![](media/image1.png){width="1.75in" height="0.6416666666666667in"}

**Seismic Noise Analysis System Using Power Spectral Density Probability
Density Functions: A Stand-Alone Software Package**

By D. E. McNamara and R.I. Boaz

Report Series XXXXXXX

U.S. Department of the Interior

U.S. Geological Survey

U.S. Department of the Interior

Gale A. Norton, Secretary

U.S. Geological Survey

P. Patrick Leahy, Acting Director

U.S. Geological Survey, Reston, Virginia 200x\
Revised and reprinted: 200x

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# Contents {#contents .TOCHeading1}

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References Cited [**Error! Bookmark not
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Glossary [**Error! Bookmark not defined.**](#__RefHeading___Toc95029652)

# Figures {#figures .TOCHeading1}

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# Tables {#tables .TOCHeading1}

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# Conversion Factors {#conversion-factors .TOCHeading1}

## Inch/Pound to SI {#inchpound-to-si .TOCHeading2}

  ------------------------- -------------------- -------------------------
  Multiply                  By                   To obtain

  Length                                         

  inch (in.)                2.54                 centimeter (cm)

  inch (in.)                25.4                 millimeter (mm)

  foot (ft)                 0.3048               meter (m)

  mile (mi)                 1.609                kilometer (km)

  mile, nautical (nmi)      1.852                kilometer (km)

  yard (yd)                 0.9144               meter (m)

  Area                                           

  acre                      4,047                square meter (m^2^)

  acre                      0.4047               hectare (ha)

  acre                      0.4047               square hectometer (hm^2^)

  acre                      0.004047             square kilometer (km^2^)

  square foot (ft^2^)       929.0                square centimeter (cm^2^)

  square foot (ft^2^)       0.09290              square meter (m^2^)

  square inch (in^2^)       6.452                square centimeter (cm^2^)

  section (640 acres or 1   259.0                square hectometer (hm^2^)
  square mile)                                   

  square mile (mi^2^)       259.0                hectare (ha)

  square mile (mi^2^)       2.590                square kilometer (km^2^)

  Volume                                         

  barrel (bbl),             0.1590               cubic meter (m^3^)
  (petroleum,\                                   
  1 barrel=42 gal)                               

  ounce, fluid (fl. oz)     0.02957              liter (L)

  pint (pt)                 0.4732               liter (L)

  quart (qt)                0.9464               liter (L)

  gallon (gal)              3.785                liter (L)

  gallon (gal)              0.003785             cubic meter (m^3^)

  gallon (gal)              3.785                cubic decimeter (dm^3^)

  million gallons (Mgal)    3,785                cubic meter (m^3^)

  cubic inch (in^3^)        16.39                cubic centimeter (cm^3^)

  cubic inch (in^3^)        0.01639              cubic decimeter (dm^3^)

  cubic inch (in^3^)        0.01639              liter (L)

  cubic foot (ft^3^)        28.32                cubic decimeter (dm^3^)

  cubic foot (ft^3^)        0.02832              cubic meter (m^3^)

  cubic yard (yd^3^)        0.7646               cubic meter (m^3^)

  cubic mile (mi^3^)        4.168                cubic kilometer (km^3^)

  acre-foot (acre-ft)       1,233                cubic meter (m^3^)

  acre-foot (acre-ft)       0.001233             cubic hectometer (hm^3^)

  Flow rate                                      

  acre-foot per day         0.01427              cubic meter per second
  (acre-ft/d)                                    (m^3^/s)

  acre-foot per year        1,233                cubic meter per year
  (acre-ft/yr)                                   (m^3^/yr)

  acre-foot per year        0.001233             cubic hectometer per year
  (acre-ft/yr)                                   (hm^3^/yr)

  foot per second (ft/s)    0.3048               meter per second (m/s)

  foot per minute (ft/min)  0.3048               meter per minute (m/min)

  foot per hour (ft/hr)     0.3048               meter per hour (m/hr)

  foot per day (ft/d)       0.3048               meter per day (m/d)

  foot per year (ft/yr)     0.3048               meter per year (m/yr)

  cubic foot per second     0.02832              cubic meter per second
  (ft^3^/s)                                      (m^3^/s)

  cubic foot per second per 0.01093              cubic meter per second
  square\                                        per square kilometer
  mile \[(ft^3^/s)/mi^2^\]                       \[(m^3^/s)/km^2^\]

  cubic foot per day        0.02832              cubic meter per day
  (ft^3^/d)                                      (m^3^/d)

  gallon per minute         0.06309              liter per second (L/s)
  (gal/min)                                      

  gallon per day (gal/d)    0.003785             cubic meter per day
                                                 (m^3^/d)

  gallon per day per square 0.001461             cubic meter per day per
  mile\                                          square\
  \[(gal/d)/mi^2^\]                              kilometer
                                                 \[(m^3^/d)/km^2^\]

  million gallons per day   0.04381              cubic meter per second
  (Mgal/d)                                       (m^3^/s)

  million gallons per day   1,461                cubic meter per day per
  per square mile                                square\
  \[(Mgal/d)/mi^2^\]                             kilometer
                                                 \[(m^3^/d)/km^2^\]

  inch per hour (in/h)      0 .0254              meter per hour (m/h)

  inch per year (in/yr)     25.4                 millimeter per year
                                                 (mm/yr)

  mile per hour (mi/h)      1.609                kilometer per hour (km/h)

  Mass                                           

  ounce, avoirdupois (oz)   28.35                gram (g)

  pound, avoirdupois (lb)   0.4536               kilogram (kg)

  ton, short (2,000 lb)     0.9072               megagram (Mg)

  ton, long (2,240 lb)      1.016                megagram (Mg)

  ton per day (ton/d)       0.9072               metric ton per day

  ton per day (ton/d)       0.9072               megagram per day (Mg/d)

  ton per day per square    0.3503               megagram per day per
  mile\                                          square\
  \[(ton/d)/mi^2^\]                              kilometer
                                                 \[(Mg/d)/km^2^\]

  ton per year (ton/yr)     0.9072               megagram per year (Mg/yr)

  ton per year (ton/yr)     0.9072               metric ton per year

  Pressure                                       

  atmosphere, standard      101.3                kilopascal (kPa)
  (atm)                                          

  bar                       100                  kilopascal (kPa)

  inch of mercury at 60ºF   3.377                kilopascal (kPa)
  (in Hg)                                        

  pound-force per square    6.895                kilopascal (kPa)
  inch\                                          
  (lbf/in^2^)                                    

  pound per square foot     0.04788              kilopascal (kPa)
  (lb/ft^2^)                                     

  pound per square inch     6.895                kilopascal (kPa)
  (lb/in^2^)                                     

  Density                                        

  pound per cubic foot      16.02                kilogram per cubic meter
  (lb/ft^3^)                                     (kg/m^3^)

  pound per cubic foot      0.01602              gram per cubic centimeter
  (lb/ft^3^)                                     (g/cm^3^)

  Energy                                         

  kilowatthour (kWh)        3,600,000            joule (J)

  Radioactivity                                  

  picocurie per liter       0.037                becquerel per liter
  (pCi/L)                                        (Bq/L)

  Specific capacity                              

  gallon per minute per     0.2070               liter per second per
  foot\                                          meter \[(L/s)/m\]
  \[(gal/min)/ft)\]                              

  Hydraulic conductivity                         

  foot per day (ft/d)       0.3048               meter per day (m/d)

  Hydraulic gradient                             

  foot per mile (ft/mi)     0.1894               meter per kilometer
                                                 (m/km)

  Transmissivity\*                               

  foot squared per day      0.09290              meter squared per day
  (ft^2^/d)                                      (m^2^/d)

  Application rate                               

  pounds per acre per year\ 1.121                kilograms per hectare per
  \[(lb/acre)/yr\]                               year\
                                                 \[(kg/ha)/yr\]

  Leakance                                       

  foot per day per foot     1                    meter per day per meter
  \[(ft/d)/ft\]                                  

  inch per year per foot    83.33                millimeter per year per
  \[(in/yr)/ft\]                                 meter\
                                                 \[(mm/yr)/m\]
  ------------------------- -------------------- -------------------------

Temperature in degrees Celsius (°C) may be converted to degrees
Fahrenheit (°F) as follows:

°F=(1.8×°C)+32

Temperature in degrees Fahrenheit (°F) may be converted to degrees
Celsius (°C) as follows:

°C=(°F-32)/1.8

Vertical coordinate information is referenced to the insert datum name
(and abbreviation) here for instance, "North American Vertical Datum of
1988 (NAVD 88)."

Horizontal coordinate information is referenced to the insert datum name
(and abbreviation) here for instance, "North American Datum of 1983 (NAD
83)."

Altitude, as used in this report, refers to distance above the vertical
datum.

\*Transmissivity: The standard unit for transmissivity is cubic foot per
day per square foot times foot of aquifer thickness
\[(ft^3^/d)/ft^2^\]ft. In this report, the mathematically reduced form,
foot squared per day (ft^2^/d), is used for convenience.

Specific conductance is given in microsiemens per centimeter at 25
degrees Celsius (µS/cm at 25 °C).

Concentrations of chemical constituents in water are given either in
milligrams per liter (mg/L) or micrograms per liter (µg/L).

