managing waveform data and related metadata for seismic networks cairo, egypt, nov 8 – 17, 2009...

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

Modern Data Acquisition Systems – Reinoud Sleeman

Modern data acquisition systems:digitizers and dynamic range

Reinoud SleemanORFEUS Data Center

Royal Netherlands Meteorological Insitute (KNMI)sleeman @ knmi.nl

IRIS - ORFEUS WorkshopManaging Waveform Data and Related Metadata for Seismic Networks

Helwan, Cairo, Egypt8 – 17 November 2009



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



N-S E-W Z

STS-2

STS-1

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

Introduction and motivation

seismic background noise (m/s2) power spectral density



from STS-2 manual

Low noise model

STS-2 noise level


STS-2 noise (Wielandt, 1991)

• Johnson-Mathiesen seismometer > 1 Hz• STS-1 < 0.01 Hz

STS-1



…..0011011110101001010100001101110101110100110111101111001001011101010010101010010101011…

analog signal

digital representation

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




…..0011011110101001010100001101110101110100110111101111……

• 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 ?




Quantization:

Variance of error:

2/

2/

2222

12

1)()( deedeepxxqerms

xxqe )(

Dynamic range of a N-bit digitizer

∆ : smallest discrete step (LSB)

Digitizing theory

+ ∆ / 2

- ∆ / 2

x, q(x)

t

xq(x)

e



∆ : smallest discrete step (LSB)2A: full scale input

Quantization:

Variance of error:

2/

2/

2222

12


xxqe )(


nA2

2

Quantization levels ina n-bit ADC:

Digitizing theory




Quantization:

Variance of error:

2/

2/

2222

12


xxqe )(


nA2

2


2/22 Asrms Sine wave (amp A):

Digitizing theory




Quantization:

Variance of error:

2/

2/

2222

12


xxqe )(


nA2

2



2

2

log10rms

rms

e

sSNRDynamic range:

(Bennett, 1948)

Digitizing theory




Quantization:

Variance of error:

2/

2/

2222

12


xxqe )(


nA2

2



2

2

log10rms

rms

e

sSNRDynamic range:

(Bennett, 1948)

02.676.112/

2/log10

2

2

nA

SNRDynamic range digitizer:

6 dB per bit

Digitizing theory



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.

Oversampling



Oversampling

sNyq

Tf

fPSD 21

~)( Ts = sampling interval (s)



sNyq

Tf

fPSD 21

~)(

Oversampling

2/

2/

2222

12


Ts = sampling interval (s)

noise power



sNyq

Tf

fPSD 21

~)(

Oversampling

2/

2/

2222

12


nA2

2

Ts = sampling interval (s)

PSD of quantization noise depends on the (initial) sampling rate, and so does the dynamic range !

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

noise power

62

21

12

22s

nNyq

TA

fPSD



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

Oversampling

dB6)4log(10




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

Oversampling

dB6)4log(10

dB24)256log(10





• 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 !

Oversampling

dB6)4log(10

dB24)256log(10





• 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.

Oversampling

dB6)4log(10

dB24)256log(10



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

Comperator: ADC or quantizerFeedback: average of y follows the average of xIntegrator: accumulates the quantization error e over timePulse train: pulse density representation of x

Inose and Yasuda, University of Tokyo, 1946



xi siui

ei

q(ui)

iii

iii

iii

euuq

usu

uqxs

)(

)(

11 )()( 11 iiii eexuq

Delta-Sigma ModulatorDelta-Sigma Modulator

IRIS Workshop, 21-26 Oct 2007, Kuala Lumpur - R. Sleeman



noise shaping

xi siui

ei

q(ui)

iii

iii

iii

euuq

usu

uqxs

)(

)(

11 )()( 11 iiii eexuq

)2()( 211 iiiii eeexuq2-nd order:

Delta-Sigma ModulatorDelta-Sigma Modulator




0 100 (Hz) 32000

PS

D n

ois

e

Assumption: quantization noise is white noise

without feedback

with feedback

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-aliasfilters (FIR) which characteristics must be known by seismologists.Therefore the FIR coefficients must be part of the metadata.


initial sample rateoutput sample rate

Improved resolution (reduced quantization error) at a lower effective sampling rate



Delta-Sigma ModulatorDelta-Sigma Modulator / Decimation

SEED



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



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)



2-channel vs. 3-channel model



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




The digitizer experiment

STS-2

Q4120

Q4120

Q4120




PSD of self-noise Q4120measured with common STS-2 vertical signal (@ 20 sps)


Power Spectral Density graph

62

22TA

PSDn

02.676.112/

2/log10

2

2

nA

SNR

143 dB



Quanterra Q4120

NARS datalogger

Does the quantization error increases during quantizing a seismic signal ?

139 dB

Q330-HR pre-amp enabled

STS-2 noise (Wielandt)

STS-2 self noise measurement needs Q330HR with pre-amp enabled !



The sensor experiment

Q330-HR; pre-amp

Q330-HR; pre-amp

Q330-HR; pre-amp

• NERIES framework (TA5) (funding)

• Conrad Observatory (infrastructure, local conditions)

• 4 STS-2 (same generation)

• 4 Q330-HR, enabled pre-amplifier

• Antelope ® acquisition

The Conrad Observatory Experiment

Q330-HR

12 dB !

Background noiseLNMWielandt (STS-2)Triplet (STS-2)

Without thermal isolation


With thermal isolation

BHLH


thermal isolation

no isolation

Seismic PSDTriplet (STS-2)

julian day (2008)

managing waveform data and related metadata for seismic networks cairo, egypt, nov 8 – 17, 2009...

Documents

waveform data

digital data

dynamic range digitizer

related metadata

seismic networks cairo

dynamic range mean

noise level dynamic

seed metadata