - Politecnico di Torino - DIATI - 53 2016

  24. Basic reflection and patterns DIFFRA FFRACT CTION ION DUE TO A POINT-LIKE OBJECT  As point-like object it must be intended a body ody whose ose size ze s (as “seen” from the EM pulse) is roug ughly ly equal ual to o the he se  . domi ominant nant wavelengt length h of the e pulse  It is worthy to note that one can also have diffraction hyperbolas with “corners” (see slide 5) and with the ends of thin plane-like objects (such as fractures).  As the slope of the asympotes are quite easy to evaluate on radargrams, diffr fractio action n even ents ts are often welcome because they allo lowed ed an estimation timation of the e pulse se velocity locity in the medium surrounding the diffracting object. L. Sambuelli - Politecnico di Torino - DIATI - 54 2016

  25. Basic reflection and patterns REFLECTOR PARALLEL TO GROUND SURFACE WITH CMP MP ACQUISI QUISITION TION In the radargram the reflected pulses are on a hyperbola which can be seen at times   2   2 x x 4 h  0 twt v 1 and it has: the slopes of its asymptotes equal to  1/v1 v1; the twt of its vertex equal to 2h/v1 v1 L. Sambuelli - Politecnico di Torino - DIATI - 55 2016

  26. Basic reflection and patterns Rx Tx_fix Rx Rx Rx x 0 x h v1 v2 twt=2h/v1 Asymptote: slope=1/v1 L. Sambuelli - Politecnico di Torino - DIATI - 56 2016

  27. Basic reflection and patterns REFLECTOR PARALLEL TO GROUND SURFACE WITH CMP MP ACQUISI QUISITION TION  Sometimes, when no diffraction events occur, it can be very useful to make two or three CMP profiles in the investigation area.  As the slope of the asympotes are quite easy to evaluate on radargrams, ref eflecti ection on even ents allow an es estim imati tion on of the e pu pulse e vel eloci city ty in the medium surrounding the targets. L. Sambuelli - Politecnico di Torino - DIATI - 57 2016

  28. Outlines of the instrument L. Sambuelli - Politecnico di Torino - DIATI - 58 2016

  29. Outlines of the instrument Block diagram of a GPR Sometimes C.U and P.C are in a single box Power High voltage pulse Data store generator P.C. C.U. Video Ampl. A/D Rx Tx Antenna/s L. Sambuelli - Politecnico di Torino - DIATI - 59 2016

  30. Outlines of the instrument The transmitting antenna emits large part of EM energy in a “cone of radiation” and the receiving antenna gathers waves travelling back in a similar cone. That’s why GPR can “see” objects out of the vertical from the antenna box. Diffractions and CMP acquisition are possible thanks to this phenomenon. MONOS OSTATIC TIC configuration: 1 dipole which transmits and receives BISTATI TIC configuration: 2 dipoles: one transmits and the other receives E orthogonal to page L. Sambuelli - Politecnico di Torino - DIATI - 60 2016

  31. Outlines of the instrument As the transmitting antenna emits large part of EM energy in a “cone of radiation” the sizes of the reflecting surface (footprint) along the dipole (B) and across the dipole (A) varies with depth D mainly in function of the EM characteristic of the soil and of the frequency.  D c     A 4    1 f r r A  B 2 L. Sambuelli - Politecnico di Torino - DIATI - 61 2016

  32. Outlines of the instrument As the transmitting antenna emits large part of EM energy in a “cone of radiation” the ion  x varies with hori rizonta zontal Spatial l Resolut solution r 1 depth D mainly in function of the EM r 2 characteristic of the soil and of the frequency.  z olution  z is usually The verti tica cal l Spatial al Resolution  x not supposed to vary with depth Spatial Resolution is the capability of recognizing the reflections from two close surfaces as distinct i.e. the capability of estimate the distance between them. R THAN  x YOU U CANNOT T EXPECT CT TO DISTI TINGU GUISH SH TWO O OBJEC ECTS TS HORIZON ZONTALL ALLY CLOSE SER ER THAN  z YOU U CANNOT T EXPECT CT TO ESTIMATE TE THE THICK CKNES ESS OF AN OBJECT ECT THINNER   D     z x 4 2 L. Sambuelli - Politecnico di Torino - DIATI - 62 2016