NOTE TO USGS USERS: Use of hectare (ha) as an alternative name for
square hectometer (hm^2^) is restricted to the measurement of small land
or water areas. Use of liter (L) as a special name for cubic decimeter
(dm^3^) is restricted to the measurement of liquids and gases. No prefix
other than milli should be used with liter. Metric ton (t) as a name for
megagram (Mg) should be restricted to commercial usage, and no prefixes
should be used with it.

## SI to Inch/Pound {#si-to-inchpound .TOCHeading2}

  ------------------------- ------------------- -------------------------
  Multiply                  By                  To obtain

  Length                                        

  centimeter (cm)           0.3937              inch (in.)

  millimeter (mm)           0.03937             inch (in.)

  meter (m)                 3.281               foot (ft)

  kilometer (km)            0.6214              mile (mi)

  kilometer (km)            0.5400              mile, nautical (nmi)

  meter (m)                 1.094               yard (yd)

  Area                                          

  square meter (m^2^)       0.0002471           acre

  hectare (ha)              2.471               acre

  square hectometer (hm^2^) 2.471               acre

  square kilometer (km^2^)  247.1               acre

  square centimeter (cm^2^) 0.001076            square foot (ft^2^)

  square meter (m^2^)       10.76               square foot (ft^2^)

  square centimeter (cm^2^) 0.1550              square inch (ft^2^)

  square hectometer (hm^2^) 0.003861            section (640 acres or 1
                                                square mile)

  hectare (ha)              0.003861            square mile (mi^2^)

  square kilometer (km^2^)  0.3861              square mile (mi^2^)

  Volume                                        

  cubic meter (m^3^)        6.290               barrel (petroleum, 1
                                                barrel = 42 gal)

  liter (L)                 33.82               ounce, fluid (fl. oz)

  liter (L)                 2.113               pint (pt)

  liter (L)                 1.057               quart (qt)

  liter (L)                 0.2642              gallon (gal)

  cubic meter (m^3^)        264.2               gallon (gal)

  cubic decimeter (dm^3^)   0.2642              gallon (gal)

  cubic meter (m^3^)        0.0002642           million gallons (Mgal)

  cubic centimeter (cm^3^)  0.06102             cubic inch (in^3^)

  cubic decimeter (dm^3^)   61.02               cubic inch (in^3^)

  liter (L)                 61.02               cubic inch (in^3^)

  cubic decimeter (dm^3^)   0.03531             cubic foot (ft^3^)

  cubic meter (m^3^)        35.31               cubic foot (ft^3^)

  cubic meter (m^3^)        1.308               cubic yard (yd^3^)

  cubic kilometer (km^3^)   0.2399              cubic mile (mi^3^)

  cubic meter (m^3^)        0.0008107           acre-foot (acre-ft)

  cubic hectometer (hm^3^)  810.7               acre-foot (acre-ft)

  Flow rate                                     

  cubic meter per second    70.07               acre-foot per day
  (m^3^/s)                                      (acre-ft/d)

  cubic meter per year      0.000811            acre-foot per year
  (m^3^/yr)                                     (acre-ft/yr)

  cubic hectometer per year 811.03              acre-foot per year
  (hm^3^/yr)                                    (acre-ft/yr)

  meter per second (m/s)    3.281               foot per second (ft/s)

  meter per minute (m/min)  3.281               foot per minute (ft/min)

  meter per hour (m/hr)     3.281               foot per hour (ft/hr)

  meter per day (m/d)       3.281               foot per day (ft/d)

  meter per year (m/yr)     3.281               foot per year ft/yr)

  cubic meter per second    35.31               cubic foot per second
  (m^3^/s)                                      (ft^3^/s)

  cubic meter per second    91.49               cubic foot per second per
  per square kilometer                          square\
  \[(m^3^/s)/km^2^\]                            mile \[(ft^3^/s)/mi^2^\]

  cubic meter per day       35.31               cubic foot per day
  (m^3^/d)                                      (ft^3^/d)

  liter per second (L/s)    15.85               gallon per minute
                                                (gal/min)

  cubic meter per day       264.2               gallon per day (gal/d)
  (m^3^/d)                                      

  cubic meter per day per   684.28              gallon per day per square
  square\                                       mile\
  kilometer                                     \[(gal/d)/mi^2^\]
  \[(m^3^/d)/km^2^\]                            

  cubic meter per second    22.83               million gallons per day
  (m^3^/s)                                      (Mgal/d)

  cubic meter per day per   0.0006844           million gallons per day
  square\                                       per square mile
  kilometer                                     \[(Mgal/d)/mi^2^\]
  \[(m^3^/d)/km^2^\]                            

  cubic meter per hour      39.37               inch per hour (in/h)
  (m^3^/h)                                      

  millimeter per year       0.03937             inch per year (in/yr)
  (mm/yr)                                       

  kilometer per hour (km/h) 0.6214              mile per hour (mi/h)

  Mass                                          

  gram (g)                  0.03527             ounce, avoirdupois (oz)

  kilogram (kg)             2.205               pound avoirdupois (lb)

  megagram (Mg)             1.102               ton, short (2,000 lb)

  megagram (Mg)             0.9842              ton, long (2,240 lb)

  metric ton per day        1.102               ton per day (ton/d)

  megagram per day (Mg/d)   1.102               ton per day (ton/d)

  megagram per day per      2.8547              ton per day per square
  square\                                       mile\
  kilometer                                     \[(ton/d)/mi^2^\]
  \[(Mg/d)/km^2^\]                              

  megagram per year (Mg/yr) 1.102               ton per year (ton/yr)

  metric ton per year       1.102               ton per year (ton/yr)

  Pressure                                      

  kilopascal (kPa)          0.009869            atmosphere, standard
                                                (atm)

  kilopascal (kPa)          0.01                bar

  kilopascal (kPa)          0.2961              inch of mercury at 60°F
                                                (in Hg)

  kilopascal (kPa)          0.1450              pound-force per inch
                                                (lbf/in)

  kilopascal (kPa)          20.88               pound per square foot
                                                (lb/ft^2^)

  kilopascal (kPa)          0.1450              pound per square inch
                                                (lb/ft^2^)

  Density                                       

  kilogram per cubic meter  0.06242             pound per cubic foot
  (kg/m^3^)                                     (lb/ft^3^)

  gram per cubic centimeter 62.4220             pound per cubic foot
  (g/cm^3^)                                     (lb/ft^3^)

  Energy                                        

  joule (J)                 0.0000002           kilowatthour (kWh)

  Radioactivity                                 

  becquerel per liter       27.027              picocurie per liter
  (Bq/L)                                        (pCi/L)

  Specific capacity                             

  liter per second per      4.831               gallon per minute per
  meter \[(L/s)/m\]                             foot \[(gal/min)/ft\]

  Hydraulic conductivity                        

  meter per day (m/d)       3.281               foot per day (ft/d)

  Hydraulic gradient                            

  meter per kilometer       5.27983             foot per mile (ft/mi)
  (m/km)                                        

  Transmissivity\*                              

  meter squared per day     10.76               foot squared per day
  (m^2^/d)                                      (ft^2^/d)

  Application rate                              

  kilograms per hectare per 0.8921              pounds per acre per year\
  year\                                         \[(lb/acre)/yr\]
  \[(kg/ha)/yr\]                                

  Leakance                                      

  meter per day per meter   1                   foot per day per foot
  \[(m/d)/m\]                                   \[(ft/d)/ft\]

  millimeter per year per   0.012               inch per year per foot
  meter\                                        \[(in/yr)/ft\]
  \[(mm/yr)/m\]                                 
  ------------------------- ------------------- -------------------------

Temperature in degrees Celsius (°C) may be converted to degrees
Fahrenheit (°F) as follows:

°F=(1.8×°C)+32

Temperature in degrees Fahrenheit (°F) may be converted to degrees
Celsius (°C) as follows:

°C=(°F-32)/1.8

Vertical coordinate information is referenced to the insert datum name
(and abbreviation) here, for instance, "North American Vertical Datum of
1988 (NAVD 88)"

Horizontal coordinate information is referenced to the insert datum name
(and abbreviation) here, for instance, "North American Datum of 1983
(NAD 83)"

Altitude, as used in this report, refers to distance above the vertical
datum.

\*Transmissivity: The standard unit for transmissivity is cubic foot per
day per square foot times foot of aquifer thickness
\[(ft^3^/d)/ft^2^\]ft. In this report, the mathematically reduced form,
foot squared per day (ft^2^/d), is used for convenience.

Specific conductance is given in microsiemens per centimeter at 25
degrees Celsius (µS/cm at 25°C).

Concentrations of chemical constituents in water are given either in
milligrams per liter (mg/L) or micrograms per liter (µg/L).

NOTE TO USGS USERS: Use of hectare (ha) as an alternative name for
square hectometer (hm^2^) is restricted to the measurement of small land
or water areas. Use of liter (L) as a special name for cubic decimeter
(dm^3^) is restricted to the measurement of liquids and gases. No prefix
other than milli should be used with liter. Metric ton (t) as a name for
megagram (Mg) should be restricted to commercial usage, and no prefixes
should be used with it.

