Computation of Geomagnetic Transfer Functions Using … derivation of this analysis can be found in Bendat and Piersol (Random Data: ... The following description uses notation similar

UNITED STATES DEPARTMENT OF THE INTERIOR

GEOLOGICAL SURVEY

Computation of Geomagnetic Transfer Functions

Using the HP9640A

by

David V. Fitterman

Open-File Report 81-361

1981

This report is preliminary and has not been reviewed for conformity with the U.S. Geological Survey editorial standards. Any use of trade names is for descriptive purposes only and does not imply endorsement by the USGS.

Contents

Page

1. Introduction 1

2. Computation of Transfer Functions 3

3. Program AUTRN 10

4. Program STACK 23

5. Program LSTRF 28

6. Program PLTRF 29

7. Appendix A - Data Formats 33

8. Appendix B - User's Guide 39

9- Appendix C - Program Listings 57

Figures

Page

Figure 2.1 Linear system representation of transfer functions 4

3.1 Flow diagram of program AUTRN 12

3.2 Amplitude and phase response of low-pass filter used by AUTR7 18

3.3 Command sequence to load program AUTRN 20

3.4 Command sequences contained in files /AUTRN and \AUTRN 21

4.1 Command sequence to load program STACK 25

4.2 Command sequences contained in files /STACK and \STACK 26

6.1 Command sequences contained in files /PLTRF and \PLTRF 32

8.1 Terminal output for program AUTRN 40

8.2 Example of input data plotting by AUTRN 41

8.3 Example of summary printed by AUTRN 43

8.4 Example of input to AUTRN showing user selected frequency

bands 45

8.5 Example of block and stack summaries 46

8.6 Commands to terminate AUTRN and run STACK 49

8.7 Summary of program STACK input files 50

8.8 Example of input of stacking parameters 51

8.9 Use of programs LSTRF and PLTRF 53

8.10 Example of summary printed by program LSTRF 54

8.11 Example of an induction arrow plot 55

ii

Tables

Page

Table. 1.1 Logical unit assignments 2

7.1 Integer format file header record format 34

7.2 Transfer function record format 37

iii

1. Introduction

This report describes a collection of programs used in the calculation,

stacking, and display of geomagnetic transfer functions. A description of the

procedure used to estimate the transfer functions is given along with a

detailed explanation of how the programs work. The programs and their

functions are: (1) AUTRN - computation of spectra and transfer function of a

data segment, (2) STACK - stacking of spectra from different data segments

and computing resulting transfer function, (3) LSTRF - listing of transfer

function files, and (4) PLTRF - plotting of induction arrows and error

estimates from transfer function files.

Software and Hardware Requirements

Most of the software is written in HP (Hewlett-Packard) FORTRAN IV with

some subroutines written in HP Assembly Language.

Some of the assembly-language routines make use of special instructions

which are not found on the older HP-2100 CPU. These instructions will have to

be simulated if the routines are not run on an HP-21MX or new CPU.

The software was designed to run on an HP-9640A Multiprogramming System,

which has been superseded by the newer HP-1000. The essential hardware are a

CPU, a disk drive, a terminal, and a printer/plotter. The plotter that was

used in the design of the system was a Varian Statos 33; it is used by

programs AUTRN and PLTRF. Plotter commands can be removed from AUTRN for

installations not having the proper hardware without affecting the rest of the

program's operation.

The logical-unit assignments used in all of the programs are shown in

Table 1.1.

Introduction

Table 1.1 Logical unit assignments

LU Name Device

1 LUTTY terminal

6 LUPRT line printer/plotter

Access to data files is done by means of the Spool Monitor Package (SMP),

which is also referred to as the File Manager. Consult the HP Batch - Spool

Monitor Reference Manual for more details.

2. Computation of Transfer Functions

Geomagnetic transfer functions are used to describe the linear

relationship between the vertical and horizontal components of magnetic field

variations at a particular frequency or frequency band. We begin with the

northward (X), eastward (Y), and downward (Z) magnetic-field components and

transform them into the frequency domain. The various power and cross power

spectra are estimated for different frequency bands. Then the linear system

of equations which relates the input and output power spectra are solved. A

detailed derivation of this analysis can be found in Bendat and Piersol

(Random Data: Analysis and Measurement Procedures, Wiley-Tnterscience, 407 p.,

1971).

The following description uses notation similar to that of Bendat and

Piersol. The three components of magnetic field are usually referred to as X,

Y, and Z corresponding to the northward, eastward, and downward directions.