  33. Outlines of the instrument L. Sambuelli - Politecnico di Torino - DIATI - 63 2016

  34. Outlines of the instrument • The GPR antennas are characterized by: a central frequency f c = frequency to which corresponds the maximum of emitted energy E max ax ; f min in and f max ax = = frequencies corresponding to an amplitue E max /2 /2 generally symmerical about f c ; BW=bandwidth. Usua uall lly y : • BW=f max max -f min min ; ; f max =f c +B +BW/2 /2 ; f min =f c -BW/2 W/2 L. Sambuelli - Politecnico di Torino - DIATI - 64 2016

  35. Outlines of the instrument • Mean spectrum from 970 traces of a profile collected on an archaeological site with a 400 MHz GSSI antenna and a K2 IDS C.U.. Frequency window from 0 to 1000 MHz. BW f c f min f max L. Sambuelli - Politecnico di Torino - DIATI - 65 2016

  36. Outlines of the instrument • The different attenuation phenomena that attenuate the GPR signal travelling r [m] down and back are taken into account for in a so called Range nge Equation quation. • For a smooth flat surface:      2 2 4 r R e   F 10log   10  2 16 r   • For a rough flat surface:      2 3 4 r R e   F 10log   10  3 32 r   • F are the dB that the equipment must have, R is the reflection coefficient L. Sambuelli - Politecnico di Torino - DIATI - 66 2016

  37. Outlines of the instrument • In the following slides the performances required to a GPR equipment for detecting object in these soils are shown   r  r 10 50 1 10 100 1 10 500 1 The estimates with these formulae are usually quite optimistic e.g. sometimes we don’t “see” as deep as we planned. L. Sambuelli - Politecnico di Torino - DIATI - 67 2016

  38. Outlines of the instrument L. Sambuelli - Politecnico di Torino - DIATI - 68 2016

  39. Outlines of the instrument L. Sambuelli - Politecnico di Torino - DIATI - 69 2016

  40. Outlines of the instrument L. Sambuelli - Politecnico di Torino - DIATI - 70 2016

  41. Outlines of the instrument The estimates with these formulae are usually quite optimistic e.g. sometimes we don’t “see” as deep as we planned. Indeed the traveling GPR pulse decays for: dissipation (α), attenuation (1/r) and scattering that is incoherent and chaotic reflections due to objects with size s<<  . . Moreover layers can be a non-homogeneous patchwork of dissipative and non-dissipative materials. L. Sambuelli - Politecnico di Torino - DIATI - 71 2016

  42. Outlines of the instrument IDS – K2 2channel GSSI- CODEVINTEC – Utility scan DF L. Sambuelli - Politecnico di Torino - DIATI - 72 2016

  43. Field operations – data acquisition L. Sambuelli - Politecnico di Torino - DIATI - 73 2016

  44. Field operations – data acquisition • Field operations need a design. • Design consists of three steps. • St Step ep 0 : antenna (frequency f c ) selection [Depth of the target, Vertical Spatial resolution, Horizontal Spatial Resolution] • St Step ep 1 : acquisition geometry that means to define:  x= x=int nter erval al betw etween two consecuti secutive radar dar traces; s;  y= y=int interval al betw etween n two adjace jacent nt GPR R prof ofil iles. s. • St Step ep 2 :acquistion parameters that means to define:  t=trace race sa sampling pling interval al; ; ion (T/  t +1=N=numbe • T=trace ace durat ation =number r of f sa samples ples per trace) e) L. Sambuelli - Politecnico di Torino - DIATI - 74 2016

  45. Field operations – data acquisition • St Step p 0 : antenna (frequency f c ) selection • This step will influence also Step 1 and Step 2. Antenna frequency selection has to be done searching for a tradeoff between frequency from Ran ange ge Eq Equation ation (R (R.E. E.) ) and Spat atial ial Resolut solution ion (S (S.R). .R). We could be interested in a high detail (good S.R.) at a significant depth (high values of F in R.E.) L. Sambuelli - Politecnico di Torino - DIATI - 75 2016