Seismic Noise Analysis System Using Power Spectral Density Probability
Density Functions: A Stand-Alone Software Package

By D. E. McNamara and R.I. Boaz[^1]

# Abstract 

In this U.S. Geological Survey open-file report, we detail the methods
and installation procedures for a stand-alone noise analysis software
package. The noise analysis system is based on the calculation of the
distribution of power spectral density using a probability density
function. Following the successful implementation of the noise analysis
system, at both the Incorporated Research Institutions in Seismology
Data management system in Seattle, Washington, and the Advanced National
Seismic System Data Collection Center in Golden, Colorado, we the system
will be available to the seismic community in a stand-alone form. This
will allow users in the broader seismic community the opportunity to
perform their own analyses on data sets not held by either of these two
data centers. Potential users might include regional earthquake
monitoring network operators, portable experiment investigators and
researchers and students interested in the quality and noise
characteristics of a particular data set. Results from this noise
analysis display the frequency dependent power distribution of the
entire data set and are useful for characterizing the performance of
existing broadband stations, for detecting operational problems, and for
learning about sources of seismic noise within a data set.

This report is divided in two sections. Section I describes how to
acquire the noise analysis software system and details data preparation
and processing as well as the noise analysis calculations and methods.
Section II is a detailed description of the software system. It will be
useful to users interested in detailed installation instructions and a
complete description of the system directory structure and operations.

## Section I: Introduction and Overview of Noise Analysis Methods

A new stand-alone system for analyzing data quality is available to the
seismology community allowing users to evaluate the long-term seismic
noise levels for broadband seismic data in miniSEED format. The new
noise processing software uses a probability density function (PDF) to
display the distribution of seismic power spectral density (PSD) (PSD
method after Peterson, 1993) and can be implemented against any
broadband seismic data with well known instrument responses. The
software system is currently running for routine noise monitoring at the
United States Geological Survey's (USGS) Advanced National Seismic
System (ANSS) National Operations Center (NOC) and at the Incorporated
Research Institutions in Seismology's (IRIS) Data Management Center (
DMC). For PDF plots from these two installations see:

> <http://geohazards.cr.usgs.gov/staffweb/mcnamara/ANSSPDFweb/ANSSPDFweb.html>
>
> and
>
> <http://www.iris.washington.edu/servlet/quackquery/>

**Software Availability**

The new stand-alone software package is available on the world wide web
(WWW) and on the USGS ANSS anonymous ftp server. To download a
compressed tar ball of the software system, go to the following website
and follow the downloading instructions.

<http://geohazards.cr.usgs.gov/staffweb/mcnamara/Software/PDFSA.html>

The download includes complete documentation on installing and running
the noise processing system. It also includes several reference
documents on interpreting the noise PDF plots (for example, McNamara and
Buland, 2004).

**Noise Analysis System Overview**

This noise processing system is unique in that there is no need to
screen the data for earthquakes, system glitches, or general data
artifacts as is commonly done in seismic noise analysis. Instead with
this new analysis, system transients map into a low-level background
probability while ambient noise conditions reveal themselves as high
probability occurrences.  In fact, examination of artifacts related to
station operation and episodic cultural noise allows the user to
estimate the overall station quality and a baseline level of earth noise
at each site. PDF noise plots are useful for characterizing the current
and past performance of existing broadband sensors, for detecting
operational problems within the recording system, and for evaluating the
overall quality of data for a particular station. The advantages of this
new approach include:

> \(1\) an analytical view representing the true ambient noise levels
> rather than a simple absolute minimum,   
>
> \(2\) an assessment of the overall health of the instrument/station,
> and  
>
> \(3\) an assessment of the health of recording and telemetry systems.

Employing the algorithm used to develop the USGS Albuquerque
Seismological Laboratory (ASL) low noise model (LNM; [Peterson,
1993](http://usgspubs.georef.org/dbtw-wpd/exec/dbtwpub.dll?AC=GET_RECORD&XC=/dbtw-wpd/exec/dbtwpub.dll&BU=http%3A%2F%2Fusgspubs.georef.org%2Fusgsnsb.htm&TN=usgspubs&SN=AUTO28351&SE=1749&RN=0&MR=20&TR=0&TX=1000&ES=0&CS=1&XP=&RF=Table&EF=&DF=Single+Record&RL=1&EL=0&DL=1&NP=255&ID=&MF=&MQ=&TI=0&DT=&ST=0&IR=106578&NR=0&NB=0&SV=0&BG=0&FG=0&QS=)),
we compute the PSD for broadband data in the following manner.
Hour-long, continuous, and over-lapping (50 percent) time-series
segments are processed. There is no removal of earthquakes, system
transients and(or) data glitches. The instrument transfer function is
removed from each segment, yielding ground acceleration (for easy
comparison to the LNM).  Each hour-long time series is divided into 13
segments, each about 15 minutes long and overlapping by 75 percent, with
each segment processed by removing the mean; removing the long period
trend; tapering using a 10 percent sine function; and transforming using
an FFT algorithm (Bendat and Piersol, 1971). Segments are then averaged
to provide a PSD for each 1-hour time series segment. For each channel,
raw frequency distributions are constructed by gathering individual PSDs
in the following manner: binning periods in 1/8 octave intervals and
binning power in 1 dB intervals. Each raw frequency distribution bin is
normalized by the total number of PSDs to construct a PDF. The
probability of occurrence of a given power at a particular period is
plotted for direct comparison to the Peterson high and low noise models
(HNM, LNM) (see Fig. 1, LTX BHZ). Also computed and plotted are the
minimum (red line), mode (black line), and maximum (blue line) powers
for each period bin. A wealth of seismic noise information can be
obtained from this statistical view of broadband seismic noise.

**Figure 1**

![](media/image2.jpeg){width="6.0in" height="5.1in"}

**Figure 1.** PDF example for LTX BHZ, with some artifacts and signals
identified. Station
[LTX](http://geohazards.cr.usgs.gov/staffweb/mcnamara/PDFweb/LTX.jpg) -
Lajitas TX, was instrumental in the original Peterson Low Noise Model
(Peterson, 1993); however, due to increased cultural noise (0.1-1s,
1-10Hz) the highest probability power levels (mode, black line) are now
significantly higher than the Peterson low noise model (LNM). The
minimum (red line) will approach the LNM \<2 percent of the time
indicating that the station minimum does not reflect actual ambient
noise conditions across the whole spectrum. Instead, ambient noise
conditions are better represented by the highest probability mode (black
line).

# Noise Analysis System Details

# Data Preparation and Processing

The approach of this noise analysis method differs from many previous
noise studies in that we make no attempt to screen the continuous
waveforms to eliminate body and surface waves from earthquakes or
transients and instrumental glitches such as data gaps, clipping,
spikes, mass recenters, or calibration pulses. These signals are
included in our processing because they are low-probability occurrences
that do not contaminate high-probability ambient seismic noise observed
in the PDFs (see below for details). In fact, transient signals often
are useful for evaluating station performance. Also, eliminating this
event-triggering and removal stage has the benefit of significantly
reducing the PSD computation time by simplifying data pre-processing.

The algorithm used to develop the Albuquerque Seismological Laboratory
(ASL) new low noise model (NLNM) and new high noise model (NHNM)
(Peterson, 1993; Bendat and Piersol, 1971) is used to calculate PSDs for
all stations in this study. The processing steps are detailed below.

*Record length*. Let a finite length seismic time series, *u(t),* have
*N* evenly sampled points at an interval of *∆t*. For our analysis, we
parse continuous time series, for each station component, into 1-hour
(*T~h~*=3600s) finite-length time series segments, overlapping by 50
pecent, distributed continuously in time. Overlapping time series
segments are used to reduce variance in the PSD estimate (Cooley and
Tukey, 1965). For this example, we assume that for the broadband seismic
data, each 3600s times series segment is sampled at 40 sample per second
(sps), such that *∆t*s, for a total *N*=144,000 data points.

*Preprocessing*. The PSD preprocessing of each 1-hour time segment
consists of several operations. First, to significantly improve the Fast
Fourier Transform (FFT) speed ratio, by reducing the number of
operations, the number of samples in the time series, *N*, is truncated
to the next lowest power of two, 2^17^, leaving *N*=131,072, thereby
reducing the series length such that *T~h~*=3276.8s. Second, in order to
further reduce the variance of the final PSD estimates, each roughly
1-hour time series record is divided into 13 segments, overlapping by 75
percent, where the length of each new time series segment is now,
*T~r~=T~h~/4*=819.2s with *N*=32,768=2^15^. The sample size *N* is
chosen based on the longest period of interest*, T~l~*, (lowest
frequency, *fl*). In general, the record length, *T~r~=N∆t*, is chosen
such that it is 10 times the longest resolvable period, *T~l~*. Given
this,*T~l~,=1/f~l~= T~r~/10*=90s. The shortest period, *Ts*, (highest
frequency, *fh*) is equivalent to the Nyquist folding frequency,
*fc*=1/2t=20Hz, and is given by *Ts = 1/fc ≤ 1/fh≤* 0.05s.

