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					                                                               Modern Data Acquisition Systems – Reinoud Sleeman




        Modern data acquisition systems:
         digitizers and dynamic range


                                       Reinoud Sleeman
                                     ORFEUS Data Center
                       Royal Netherlands Meteorological Insitute                  (KNMI)
                                      sleeman @ knmi.nl




                               IRIS - ORFEUS Workshop
            Managing Waveform Data and Related Metadata for Seismic Networks
                                 Helwan, Cairo, Egypt
                                8 – 17 November 2009


Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman


           Layout


         • introduction

         • digitizing theory (dynamic range, oversampling)

         • ADC - delta sigma modulator

         • decimation (SEED)

         • measuring and representing instrumental noise

         • instrumental noise of today’s dataloggers

         • instrumental noise of the STS-2




Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
    Introduction and motivation                                Modern Data Acquisition Systems – Reinoud Sleeman




                seismic background noise (m/s2) power spectral density




                                                                                     STS-2




                                  N-S                              E-W             STS-1                    Z




            •    seismic station: Heimansgroeve (HGN), Netherlands
            •    sensors:         STS-1, STS-2
            •    time windows: 2002 (302 - 309) and 2003 (029 – 043)


Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
    Introduction and motivation                                Modern Data Acquisition Systems – Reinoud Sleeman




                                        from STS-2 manual




Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
   • Johnson-Mathiesen seismometer > 1 Hz
   • STS-1 < 0.01 Hz




STS-1
                              STS-2 noise (Wielandt, 1991)
    Introduction and motivation                                Modern Data Acquisition Systems – Reinoud Sleeman



                                                                                       analog signal




                          How do we make a digital (bit stream) representation from
                          an analog signal ?




                                                                          digital representation

                                  …..0011011110101001010100001101110101110100110
                                  111101111001001011101010010101010010101011…



Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
    Introduction and motivation                                Modern Data Acquisition Systems – Reinoud Sleeman




          • How do we get a digital (bit stream) representation from an
            analog signal ?

          • How accurate is the representation ?

          • Does the digitizing system bias the digital data ?

          • What does ‘dynamic range’ mean and how must we interpret
            these numbers (e.g. 145 dB) given by vendors ?

          • How can we measure the noise level (dynamic range) ?

          • What information about the recording system is useful or
            important for seismologists and needs to be stored as (SEED)
            metadata ?


                …..0011011110101001010100001101110101110100110111101111……


Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
    Digitizing theory                                          Modern Data Acquisition Systems – Reinoud Sleeman


              Dynamic range of a N-bit digitizer

     Quantization:                          e  q ( x)  x
                                                                                         /2
                                                                                         2
                                                     q( x)  x p(e)de    e 2 de 
                                             2                       2     1
     Variance of error:                     erms
                                                     
                                                                             / 2      12

    x, q(x)


                                                                   ∆ : smallest discrete step (LSB)




                                                                    q(x)                           +∆/2
                                                                             e
                                                                      x
                                                                                                    -∆/2
                                                      t


Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
    Digitizing theory                                          Modern Data Acquisition Systems – Reinoud Sleeman


              Dynamic range of a N-bit digitizer

     Quantization:                          e  q ( x)  x
                                                                                         /2
                                                                                         2
                                                     q( x)  x p(e)de    e 2 de 
                                             2                       2     1
     Variance of error:                     erms
                                                     
                                                                             / 2      12

     Quantization levels in                  2A                    ∆ : smallest discrete step (LSB)
                                                 2n               2A: full scale input
     a n-bit ADC:                            




Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
    Digitizing theory                                          Modern Data Acquisition Systems – Reinoud Sleeman


              Dynamic range of a N-bit digitizer

     Quantization:                          e  q ( x)  x
                                                                                         /2
                                                                                         2
                                                     q( x)  x p(e)de    e 2 de 
                                             2                       2     1
     Variance of error:                     erms
                                                     