  46. Field operations – data acquisition p 1 : acquisition geometry  x. • St Step •  x: x: according to the Shannon sampling theorem should be  c    x c in m/ns, f in GHz  2 2 f max r • Example: f=500 MHz,  r =8 (c=0.3)  x  0.07 m • Usually GPR trace intervals are around few centimeters L. Sambuelli - Politecnico di Torino - DIATI - 76 2016

  47. Field operations – data acquisition p 1 : acquisition geometry  y. • St Step •  y: according to the Shannon sampling theorem should also be  c    y c in m/ns, f in GHz  2 2 f max r • However a good compromise between spatial sampling and acquistion time ( € or $) is  y =0.5m. Only when acquiring data with 900 MHz or higher frequencies  y= y=0.1  0.2 m L. Sambuelli - Politecnico di Torino - DIATI - 77 2016

  48. Field operations – data acquisition p 2 : acquisition parameters  t. • St Step •  t: t: according to the Shannon sampling theorem 1 1     t but it's better t 2 f 6 f max max • Using the second rule more information can be extracted from the radar traces L. Sambuelli - Politecnico di Torino - DIATI - 78 2016

  49. Field operations – data acquisition • St Step p 2 : acquisition parameter T. • T: has to do with the maximum depth D from which one wants to get a reflection 4 D  T v max • Here v max ax is the maximum expected velocity • Some GPR’s instead of asking  t t ask for T and the number of sample per trace N. But          T N 1 t N T t 1 L. Sambuelli - Politecnico di Torino - DIATI - 79 2016

  50. Field operations – data acquisition • St Step p 2 : acquisition parameter T. • Of course the selection of T does not guarantee the reflection from a target at depth D D because of attenuations, remember the range equation (slides 66 to 71) L. Sambuelli - Politecnico di Torino - DIATI - 80 2016

  51. Field operations – data acquisition 1. Survey area delimitation and line tracking with non metal rulers; 2. Area surveying with forward and backward parallel paths without turning the antenna; 3. Eventually cross paths to have denser data set and information on orthogonal structures; 4. Even if the antenna is tracked with a RTK GPS always pick the coordinates of the area corners to be able to produce a readable final graphic document L. Sambuelli - Politecnico di Torino - DIATI - 81 2016

  52. Field operations – data acquisition L. Sambuelli - Politecnico di Torino - DIATI - 82 2016

  53. Field operations – data acquisition L. Sambuelli - Politecnico di Torino - DIATI - 83 2016

  54. Field operations – data acquisition L. Sambuelli - Politecnico di Torino - DIATI - 84 2016

  55. Field operations – data acquisition L. Sambuelli - Politecnico di Torino - DIATI - 85 2016

  56. Field operations – data acquisition L. Sambuelli - Politecnico di Torino - DIATI - 86 2016

  57. Field operations – data acquisition L. Sambuelli - Politecnico di Torino - DIATI - 87 2016

  58. Data processing L. Sambuelli - Politecnico di Torino - DIATI - 88 2016

  59. Data processing • Data processing is of paramount importance in GPR; • In archaeological prospecting usually it is done in two main steps: 1) survey lines (radargrams) processing; 2) data- cube (spatially assembled radargrams) processing. L. Sambuelli - Politecnico di Torino - DIATI - 89 2016

  60. Data processing • Survey lines (radargrams) processing may consists of many steps with the aim of cleaning as much as possible the radargrams i.e. reducing noises (random reflections, parallel lines due to ringing, frequencies out of band, d.c. shift... ) and enhancing “useful signals” . • Often raw data are awful and seem meaningless… but do not despair ! • Even at the end of step 1) there can be a lack of structures but, again, do not give up ! Step 2) can do miracles. L. Sambuelli - Politecnico di Torino - DIATI - 90 2016

  61. Data processing Raw data Processed data Novalesa\smaria.MIS\150923AB.ZON\PROCDATA\LTT10012.06T subtract-mean(dewow) / 5 / 0 / 0 / 0 / / 0 / 0 / 1 / 869 move starttime / -3.5 / 0 / 0 / 0 / / 1 / 0 / 1 / 866 Step 1) time cut / 75 / 0 / 0 / 0 / / 1 / 0 / 1 / 866 manual gain (y) / -19.57447 / 8.116377E-7 / 0 / 0 / / 1 / 0 / 1 / 870 bandpassbutterworth / 100 / 400 / 0 / 0 / / 1 / 0 / 1 / 871 background removal / 0 / 75 / 0 / 55 / / 0 / 0 / 1 / 870 L. Sambuelli - Politecnico di Torino - DIATI - 91 2016