Third, in order to minimize long-period contamination, the data are
transformed to a zero mean value, and any long period linear trend is
removed by the average slope method. If *u~n~* are the data values in
the time series *u(t)* of length *T~r~* and *N* samples, the data mean
is given by:

> $u_{\text{mean}} = \frac{1}{N}\sum_{n = 1}^{N}u_{n}$(1)

Long period trend, *T~lp~*, is defined as any frequency component whose
period is longer than the record length, *T~r~,* and is defined as:

> $T\text{lp} = \alpha_{u}\left( t - \frac{Tr}{2} \right)$(2)

$\alpha_{u} = \frac{1}{\left( \frac{\text{Tr}}{3} \right)\left( \frac{2\text{Tr}}{3} \right)}\left\lbrack \int_{\frac{2\text{Tr}}{3}}^{\text{Tr}}{u(t)\text{dt} - \int_{0}^{\frac{\text{Tr}}{3}}{u(t)\text{dt}}} \right\rbrack$where
*0≤t≤ T~r\ ~*and

> \(3\)

If trends are not eliminated in the data, large distortions can occur in
spectral processing by nullifying the estimation of low frequency
spectral quantities. Subtracting (1) and (2) from the original time
series, *u(t),* produces a new time series , *u(t),* that has zero mean
and long period trends removed: (4)

$x(t) = u(t) - u_{\text{mean}} - T\text{lp}$

Fourth, to suppress side lobe leakage in the resulting FFT, a 10 percent
sine taper is applied to the ends of the time series, *x(t).* We define
a new tapered time series, *y(t),* such that:

*y(t) = x(t) \* sin(r \* t) 0 ≤ t ≤ Tr/10*

*y(t) = x(t) Tr/10 ≤ t ≤ (Tr-Tr/10)* (5)

*y(t) = x(t) \* sin(r \* (Tr-t)) (Tr-Tr/10) ≤ t ≤ Tr.*

Tapering the time series has the effect of smoothing the FFT and
minimizing the effect of the discontinuity between the beginning and end
of the time series. The time series variance reduction can be quantified
by the ratio of the total power in the raw FFT to the total power in the
smoothed filter (1.142857) and will be used to correct absolute power in
the final spectrum (Bendat and Piersol, 1971).

**Power Spectral Density**

The standard method for quantifying seismic background noise is to
calculate the noise PSD. The most common method for estimating the PSD
for stationary random seismic data is called the direct Fourier
transform or Cooley-Tukey method (Cooley and Tukey, 1965). The method
computes the PSD via a finite-range fast Fourier transform (FFT) of the
original data and is advantageous for its computational efficiency.

The finite-range Fourier transform of a periodic time series *y(t)* is
given by:

$Y(f,T) = \int_{0}^{\text{Tr}}{y(t)}e^{- i2p\text{ft}}\text{dt}$ (6)

where the number of frequency amplitude estimates *nfft=(N/2)+1=16385*.
For discrete frequency values, *f~k~,* the Fourier components are
defined as:

$Yk = \frac{Y(fk,T)}{Dt}$ (7)

> For , *f~k~=k/Nt when k = 1, 2, ..., N-1*.

Hence, using the Fourier components defined above, the total power
spectral density estimate is defined as: (8)

$Pk = \frac{2Dt}{N}|Yk|^{2}$

As is apparent from (8), the total power, *P~k~*, is simply the square
of the amplitude spectrum with a normalization factor of *2∆t/N*. The
PSD process is repeated for each of the 13 separate overlapping time
segments within the one-hour record. After all 13 segment PSD estimates
are computed, powers are averaged for *q=13* separate time segments,
where each time segment is of length *T~r~.* The final smooth PSD
estimate is given by:

$Pk = \frac{1}{q}\left( P_{k,1} + P_{k,2} + \text{.}\text{.}\text{.} + P_{k,q} \right)$
(9)

where *P~k,q~* is the raw estimate at frequency *f~k~* of the *qth* time
segment. Due to segment averaging, the quantity *P~k~* has *2q=26*
degrees of freedom giving a 95 percent level of confidence that the
spectral point lies within --2.14dB to +2.87dB of the estimate
(Peterson, 1993).

At this point we correct *P~k~* for the 10 percent sine taper applied
earlier in the processing such that *P~k~ = P~k~\*1.142857* and then
deconvolve the seismometer instrument response by dividing the PSD,
*P~k~,* estimate by the instrument transfer function to acceleration, in
the frequency domain. Finally, we convert the smoothed PSD estimate into
decibels (dB) with respect to acceleration (m/s^2^)^2^/Hz, for direct
comparison to the NLNM,by:

> *P~k~ = 10\*log~10~(P~k~).* (10)

*Limitations*. The PSD technique described above provides stable spectra
estimates over a broad range of periods (0.05-90s); however, it suffers
from poor time resolution due to the long transforms and requires
hundreds to thousands of hours of data to compile good statistics for
the PDFs. For better resolution at shorter periods, a larger number of
shorter records should be analyzed. Future work will investigate methods
to improve resolution of higher frequencies.

**Probability Density Functions**

Our goal is to get a sense of the true variation of noise at a given
station. We do this by generating seismic noise PDFs from the PSDs
processed by using the methods discussed in the previous section. In
order to adequately sample the PSDs, full octave averages are taken in
1/8 octave intervals. This procedure reduces the number of frequencies
by a factor of 169 from *nfft*=16,385 to 97. Thus, power is averaged
between a short period (high frequency) corner, *T~s~*, and a long
period (low frequency) corner of *T~l~=2\*T~s~*, with a center period,
*T~c~,* such *that T~c~=sqrt(T~s~\*T~l~)* is the geometric mean period
within the octave. The geometric means are evenly spaced in log space.
The average power for that octave, period range from *T~s~* to *T~l~*,
is stored with the center period of the octave, *T~c~*, for future
analysis. *T~s~* is incremented by one 1/8 octave such that *T~s~ =
T~s~\*2^0.125^*, to compute the average power for the next period bin.
*T~l~* and *T~c~* are recomputed, powers are averaged within the next
period range *T~s~* to *T~l~,* and the process continues until we reach
the longest resolvable period given the time series window length of the
original data, *T~r~/10* (Fig. 2). This process is repeated for every
1-hour PSD estimate, resulting in thousands of smooth PSD estimates for
each station-component. Powers are accumulated in 1 dB intervals to
produce frequency distribution plots (histograms), for each period (Fig.
3).

![](media/image3.pct){width="5.996527777777778in"
height="4.636805555555555in"}

**Figure 2**. SDCO BHZ July 28, 2002, 06:00:00, PSD. Powers are averaged
over full octaves in 1/8 octave intervals. Center points of averaging
are shown.

![](media/image4.pct){width="5.458333333333333in"
height="5.013888888888889in"}

**Figure 3**. Histograms of powers, in 1dB bins, at four separate period
bands for station AHID BHZ.

The next step is to plot the distribution of powers per period, as
observed in figure 3, using a probability density function (PDF). The
PDF, for a given center period, *T~c~,* can be estimated as:

> *P(T~c~) = N~PTc~/N~Tc~* (11)

where *N~PTc~* is the number of spectral estimates that fall into a 1 dB
power bin, *P*, with a range from --200 to --80 dB, and a center
period*, T~c~. N~Tc~* is the total number of spectral estimates over all
powers with a center period, *T~c~*. We then plot the probability of
occurrence of a given power at a particular period for direct comparison
to the high and low noise models (Figs. 1 and 4) (Peterson, 1993). We
also compute and plot the minimum, mode, and maximum powers for each
period bin. A wealth of seismic noise information can be obtained from
this statistical view of broadband PDFs as discussed in the following
section.

**Characterizing Sources of Noise and Signal in the PDFs**

*Cultural Noise*. The most common source of seismic noise is from the
actions of human beings at or near the surface of the Earth. This often
is referred to as "cultural noise" and primarily originates from the
coupling of traffic and machinery energy into the earth. Cultural noise
propagates mainly as high-frequency surface waves (\>1-10Hz,1-0.1s) that
attenuate within several kilometers in distance and depth. For this
reason, cultural noise generally is significantly reduced in boreholes,
deep caves, and tunnels. Cultural noise shows very strong diurnal
variations and has characteristic frequencies depending on the source of
the disturbance (Figs. 1 and 4). Another source of noise with a strong
diurnal is from thermal instabilities. Heating during the day and
cooling at night can cause ground fluctuations that induce tilt and
long-period noise.

*Earthquakes*. Our approach differs from many previous noise studies in
that we make no attempt to screen the continuous waveforms to eliminate
body and surface waves from naturally occurring earthquakes. Earthquake
signals are included in our processing because they are low-probability
occurrences even at low power levels (small magnitude events) compared
to the ambient conditions at the seismic station. We are interested in
the true noise that a given station will experience; therefore we
include all input signals. For example, including earthquakes tells us
something about the probability of teleseismic signals being obscured by
small local events as well as various noise sources. Large teleseismic
earthquakes can produce powers above ambient noise levels across the
entire spectrum and are dominated by surface waves \>10s, while small
events dominate the short period, \<1s. Earthquakes are observed in the
PDFs as low probability smeared signal at short and long periods (Fig.
4).

*System Artifacts*. Since we make no attempt to screen waveforms for
system transients such as data gaps and sensor glitches, the PDF plots
contain numerous system generated artifacts that can be very useful for
network quality-control purposes. We have attempted to determine the
source of several coherent, high power, low-probability noise artifacts
in the PDF plots. Several artifacts in the PDFs are easily explained and
may be useful to the network operator. For example, data-gaps (due to
telemetry dropouts) and automatic mass recenters (necessitated by
"drift" in sensor mass position) are easily identifiable in the PDFs. 
Should the probability of mass recentering and(or) telemetry dropouts
drastically increase, a remote network operator could readily diagnose
the problem (Figs. 1 and 4). Additional features and artifacts observed
in the PDFs are described online at:
[http://geohazards.cr.usgs.gov/mcnamara/PDFweb/Noise_PDFs.html](http://geohazards.cr.usgs.gov/staffweb/mcnamara/PDFweb/Noise_PDFs.html)
and in McNamara and Buland (2004).