                                                                             / 2      12

     Quantization levels in                  2A                    ∆ : smallest discrete step (LSB)
                                                 2n               2A: full scale input
     a n-bit ADC:                            

     Sine wave (amp A):                     srms  A2 / 2
                                             2




Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
    Digitizing theory                                          Modern Data Acquisition Systems – Reinoud Sleeman


              Dynamic range of a N-bit digitizer

     Quantization:                          e  q ( x)  x
                                                                                         /2
                                                                                         2
                                                     q( x)  x p(e)de    e 2 de 
                                             2                       2     1
     Variance of error:                     erms
                                                     
                                                                             / 2      12

     Quantization levels in                  2A                    ∆ : smallest discrete step (LSB)
                                                 2n               2A: full scale input
     a n-bit ADC:                            

     Sine wave (amp A):                     srms  A2 / 2
                                             2




     Dynamic range:                                        s rms
                                                              2
                                                                         
     (Bennett, 1948)
                                           SNR  10  log  2
                                                          e             
                                                                         
                                                           rms          



Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
    Digitizing theory                                          Modern Data Acquisition Systems – Reinoud Sleeman


              Dynamic range of a N-bit digitizer

     Quantization:                          e  q ( x)  x
                                                                                         /2
                                                                                         2
                                                     q( x)  x p(e)de    e 2 de 
                                             2                       2     1
     Variance of error:                     erms
                                                     
                                                                             / 2      12

     Quantization levels in                  2A                    ∆ : smallest discrete step (LSB)
                                                 2n               2A: full scale input
     a n-bit ADC:                            

     Sine wave (amp A):                     srms  A2 / 2
                                             2




     Dynamic range:                                        s rms
                                                              2
                                                                         
     (Bennett, 1948)
                                           SNR  10  log  2
                                                          e             
                                                                         
                                                           rms                           6 dB per bit

                                              A2 / 2 
                                               / 12   1.76  n  6.02
     Dynamic range digitizer: SNR  10  log  2      
                                                     
Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman


             Oversampling



                                                              PSD vs. sampling rate




      • In an ideal digitizer (assuming white digitizer noise) the quantization noise
         power is uniformly distributed between [0 – fNYQ] Hz.
      • The noise power does not depend on the sampling rate.
      • For higher sampling rates the power spreads over a wider frequency range,
        so decreasing the power spectral density (and thus decreasing the
        quantization error) !
      • Higher sampling rate improves the accuracy of the estimate of the (analog)
        input signal.
Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman


             Oversampling

                               1
          PSD ( f ) ~                 2  Ts            Ts = sampling interval (s)
                             f Nyq




Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman


               Oversampling

                               1
          PSD ( f ) ~                   2  Ts          Ts = sampling interval (s)
                             f Nyq

                                                      /2
                                                     2
                 q( x)  x p(e)de    e 2 de 
         2                         2   1                                      noise power
        erms
                 
                                         / 2      12




Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman


               Oversampling

                               1
          PSD ( f ) ~                   2  Ts          Ts = sampling interval (s)
                             f Nyq

                                                      /2
                                                     2
                 q( x)  x p(e)de    e 2 de 
         2                         2   1                                      noise power
        erms
                 
                                         / 2      12


       Theoretical expression for the (one-sided) PSD of quantization noise in a
       n-bit digitizer:


             2 1
                                            2
                       2 A  Ts                                            2A
                                                                                2n
        PSD         n  
             12 f Nyq  2  6                                               

       PSD of quantization noise depends on the (initial) sampling rate, and so
       does the dynamic range !
Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman


             Oversampling


        • oversampling factor 4 leads to increase of SNR of ~ 6 dB (or 1 bit)

                                     10  log( 4) 6 dB




Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman


             Oversampling


        • oversampling factor 4 leads to increase of SNR of ~ 6 dB (or 1 bit)

                                     10  log( 4) 6 dB

        • 1-bit ADC with 256x oversampling achieves a resolution of 4 bits

                                 10  log( 256 )  24 dB




Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman


             Oversampling


        • oversampling factor 4 leads to increase of SNR of ~ 6 dB (or 1 bit)

                                     10  log( 4) 6 dB

        • 1-bit ADC with 256x oversampling achieves a resolution of 4 bits

                                 10  log( 256 )  24 dB
        •   to achieve 16 bits resolution (96 dB) you must oversample with factor
            4^16 (~ 4000 000 000), and for 24 bits resolution this factor is
            4^24 (~280 000 000 000 000 ); both can not be realized !




Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman


             Oversampling


        • oversampling factor 4 leads to increase of SNR of ~ 6 dB (or 1 bit)

                                     10  log( 4) 6 dB

        • 1-bit ADC with 256x oversampling achieves a resolution of 4 bits

                                 10  log( 256 )  24 dB
        •   to achieve 16 bits resolution (96 dB) you must oversample with factor
            4^16 (~ 4000 000 000), and for 24 bits resolution this factor is
            4^24 (~280 000 000 000 000 ); both can not be realized !

        • this problem is overcome by the delta-sigma modulator with the
          property of noise shaping, to enable a gain of more than 6 dB for
          each factor of 4x oversampling.




Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman



                  Delta-Sigma Analog-Digital (A/D) Modulator
                                (one-bit noise shaping converter)

                          Inose and Yasuda, University of Tokyo, 1946




  Comperator:                            ADC or quantizer
  Feedback:                              average of y follows the average of x
  Integrator:                            accumulates the quantization error e over time
  Pulse train:                           pulse density representation of x


Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
                                                                Modern Data Acquisition Systems – Reinoud Sleeman


             Delta-Sigma Modulator
                         Delta-Sigma Modulator


                                                                   ei

                  xi          si                      ui                    q(ui)




                       si  xi  q(ui )
                       ui  si 1  ui 1                  q (ui )  xi 1  (ei  ei 1 )
                       q(ui )  ui  ei




Managing Waveform Data and Related Metadata for Seismic Networks                           Cairo, Egypt, Lumpur - R. Sleeman
                                                                        IRIS Workshop, 21-26 Oct 2007, KualaNov 8 – 17, 2009
                                                                Modern Data Acquisition Systems – Reinoud Sleeman


             Delta-Sigma Modulator
                         Delta-Sigma Modulator


                                                                   ei

                  xi          si                      ui                    q(ui)




                       si  xi  q(ui )
                       ui  si 1  ui 1                  q (ui )  xi 1  (ei  ei 1 )
                       q(ui )  ui  ei
                                                                          noise shaping


                         2-nd order:              q(ui )  xi 1  (ei  2ei 1  ei 2 )


Managing Waveform Data and Related Metadata for Seismic Networks                           Cairo, Egypt, Lumpur - R. Sleeman
                                                                        IRIS Workshop, 21-26 Oct 2007, KualaNov 8 – 17, 2009
                                                                           Modern Data Acquisition Systems – Reinoud Sleeman


                       Assumption: quantization noise is white noise




                                   PSD noise
                                                                                      with feedback


                                                                                      without feedback




                                                0   100             (Hz)       32000


                                               output sample rate          initial sample rate




         The feedback loop in the quantizer shapes (differentiates) the quantization noise, with the result of
         smaller quantization noise at lower frequencies at the price of larger quantization noise at higher
         frequencies.

         Noise shaping does not change the total noise power, but its distribution.

         The downsampling (decimation) process uses digital anti-alias
         filters (FIR) which characteristics must be known by seismologists.
         Therefore the FIR coefficients must be part of the metadata.