  62. Data processing Same survey as in the previous slides after data-cube processing. The red dashed line corresponds to the track of the radargrams in the previous slides. The processing here shown is a time-slice that is a horizontal cut at about 9 ns of the data-cube obtained after having assembled in the correct spatial positions all the radargrams, acquired along both x and y directions. Step 2) L. Sambuelli - Politecnico di Torino - DIATI - 92 2016

  63. Data processing Novalesa\smaria.MIS\150923AB.ZON\PROCDATA\LTT10012.06T move starttime / 0 / 0 / 0 / 0 / / 0 / 0 / 1 / 870 subtract-mean(dewow) / 5 / 0 / 0 / 0 / / 0 / 0 / 1 / 869 move starttime / -3.5 / 0 / 0 / 0 / / 1 / 0 / 1 / 866 time cut / 75 / 0 / 0 / 0 / / 1 / 0 / 1 / 866 manual gain (y) / -19.57447 / 8.116377E-7 / 0 / 0 / / 1 / 0 / 1 / 870 bandpassbutterworth / 100 / 400 / 0 / 0 / / 1 / 0 / 1 / 871 background removal / 0 / 75 / 0 / 55 / / 0 / 0 / 1 / 870 THIS SEQUENCE NCE IS NOT T MANDATORY Y OTH THER ER SURVEYS EYS MAY REQUIRE SHORTER ER OR LONGER R SEQUENCES NCES L. Sambuelli - Politecnico di Torino - DIATI - 93 2016

  64. Data processing Step 1 L. Sambuelli - Politecnico di Torino - DIATI - 94 2016

  65. Data processing The step 1a consists of a «Dewow» that is a high pass filter which is used to attenuate the continuous component and the very low frequencies from each trace. In the following slide: on the left the raw data; in the middle the dewowed data; on the right en example of the effect on one trace. In this latter the red line is the raw trace while the black line is the dewowed trace. L. Sambuelli - Politecnico di Torino - DIATI - 95 2016

  66. STEP_1a L. Sambuelli - Politecnico di Torino - DIATI - 96 2016

  67. Data processing The step 1b consists of «Move start time» that means to delete the samples before the Main Bang (that is the direct signal from Tx to Rx+the reflection air-ground surface) from each trace. In the following slide: on the left the original data; in the middle the corrected data; on the right an example of the effect on one trace. In this latter the red line is the raw trace while the black line is the corrected trace. L. Sambuelli - Politecnico di Torino - DIATI - 97 2016

  68. STEP_1b L. Sambuelli - Politecnico di Torino - DIATI - 98 2016

  69. Data processing The step 1c consists of «Time cut» that means to delete the samples after a selected twt from each trace. Looking at the radargrams very often it is easy to recognize where there is likely only noise; deleting the samples containing noise reduces the size of the files to be processed thus speeding up the work. In the following slide: on the left the original data; on the right the reduced data. L. Sambuelli - Politecnico di Torino - DIATI - 99 2016

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Basic Number Theory The integers are the natural numbers, 0 and the additive inverses of the

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Supplementary Networking Slides These slides provide more detail than we covered in lecture

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Previous Lecture Todays Lecture Slides for Lecture 33 ENEL 353: Digital Circuits Fall

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Previous Lecture Todays Lecture Slides for Lecture 26 ENEL 353: Digital Circuits Fall

Previous Lecture Todays Lecture Slides for Lecture 26 ENEL 353: Digital Circuits Fall

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Previous Lecture Todays Lecture Slides for Lecture 35 ENEL 353: Digital Circuits Fall

Previous Lecture Todays Lecture Slides for Lecture 35 ENEL 353: Digital Circuits Fall

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Previous Lecture Todays Lecture Slides for Lecture 2 ENEL 353: Digital Circuits Fall 2013

Previous Lecture Todays Lecture Slides for Lecture 2 ENEL 353: Digital Circuits Fall 2013

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CS 730/830: Intro AI 1 handout: slides Search Basic Algorithms A Clever Algorithm EOLQs

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