**Summary and Conclusions: Section I**

We have presented a new method for more realistically evaluating ambient
seismic noise levels at a station based on the PSD methods used to
generate the NLNM of Peterson (1993). This approach is useful because
seismic stations exhibit considerable variations in noise levels as a
function of time of day, season, location, and installation type. This
type of information is not readily observed when only minimum noise
levels are analyzed. The results of this type of background noise
analysis are useful for characterizing the performance of existing
stations, for detecting operational problems, and should be relevant to
the future siting of broadband seismic stations. Details on software
system installation and operations will be discussed in Section II.

**References**

Bendat, J.S. and A.G. Piersol, 1971, Random data: analysis and
measurement procedures. John Wiley and Sons, New York, 407p.

Cooley, J.W., and J. W. Tukey, 1965, An algorithm for machine
calculation of complex Fourier series, *Math. Comp*., 19, p. 297-301.

McNamara, D.E. and R.P. Buland, 2004, [Ambient Noise Levels in the
Continental United
States](http://geohazards.cr.usgs.gov/staffweb/mcnamara/PDFweb/McNamaraBuland.pdf),
Bull. Seism. Soc. Am., 94, 4, 1517-1527.

Peterson, J., 1993, Observation and modeling of seismic background
noise, [U.S. Geol. Surv. Tech. Rept.,
93-322](http://usgspubs.georef.org/dbtw-wpd/exec/dbtwpub.dll?AC=GET_RECORD&XC=/dbtw-wpd/exec/dbtwpub.dll&BU=http%3A%2F%2Fusgspubs.georef.org%2Fusgsnsb.htm&TN=usgspubs&SN=AUTO28351&SE=1749&RN=0&MR=20&TR=0&TX=1000&ES=0&CS=1&XP=&RF=Table&EF=&DF=Single+Record&RL=1&EL=0&DL=1&NP=255&ID=&MF=&MQ=&TI=0&DT=&ST=0&IR=106578&NR=0&NB=0&SV=0&BG=0&FG=0&QS=),
1-95.

Wessel, P. and W. Smith, 1991, Free software helps display data, *EOS*,
72, 445-446.

**Acknowledgements**

The algorithm and initial software was first developed by Dan McNamara
and Ray Buland, with contributions from Harold Bolton and Paul Earle, at
the United States Geological Survey (USGS) as a part of the ANSS IDCC
quality-control (QC) system. Further development, supported by IRIS
through funds it receives from the National Science Foundation (NSF)
allowed for Richard Boaz to develop the system for implementation
against the real-time BUD dataset and the real-time data stream at the
USGS ANSS NOC. Additional support was provided by the USGS to produce
the stand-alone software package discussed in this report. PDF plots are
generated with the GMT plotting tools (Wessel and Smith, 1991).
Appropriate citation for this noise analysis method is McNamara and
Buland (2004) (see references).

![](media/image5.jpeg){width="6.083333333333333in"
height="5.170833333333333in"}

**Figure 4.** HLID - Typical ANSS station \~10km from  Hailey Idaho.
Automobile traffic along a dirt road only 20 meters from station HLID
creates a 20-30dB increase in power at about 0.1 sec period (10Hz). This
type of cultural noise is observable in the PDFs as a region of low
probability at high frequencies (1-10Hz, 0.1-1s). Body waves occur as
low probability signal in the 1-sec range while surface waves are higher
power at longer periods. Automatic mass recentering and calibration
pulses show up as low probability occurrences in the PDF.

**Section II: System Description and Installation Instructions**

Table of Contents

[Introduction 1](#introduction)

[Quick Install 1](#quick-install)

[Audience 1](#audience)

[Scope 1](#scope)

[Acknowledgments 1](#acknowledgments)

[Authorship 1](#authorship)

[References 2](#references)

[PDF Analysis System Overview 2](#__RefHeading___Toc86804796)

[Description 2](#description)

[Requirements 2](#requirements)

[Hardware 2](#hardware)

[Software 3](#software)

[PDF Source Code Organization 3](#pdf-source-code-organization)

[Input and Output Files 3](#input-and-output-files)

[Input 3](#input)

[Output 5](#output)

[System Configuration 5](#system-configuration)

[Data Directories 6](#data-directories)

[MiniSeed Data Directory and Files
6](#miniseed-data-directory-and-files)

[Response File Directory 6](#response-file-directory)

[Web Directory 7](#web-directory)

[Script Variables 8](#script-variables)

[Source Code Header File Modification
8](#source-code-header-file-modification)

[System Compilation and Installation
8](#system-compilation-and-installation)

[Compilation 8](#compilation)

[Compiler Options 8](#compiler-options)

[Installation 9](#installation)

[PDF System Execution 9](#pdf-system-execution)

[Channel-Specific Shell Script 9](#channel-specific-shell-script)

[Overall Execution 10](#overall-execution)

[Execution Features 10](#execution-features)

[Error Processing 10](#error-processing)

[Release Notes 11](#release-notes)

[Current Limitations 11](#current-limitations)

[Version Control 11](#version-control)

[Version 1.1 11](#version-1.1)

[Appdendix I -- File Formats 11](#appdendix-i-file-formats)

[Djjj.bin File 11](#djjj.bin-file)

[Hour.idx File 11](#hour.idx-file)

[Hjjj.bin File 12](#hjjj.bin-file)

[PDFAnalysis.bin File 12](#pdfanalysis.bin-file)

[PDFAnalysis.inf File 12](#pdfanalysis.inf-file)

[PDFanalysis.sts File 13](#pdfanalysis.sts-file)

[PDFAnalysisSR.bin File 13](#pdfanalysissr.bin-file)

[Appendix II -- Installation and Configuration Checklist
1](#appendix-ii-installation-and-configuration-checklist)

# PDF Analysis System -- Stand Alone Installation

## Introduction

Following from the successful implementation of the PDF Noise Analysis
System at the IRIS DMC in Seattle, Wash., and at the NEIC in Golden,
Colo., it is desired to provide the system to the seismic community in a
stand-alone form. The stand-alone software package will allow seismic
community users the opportunity to perform their own analyses against
data sets not held by the two data centers.

## Quick Install

If the time required to read and understand this document in total is
unavailable (but you'd like it installed and working as quickly as
possible), you must at least read the sections **System Configuration**,
**System Compilation and Installation**, and **PDF System Execution**
and follow the steps outlined there. Where problems occur, be certain to
consult the other various sections of this document that may provide
further information to solve your issue.

## Audience

This document is intended for all users of the siesmic community with an
interest in producing noise analyses of seismic data following the
algorithm laid out by McNamara and Buland of the USGS ANSS National
Operations Center (NOC) in Golden, Colo.

## Scope

This document is limited to the technical aspects of the **PDF Analysis
System**: installation, configuration, and execution. As such, it does
not treat the functional aspects of the system: methodologies,
algorithm, philosophy, interpretation possibilities, usage of results,
etc. For a complete discussion of these and more, please consult the
various documents listed below.

## Acknowledgments

The following parties have significantly contributed to the development
of this system and are hereby acknowledged thus:

  ------------------ ----------------------------------------------------
  **Party**          **Contribution**

  Ray Buland and     Provided the original algorithm and proof-of-concept
  Daniel McNamara    implementation
  (of USGS NEIC,     
  Golden, CO)        

  USGS NEIC          Provided the funds for original development of
                     algorithm.

  NSF                Provided funds for original system development of
                     generic implementation at the IRIS Data Management
                     Center (Seattle, Wash).

  IRIS               Sponsored the development of the generic
                     implementation at the DMC.

  Bruce Weertman (of Responsible for integration of the PDF system within
  IRIS)              the IRIS DMC's Quack framework.
  ------------------ ----------------------------------------------------

## Authorship

This document and the PDF analysis system was written by Richard Boaz
(of Boaz Consultancy:
[http://www.boazconsultancy.com](http://www.boazconsultancy.com/)) and
Dan McNamara (USGS). Any and all comments and(or) bug reports are
welcome and are encouraged to be forwarded to <riboaz@xs4all.nl>.

## References

The following table provides various references which may be of interest
to the reader:

  ----------------- -------------------- ------------------------------------------------------------------------------
  **Description**   **Name**             **Location**

  Original Abstract Ambient Noise Levels PDF Stand-Alone distribution docs directory
  (Adobe pdf)       in the Continental   
                    United States        

  Power Point       Noise Based          PDF Stand-Alone distribution docs directory
  Presentation      Detection Method for 
                    the ANSS             

  Discussion Paper  Determining True     PDF Stand-Alone distribution docs directory
  (Adobe pdf)       Global Ambient Noise 

  PDF Analysis      Ambient Noise        PDF Stand-Alone distribution docs directory
  Interpretation    Probability Density  
  (html document)   Functions            

  PDF Analyses at   USGS/ANSS Noise      <http://geohazards.cr.usgs.gov/staffweb/mcnamara/ANSSPDFweb/ANSSPDFweb.html>
  the USGS NEIC     Monitor              

  PDF Analyses at   DMC QUACK            <http://www.iris.washington.edu/servlet/quackquery/>
  the IRIS DMC      Information Query    

  PDF Analyses at   DMC QUACK            <http://www.iris.washington.edu/servlet/quackquery_us>
  the IRIS DMC (US  Information Query    
  Array)                                 
  ----------------- -------------------- ------------------------------------------------------------------------------

## Description

The PDF Analysis system is comprised of three separate processing
components:

1.  An analysis program (written in C), responsible for producing
    analysis statistics for a single channel;

2.  A shell program (using GMT) to convert the analysis results produced
    in step 1 to a plot, in the form of a postscript format file;

3.  Image manipulation (using ImageMagick) commands to convert the
    postscript file created in step 2 to an actual graphical image (.png
    format).