        Improved resolution (reduced quantization error) at a lower
        effective sampling rate
Managing Waveform Data and Related Metadata for Seismic Networks                                         Cairo, Egypt, Lumpur - R. Sleeman
                                                                                      IRIS Workshop, 21-26 Oct 2007, KualaNov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman



                         Delta-Sigma Decimation
             Delta-Sigma Modulator / Modulator




                                                                                             SEED




Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman


           Layout


         • introduction

         • digitizing theory (dynamic range, oversampling)

         • ADC - delta sigma modulator

         • decimation (SEED)

         • measuring instrumental noise

         • instrumental noise of today’s dataloggers

         • instrumental noise of the STS-2




Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman




           Measurement of instrumental noise (dynamic range)


       •    50 ohm shortened input recording (digitizer)

       •    common input recording (digitizer or sensor)


                   coherency analysis of 2 channels (Holcomb, 1989)
                   coherency analysis of 3 channels (Sleeman et. al., 2006) -
                    triplet method



       Holcomb, L. G., A direct method for calculating instrument noise levels in
       side-by-side seismometer evaluations. U.S. Geol. Surv., Open-File
       Report 89-214 (1989)

       Sleeman, R., A. van Wettum and J. Trampert. Three-channel correlation
       analysis: a new technique to measure instrumental noise of digitizers
       and seismic sensors. Bull. Seism. Soc. Am., 96, 1, 258-271 (2006)


Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman

                                 2-channel vs. 3-channel model




Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman




             Three-channel technique:


                direct method for estimating instrumental noise and relative
                  transfer functions (relative calibration!) based on the
                  recordings only


                no a-priori       information required about transfer functions
                         method not sensitive for errors in gain




Managing Waveform Data and Related Metadata for Seismic Networks                        Cairo, Egypt, Lumpur - R. Sleeman
                                                                     IRIS Workshop, 21-26 Oct 2007, KualaNov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman




                The digitizer experiment




                                          Q4120



                 STS-2                    Q4120




                                          Q4120




Managing Waveform Data and Related Metadata for Seismic Networks                        Cairo, Egypt, Lumpur - R. Sleeman
                                                                     IRIS Workshop, 21-26 Oct 2007, KualaNov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman

                  PSD of self-noise Q4120
                  measured with common STS-2 vertical signal (@ 20 sps)


                                                   Power Spectral Density graph


                                                                               A2 / 2 
                                                                                / 12   1.76  n  6.02
                                                               SNR  10  log  2      
                                                                                      

                                                                            2
                                                                      2A  T
                                                               PSD   n  
                                                                     2  6




                                                                                                           143 dB




Managing Waveform Data and Related Metadata for Seismic Networks                        Cairo, Egypt, Lumpur - R. Sleeman
                                                                     IRIS Workshop, 21-26 Oct 2007, KualaNov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman


     Does the quantization error increases during quantizing a seismic signal ?




                                                                              Quanterra Q4120

                                                               139 dB




                                                                              NARS datalogger




Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
                                                               Modern Data Acquisition Systems – Reinoud Sleeman




Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
STS-2 self noise measurement needs Q330HR
with pre-amp enabled !




                            STS-2 noise (Wielandt)


                         Q330-HR pre-amp enabled
                                                               Modern Data Acquisition Systems – Reinoud Sleeman




                        The sensor experiment




                                                        Q330-HR; pre-amp




                                                        Q330-HR; pre-amp




                                                        Q330-HR; pre-amp




Managing Waveform Data and Related Metadata for Seismic Networks                    Cairo, Egypt, Nov 8 – 17, 2009
 The Conrad Observatory Experiment

• NERIES framework (TA5) (funding)

• Conrad Observatory (infrastructure, local conditions)

• 4 STS-2 (same generation)

• 4 Q330-HR, enabled pre-amplifier

• Antelope ® acquisition
Q330-HR
Without thermal isolation



                  Background noise
                  LNM
                  Wielandt (STS-2)
                  Triplet (STS-2)




                                     12 dB !
With thermal isolation



                  Background noise
                  LNM
                  Wielandt (STS-2)
                  Triplet (STS-2)




                   BH
         LH
                            Background noise
                            LNM
                            Wielandt (STS-2)
                            Triplet (STS-2)




                    no isolation


thermal isolation
             Seismic PSD
             Triplet (STS-2)




julian day (2008)

				
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