Execution is provided in the form of a shell script per channel to
analyze, responsible for calling each of these components in turn (see
section **PDF System Execution** below for details).

## Requirements

### Hardware

No specific hardware requirements exist, per se. The program will
execute on any platform supporting a C compiler in addition to the other
software requirements listed below.

Depending on which compile time output option is chosen (please see
section **System Compilation and Installation: Compilation: Compile
Options** for a complete discussion of these options and their effects),
disk storage requirements are approximately the following (per channel
analyzed):

  -------------------------------------------- --------------------------
  **Output Option**                            **Maximum disk storage
                                               requirement**

  No Daily or Hourly .bin output               5 Mb

  Only Daily .bin output                       15 Mb

  Both Daily and Hourly .bin output            50 Mb
  -------------------------------------------- --------------------------

### Software

The following table defines the software dependencies currently en
force:

  -------------- ------------- -------------------- --------------------------------
  **Software**   **Version**   **Description**      **Available at**

  C Compiler     User          Compiler (program    <http://gcc.gnu.org/>
                 preference    developed under gcc) 

  Scripting      Bash shell    Scripting tools      Local machine executing analysis

  GMT            Latest        Plotting tool        <http://gmt.soest.hawaii.edu/>
                 available                          

  ImageMagick    Latest        Image manipulation   <http://www.imagemagick.org/>
                 available     tool                 
  -------------- ------------- -------------------- --------------------------------

## PDF Source Code Organization

The following table defines the directories and files which make up the
source tree of the PDF Analysis System:

+---------------------+------------------------------------------------+
| **Directory/File**  | **Description**                                |
+---------------------+------------------------------------------------+
| PDF                 | Root system directory                          |
+---------------------+------------------------------------------------+
| PDF/PROD            | Production directory containing production     |
|                     | relevant files                                 |
+---------------------+------------------------------------------------+
| PDF/PROD/bin        | Directory containing shells and executables,   |
+---------------------+------------------------------------------------+
| PDF/PROD/script     | Directory containing executable scripts        |
+---------------------+------------------------------------------------+
| PDF/PROD/support    | Directory containing all necessary production  |
|                     | support files                                  |
+---------------------+------------------------------------------------+
| PDF/PROD/helper     | Directory containing helper scripts (system    |
|                     | mgmt, etc.)                                    |
+---------------------+------------------------------------------------+
| PDF/src             | Directory holding all source code:             |
|                     |                                                |
|                     | -   PDF analysis program                       |
|                     |                                                |
|                     | -   GMT plotting script                        |
|                     |                                                |
|                     | -   Execution scripts                          |
+---------------------+------------------------------------------------+
| P                   | Directory holding all source code for version  |
| DF/src/v*x*.*x*.*x* | *x*.*x*.*x* of the system                      |
+---------------------+------------------------------------------------+
| PDF/src/            | Source code directory of analysis program (C   |
| v*                  | code)                                          |
| x*.*x*.*x*/analysis |                                                |
+---------------------+------------------------------------------------+
| PDF/src/            | Miniseed data file reader source code - as     |
| v*x*.*x*            | library to main()                              |
| .*x*/analysis/mseed |                                                |
+---------------------+------------------------------------------------+
| PDF/src/            | Instrument response interpreter source code -  |
| v*x*.*x             | as library to main()                           |
| *.*x*/analysis/resp |                                                |
+---------------------+------------------------------------------------+
| PDF/src/            | Directory holding GMT source code - scripts    |
| v*x*.*x*.*x*/GMT    | and support files                              |
+---------------------+------------------------------------------------+
| PDF/src/            | Directory holding execution scripts            |
| v*x*.*x*.*x*/script |                                                |
+---------------------+------------------------------------------------+

# Input and Output Files

## Input

The following table defines the directories and files which are required
input, see sections **System Configuration** and **PDF System
Execution** for full description of specification and use:

+-----------------------+----------------------------------------------+
| **Directory/File**    | **Description**                              |
+-----------------------+----------------------------------------------+
| Data Directory        | Directory holding the miniseed data files to |
|                       | be analyzed.                                 |
|                       |                                              |
|                       | **Note:** All data files requiring analysis  |
|                       | as part of a single execution must reside in |
|                       | this single directory.                       |
+-----------------------+----------------------------------------------+
| Miniseed Data Files   | Files to analyze, miniseed format only.      |
+-----------------------+----------------------------------------------+
| Analysis Directory    | Directory holding all output files.          |
|                       |                                              |
|                       | See section **Output** for a complete        |
|                       | description.                                 |
+-----------------------+----------------------------------------------+
| Response File         | Directory holding response files for         |
| Directory             | channels being analyzed.                     |
|                       |                                              |
|                       | See section **System Configuration** for a   |
|                       | complete discussion on set-up.               |
+-----------------------+----------------------------------------------+
| RESP.*N               | The file holding the response information    |
| TW*.*STN*.*LOC*.*CHN* | for the instrument and channel. This must be |
|                       | formatted as for input to the evresp()       |
|                       | function (format as produced by the rdseed   |
|                       | program).                                    |
|                       |                                              |
|                       | Where:                                       |
|                       |                                              |
|                       | *NTW* is the network name\                   |
|                       | *STN* is the station name\                   |
|                       | *LOC* is the location identifier\            |
|                       | *CHN* is the channel identifier              |
+-----------------------+----------------------------------------------+

##  

## Output

The following table defines the directories and files which are created
in the course of the PDF Analysis execution. All are located as
subdirectories to the analysis directory defined in the section
**Input** above and are automatically created in the course of
execution. Please consult **Appendix I -- File Formats** for a detailed
description of their contents.

+-----------------------+----------------------------------------------+
| **Directory/File**    | **Description**                              |
+-----------------------+----------------------------------------------+
| *NTW*.                | Graphical representation of analysis.        |
| *STN*.*LOC*.*CHN*.png |                                              |
+-----------------------+----------------------------------------------+
| Y*yyyy*               | Directory holding daily PSD .bin files, by   |
|                       | year                                         |
|                       |                                              |
|                       | Where:\                                      |
|                       | *yyyy* is the year                           |
+-----------------------+----------------------------------------------+
| Y*yyyy*/HOUR          | Directory holding the hourly PSD .bin files  |
+-----------------------+----------------------------------------------+
| LOG                   | Directory holding the various log files      |
|                       | created during the course of execution.      |
+-----------------------+----------------------------------------------+
| wrk                   | Directory holding various work files         |
+-----------------------+----------------------------------------------+
| Y*yyyy*/D*jjj*.bin    | Files holding individual day\'s PSD analysis |
|                       | results (currently unused, for future use).  |
|                       |                                              |
|                       | Where:\                                      |
|                       | *jjj* is the julian day                      |
+-----------------------+----------------------------------------------+
| Y*yyyy*/HOUR/hour.idx | Index file to H*jjj*.bin file.               |
+-----------------------+----------------------------------------------+
| Y*                    | Files holding individual hour\'s PSD         |
| yyyy*/HOUR/H*jjj*.bin | analysis results (currently unused, for      |
|                       | future use).                                 |
+-----------------------+----------------------------------------------+
| LOG/*NTW*.            | Log file of analysis program.                |
| *STN*.*LOC*.*CHN*.log |                                              |
+-----------------------+----------------------------------------------+
| LOG/plotGMT.log       | Log file of GMT plotting program.            |
+-----------------------+----------------------------------------------+
| LOG/convert.log       | Log file of ImageMagick convert program,     |
|                       | nothing output for normal execution.         |
+-----------------------+----------------------------------------------+
| LO                    | Analysis program error file, by year and     |
| G/*NTW*.*STN*.*LOC*.* | julian day.                                  |
| CHN*.*yyyy*.*jjj*.err |                                              |
+-----------------------+----------------------------------------------+
| LOG/PDFanalysis.skp   | File listing those days when problems        |
|                       | occurred, information only.                  |
+-----------------------+----------------------------------------------+
| wrk/PDFanalysis.bin   | Cumulative dB-based .bin file, results to    |
|                       | graph are contained here.                    |
+-----------------------+----------------------------------------------+
| wrk/PDFanalysis.inf   | Information file holding various analysis    |
|                       | settings.                                    |
+-----------------------+----------------------------------------------+
| wr                    | Cumulative period-based .bin file.           |
| k/PDFanalysis*SR*.bin |                                              |
|                       | Where:\                                      |
|                       | *SR* is the sample rate of the channel       |
+-----------------------+----------------------------------------------+
| wr                    | Information file as before, sample-rate      |
| k/PDFanalysis*SR*.inf | specific.                                    |
+-----------------------+----------------------------------------------+
| wrk/PDFanalysis.sts   | File holding various statistics for analysis |
|                       | results, input to GMT.                       |
+-----------------------+----------------------------------------------+
| wrk/PDFanalysis.ps    | GMT postscript file output, deleted upon     |
|                       | conversion to .png file.                     |
+-----------------------+----------------------------------------------+
| wrk/pdf.grd           | GMT temp file, deleted upon completion of    |
|                       | GMT step.                                    |
+-----------------------+----------------------------------------------+

# System Configuration

Configuration of the PDF system amounts to the setup of various
directories and script variables. This section lays out these
requirements for the PDF system setup to result in a successful
installation and subsequent execution. Failure to define these precisely
as described herein will result in a nonfunctioning system.

**Appendix II** provides a checklist for each parameter and variable
which must be defined as part of system setup. Please print, define the
values accordingly, and supply them in their proper location.

## Data Directories

### MiniSeed Data Directory and Files

A directory is required to contain the miniseed data files to be
analyzed. This directory and the miniseed data files must adhere to the
following:

1.  All miniseed data files representing a single channel's worth of
    waveform data, for all time, must be contained within the same
    directory.

2.  All miniseed data files must contain exactly (or as close to) 1
    day's worth of data, from 00:00 hours to 24:00 hours.

3.  The directory structure must conform to the following conventions:

> *DATAROOT*/*NTW*/*STN*
>
> Where
>
> *DATAROOT* is the root directory of the miniseed data files (script
> variable of such specified below)
>
> *NTW* is the name of the network
>
> *STN* is the name of the station

4.  The name of the miniseed file itself must conform to the following
    naming convention:

> *STN*. *NTW*.*LOC*.*CHN*.*yyyy*.*jjj*
>
> Where
>
> *STN* is the name of the station
>
> *NTW* is the name of the network
>
> *LOC* is the location identifier
>
> *CHN* is the channel identifier
>
> *yyyy* is the year of the data file
>
> *jjj* is the julian day of the data file

(Note: Where no location identifier exists, field should be null. This
would render, for example, a filename for station ATKA and network AK
as: ATKA.AK..BHE.2004.261)

Assuming your directory structure and miniseed data files do not
naturally conform to these requirements, this directory structure and
filenaming convention can be easily accommodated for through the
following:

-   Create the fixed directory structure itself: *DATAROOT*/*NTW*/*STN*

-   For each miniseed data file, create softlinks (ln --s) to the
    actual/real miniseed data files such that the naming convention
    above is adhered to.

Further, this can be automated via a script rendering this requirement
as trivial as possible. Please see the script linkMseed.US (located in
pdf/PROD/helper/linkmseed) for an example and modify as necessary.

Because the filenaming convention uniquely identifies the channel of
data, this directory may contain all miniseed data file for all channels
of a station. It is not necessary to create separate directories for
each channel, rather, a separate directory only for the station itself
and containing the miniseed data files for all channels.

### Response File Directory

A directory must exist containing all response files used to deconvolve
the signal back to absolute ground motion in the course of analysis.
This directory and the files themselves must adhere to the following:

1.  The directory may be specified as per user desires/requirements. No
    specific directory structure requirement exists. The directory
    holding these response files must be specified in two places: in the
    script variable RESPDIR (see section **Script Vaiables** below), and
    within the PDFuser.h file of the PDF analysis program source code
    (see section **Source Code Header File Modification** below).

2.  The filename of the response file must conform to the following
    naming convention:

> RESP.*NTW*.*STN*.*LOC*.*CHN*
>
> Where
>
> RESP is exactly as specified: RESP
>
> *NTW* is the name of the network
>
> *STN* is the name of the station
>
> *LOC* is the location identifier

*CHN* is the channel identifier

> (Note: This naming convention follows from the response file output
> generated by the rdseed program. As before, where no location
> identifier exists, field should be null.)

3.  The internal format of the response file information must conform to
    the format produced by the rdseed program, subsequently readable by
    evresp().

### Web Directory

A directory must be created to collect all .png files created during the
course of execution. The .png files are contained in the analysis
directory for the channel being analyzed, making collective viewing
annoying since all are held within disparate directories. This annoyance
is alleviated through the existence of this directory.

Create a directory for these to be contained in and define this location
in the **.vars-user** file. With this directory, the last action in the
course of analysis is for a softlink to be created in this directory
pointing to the .png file found in the analysis directory.

Additionally, if it is desired to publish the results, it is this
directory that can be made available to the web in whatever manner/means
appropriate.

## Script Variables 

The following script variables are installation specific and must be
predefined by the user and provided in the shell script file
**.vars-user** (located in directory PDF) before the system can be
installed. Failure to do so will result in a non-functioning system.

  ---------------- ------------------------------------------------------
  **Script         **Description**
  variable name**  

  PDFROOT          Root directory of PDF analysis system (directory
                   holding the .vars-user file)

  WEBDIR           Directory of collected .png files

  RESPDIR          Directory holding response files

  DATAROOT         Root directory of miniseed data files (parent to
                   *NTW*/*STN*)

  STATSROOT        Root directory of PDF analysis results/statistics

  GMTROOT          GMT installation root directory

  IMROOT           ImageMagick installation root directory
  ---------------- ------------------------------------------------------

## Source Code Header File Modification

The sole configuration requirement within the source code of the PDF
analysis program is the following #define parameter to be specified:
(Note: this must be the same as defined as part of the Script Variables
above.)

  ---------------- ----------------------- -----------------------------------------
  **#define        **Description**         **Location**
  parameter**                              

  #define RESPDIR  Directory holding       PDF/src/v*x*.*x*.*x*/analysis/PDFuser.h
                   response files, inside  
                   quotes "".              
  ---------------- ----------------------- -----------------------------------------

# System Compilation and Installation

## Compilation

Compilation of the PDF Analysis program employs straightforward C/Unix
standards, that is, a **C compiler** and **make**. In addition to the
analysis portion of the program, there are two subdirectories of
libraries requiring compilation as well. As such, a script is provided
that will traverse each of these subdirectories, making the dependent
libraries in turn. This script is located in the PDF Analysis source
directory and conforms to the following invocation specifications:

**makesh \[ *clean \|* *all* \]**

where

***clean*** will execute **make clean**, removing all dependent
libraries and object files.

***all*** will execute **make all** in each directory of the PDF
analysis program, creating all dependent libraries and object files
necessary to ultimately link the PDF analysis executable.

Alternatively, the program may be built when installing the system as a
whole, alleviating the need to compile and link by hand. Please see the
section **Installation** below for details.

### Compiler Options

Two compile-time options exist for the PDF Analysis program. Namely,
defining whether or not daily and(or) hourly PSD information is output.
(Please see section **Requirements: Hardware** for detailed overall disk
storage requirements.)

With daily PSD information output, cumulative .bin files are generated
for each day analyzed (amounting to \~30Kb/day/channel analyzed).

With hourly PSD information output, .bin files are generated for each
hour analyzed (amounting to \~100Kb/day/channel analyzed).

The system is delivered, by default, to output daily and hourly .bin
files. Output of this data is anticipated to be used in future versions
of the software, such that existence of these files will allow PDFs to
be produced for specific user-defined time periods. For example, a PDF
graph representing only the months of January thru March or a PDF graph
representing all months but only between the hours of 6AM and 6PM.

If it is anticipated that these more specific sorts of analyses will be
of interest, no action is required, daily and hourly .bin files will be
generated.

If this is not desired, or disk space is an issue, both daily and hourly
.bin file generation may be suppressed. The following table defines
these compile time options:

  ---------------------------- ------------------------------------------
  **Compiler option**          **Effect**

  -DNO_DAILY_PSD               No daily PSD .bin files output

  -DNO_HOURLY_PSD              No hourly PSD .bin files output
  ---------------------------- ------------------------------------------

Either or both (they are mutually independent) of these options can be
specified in the **CFLAGS** section of the **Makefile** for the main PDF
Analysis program. The resulting executable will subsequently **NOT**
output incremental PSD information.

Since these are compiler options, these settings have a system-wide
influence, that is, these options **cannot** be implemented on a per
channel basis. (One way around this, however, would be to install more
than a single system.)

## Installation

Installation is provided via the shell script **installPDF** located in
the directory PDF and provides for the following functionality:

1.  optionally compiles the PDF Analysis program,

2.  copies all relevant files to the PROD directory, and

3\. conforms to the following usages:

**command**: *installPDF --h*

**output**: Usage: install \[-h\] \[make\] version#

**description:** prints the usage for the command.

**command**: *installPDF v1.1*

**output**: Copying v1.1 executables and support files to PROD dir...

**description:** installs all relevant executables, scripts and support
files for *version#* to the PROD directory structure. (Note: command
line argument *version#* must be as specified in the PDF source
directory structure.)

**command**: *installPDF make v1.1*

**output**: Compiling v1.1 PDF Analysis program...

Copying v1.1 executables and support files to PROD dir...

**description:** as for command *installPDF v1.1*, however, cleans and
compiles the PDF analysis program before copying and installing to the
PROD directory structure (recommended for first install since no object
files exist as part of delivery).

# PDF System Execution

System execution comes in the form of two scripts, **executePDF** and
**PDFscript** (both located in PDF/PROD/bin).

**PDFscript** is a shell script template used to create the individual
channel-specific execution script. This script is ultimately responsible
for the PDF analysis execution of a specific channel.

The **executePDF** script executes all channel-specific scripts located
in PDF/PROD/script in turn.

## Channel-Specific Shell Script

Execution of the PDF Analysis System is provided in the form of a shell
executable script (**PDFscript**) responsible for carrying out the three
steps of execution described in section **PDF Analysis System Overview:
Description**. This execution script is created by replacing various
strings in the generic file PDFscript with execution-specific values,
thus creating a unique script for each channel to be analyzed.

This channel-specific executable shell can be easily created using the
following shell script command:

**makePDFscript** *NTW STN LOC CHN*

where

> *NTW* is the network name\
> *STN* is the station name\
> *LOC* is the location identifier (use \-- for no location)\
> *CHN* is the channel identifier

This will create the channel-specific script to be executed, named
*NTW*.*STN*.*LOC*.*CHN*.sh and saved to the directory PDF/PROD/script.
In addition, the analysis directory will be created if it does not exist
(assuming the STATSROOT directory exists).

Once this script has been created for a specific channel, it can be
executed repeatedly (daily, weekly, monthly, as desired) to update the
analysis results.

## Overall Execution

Executing the script **executePDF** will result in all scripts located
in PDF/PROD/script to be executed in turn. Specifically, it will execute
all files having ".sh" as their filename suffix. Thus, individual
analyses can be turned on and off by renaming the suffix of the
executable script in question.

A simple logfile of **executePDF**, detailing the channels analyzed, is
generated and written to the file PDF/PROD/LOG/PDF.log.

Further, this process may be automated by using the UNIX **crontab**
command. At specified times, merely execute the **executePDF** script,
and all analyses will be performed and updated.

## Execution Features

Please note the following features of the PDF analysis system:

1.  Analysis is performed against all data files found in the specified
    data directory only up to and until 2 days prior to analysis
    execution date. This allows for systems where data availability can
    suffer up to 2 days of latency.

2.  The program does cross the day boundary to analyze the last hour of
    data held within the miniseed files. As such, the last file
    identified for analysis is not fully analyzed; it is treated in
    subsequent executions.

3.  When crossing the day boundary, program assumes data are coincident
    if ending time and starting time of respective miniseed files differ
    by less than one sample (1) of time. Where data are identified not
    to be coincident, an error message is output to the channel-specific
    log file.

## Error Processing

Error handling is very much dependent on the type of error encountered.
The following table lists the major errors that may be encountered, how
each is handled, and suggested follow-up action.

  ------------- ---------- ----------------------- -------------------------
  **Error**     **Type**   **How handled**         **User follow up**

  Response File Fatal      Analysis execution      Provide proper response
  not found                suspended; error        file, verify naming
                           message written to Log  convention is adhered to.
                           file                    

  Response      Fatal      Analysis execution      Provide file containing
  Information              suspended; error        response information for
  not found                message written to Log  appropriate date/time
                           file                    range, verify file format
                                                   is adhered to.

  Error reading Nonfatal   Analysis execution      Determine if miniseed
  miniseed data            skips this day of data; data file can be
  file                     error message written   repaired.
                           to day-specific error   
                           file located in LOG     
                           directory of analysis   
                           output.                 

  Internal      Fatal      Analysis execution      Contact
  Processing               suspended               <riboaz@xs4all.nl> with
  Error                                            all relevant information

  No files ever Nonfatal   Program successfully    Verify miniseed directory
  found to                 executes but nothing    structure and filenaming
  analyze                  analyzed                conventions are adhered
                                                   to.

  Unable to     Fatal      Analysis execution      Confirm existence and
  create or                suspended               access permissions of
  access                                           directory in question.
  directories                                      
  ------------- ---------- ----------------------- -------------------------

# Release Notes

## Current Limitations

The limitations are defined to be:

1.  Unable to analyze long period channels, limited to 20 samples/sec or
    more,

2.  unable to provide analysis for user-defined time periods, only
    analysis of all data available is currently provided for,

3.  output provided to end-user currently limited to .png graphical file
    format, and

4.  unable to analyze any data prior to the last day analyzed. This
    means that the program cannot fill in gaps nor replace the results
    of previously analyzed data. This will be treated in a future
    release.

## Version Control

This section defines the current and historical releases of the PDF
Analysis System.

### Version 1.1

Release Date: 29 October 2004

**Modifications**

1.  Stand-alone version created and made available for general release.

# Appdendix I -- File Formats

This appendix defines the formats of the various files produced by the
PDF analysis system.

## Djjj.bin File

Definition: Cumulative db-based .bin file holding **daily** PSD analyses
for julian day *jjj*.

Directory: Y*yyyy*

Internal Format:

-   Data Format: ASCII

-   Individual lines each defining:

*FREQ POWER #HITS*

Where:

*FREQ* is the frequency (in Hz)

*POWER* is the power bin (in dB)

*#HITS* is the number of times

## Hour.idx File

Definition: Index file to H*jjj*.bin file, index defined by julian day
and *HH:MM* start time of PSD.

Directory: Y*yyyy/*HOUR

Internal Format:

-   Data Format: ASCII

-   Individual lines each containing:

*JDAY HH:MM REF*

Where:

*JDAY* is the julian day\
*HH:MM* is the hour and minute start time of the PSD\
*REF* is the reference identifier, for accessing/extracting from the
H*jjj*.bin file

## Hjjj.bin File

Definition: Cumulative db-based .bin file holding **hourly** PSD
analyses for julian day *jjj*.

Directory: wrk

Internal Format:

-   Data Format: ASCII

-   Individual lines each containing:

*REF FREQ POWER*

Where:

*REF* is the reference identifier from the hour.idx file\
*FREQ* is the frequency (in Hz)\
*POWER* is the power bin (in dB)

## PDFAnalysis.bin File

Definition: Cumulative db-based .bin file holding **overall** PSD
probabilities for julian day *jjj*.

Directory: wrk

Internal Format:

-   Data Format: ASCII

-   Individual lines each defining:

*FREQ POWER PROB*

Where:

*FREQ* is the frequency (in seconds)

*POWER* is the power bin (in dB)

*PROB* is the normalized (to probability) number of hits

## PDFAnalysis.inf File

Definition: Information file containing various settings/values
pertaining to analysis.

Directory: wrk

Internal Format:

-   Data Format: ASCII

-   Individual lines each defining:

*VALUE* :SETTING

-   With the following SETTINGs currently being provide for, appearing
    in the following order:

  ------------------------ ----------------------------------------------
  **Setting**              **Definition**

  Analysis Start Date      Start day of the analysis (format: *YYYY:JJJ*)

  Analysis Stop Date       Stop day of the analysis (format: *YYYY:JJJ*)

  Total Number of Days     Total number of days analyzed

  Total Number of PSD\'s   Total number of PSD's making up the analysis

  Total Number of Problem  Total number of days encountering a problem
  Days                     (information only)

  SAMPLE RATE              Sample rate of the channel

  NETWORK                  Network name

  STATION                  Station name

  LOCATION                 Location identifier

  CHANNEL                  Channel identifier

  NYQUIST                  Nyquist value for this analysis
  ------------------------ ----------------------------------------------

## PDFanalysis.sts File

Definition: File holding various statistics for this analysis.

Directory: wrk

Internal Format:

-   Data Format: ASCII

-   Individual lines each defining:

*FREQ MIN AVE 50% 90% MAX MODE*

Where:

*FREQ* is the frequency in question (in Hz)

*MIN* is the minimum PSD value

*AVE* is the average PSD value

*50%* is the 50th percentile PSD value

*90%* is the 90th percentile PSD value

*MAX* is the maximum PSD value

*MODE* is the mode PSD value (most common)

## PDFAnalysisSR.bin File

Definition: Cumulative db-based .bin file holding **overall** PSD for
julian day *jjj*.

Directory: wrk

Internal Format:

-   Data Format: ASCII

-   Individual lines each defining:

*FREQ POWER PROB*

Where:

*FREQ* is the frequency (in Hz)

*POWER* is the power bin (in dB)

*PROB* is the number of hits for this bin

# Appendix II -- Installation and Configuration Checklist

This appendix contains a table listing all of the required configuration
parameters. Please print this page, it provides the appropriate values
to be used. Confirm that all values have been properly defined in the
specified file(s).

  ------------- ------------------- ----------------------------------------- ---------------------------
  **Config      **Description**     **Where specified**                       **Value**
  parameter**                                                                 

  PDFROOT       Root directory of   PDF/.vars-user file                       
                PDF analysis system                                           

  WEBDIR        Directory of .png   PDF/.vars-user file                       
                files accessible                                              
                from www                                                      

  RESPDIR       Directory           PDF/.vars-user file                       
                containing response                                           
                files                                                         

  DATAROOT      Root directory of   PDF/.vars-user file                       
                miniseed data files                                           

  STATSROOT     Root directory of   PDF/.vars-user file                       
                PDF analysis                                                  
                results                                                       

  GMTROOT       GMT installation    PDF/.vars-user file                       
                root directory                                                

  IMROOT        ImageMagick         PDF/.vars-user file                       
                installation root                                             
                directory                                                     

  RESPDIR       Directory           PDF/src/v*x*.*x*.*x*/analysis/PDFuser.h   
                containing response                                           
                files                                                         
  ------------- ------------------- ----------------------------------------- ---------------------------

[^1]: Boaz Consultancy