For ease of notation we consider the inputs of the system as channels 1 and 2,

which correspond to components X and Y, while the system output (Z field) is

channel y (see Figure 2.1). All inputs as a group are referred to as x. We

use the symbol X^ to refer to the Fourier transform of channel x^. Thus X^

and X2 refer to the Fourier transform of the two inputs, while Xy is the

Fourier transform of the system output. The following paragraphs outline the

steps in computing the transfer functions, coherency functions, and error

estimates.

We define the cross power spectra as

su - < Y 2- !where the angle brackets represent averaging over frequency bands, and the

* asterisk denotes complex conjugate. Notice that S . = S. .

Transfer Functions

Figure 2.1 Linear system representation of transfer functions. The magnetic

field components are X, Y, and Z. For notation purposes in

section 2, inputs are designated by numbers, the output by y and

all of the inputs together by x.

X(north)

channel 1

Z (down) »channel y

Y(east)

channel 2

H9 (f)

Transfer Functions

The augmented spectral matrix [S,,____] is computedV XX

yy yi y2S ly S ll S 12

S2v S 21 S 22

2-2

from which one can form the output cross spectral vector

[S ly S 2y]

and the spectral matrix

2-3

12

S 21 S 22

2-4

The set of equations describing the linear system are then given by

where

[H] = [H! H2 ]

is the desired transfer function.

Solving (2-5) one obtains

[HI* = [S]-lxx

More specifically

H,S 22S ly " S 12 S 2y

ISxx

S ll S 2y " S 21 S ly

2-5

2-6

2-7

2-8a

2-8bxx

Transfer Functions

This expression is the same as would be obtained by using a least-squares

technique to reduce the residual vertical field for a two input system.

For purposes of determining how good the transfer function estimates are,

coherence functions are computed. The value of the coherency varies between

zero and unity. A large coherence between two signals indicates that one of

the signals can be used along with the appropriate transfer function to obtain

a good prediction of the other function. The following coherence functions

are computed.2 |S 12'G 2-9a

ll > 22

2 |Syl |2

8Syy

To easily compute the partial and multiple coherence, it is useful to

first calculate the residual cross spectra. Consider for the moment the

residual cross spectra, S^y> 2* This is the cross spectra between the residual

of input channel 1 and the output y, and their respective linear least-squares

predicted values using channel 2 as the predictor. The six residual cross

spectra computed are:

S 11.2 ' S ll (1 - G 12>

S22.1 ' S22 (1 - G 12 )

S . = S (1 - G2 ) 2-10c yy.l yy yl'

Transfer Functions

V2 = syy

<; = <? c\ - - ^ ?-i Of S2y-l S2y (1 Su S2y) 2 10f

The partial coherencies, which is the coherence between one input and the

output when the effect of all other inputs is removed, are given by

G2

|q |2G2 . Is 2y-i 2_ llb** * S22.1Syyl

Finally the multiple coherence, which is the coherence between all the inputs

and the outputs, is9 IS I

G = 1 - , ^X , 2-12y.x S SJ yy xxThe partial and multiple coherency functions give a measure of how well

the output can be predicted by the various inputs. I have defined a quality

factor, QF, which can sometimes be used as a measure of how reliable the

transfer function estimate is, as the geometric mean of the two partial and

the multiple coherencies.

QF = (G2 . 0 G2 .G2 ) 1/3 2-13 x ly.2 2y.l y.x

This variable ranges between 0 and 1. Whenever the two horizontal components

of magnetic field are linearly polarized, there are not enough degrees of

freedom in the data to estimate both H^ and I^- In this case, the transfer

function can then be represented by a single complex number, and the quality

Transfer Functions

factor QF can be shown to equal zero. Thus the quality factor would warn

against using this data to estimate the transfer function of a two-input, one-

output system.

The last quantity computed is the formal random error of the transfer

function estimates. The squared random error for the two transfer functions

H^ and H£ are given by

r2 = K E Sit ,i - 1,2 2-14

whereS UC __ 13 O n,o 1 "~ nô np. _ yy 1 yl 2 y2 9 .

X* "~ 00 £.-LJb !2 b21

and

V as 4 -ri 9 1 fiK n-4 F4, n-4; 0.95 2 16

The function F is the F distribution for the 95% confidence level and n is the

number of degrees of freedom used in the estimate. If m harmonics are

combined to form the spectral estimates, then there are 2m degrees of freedom.

Three techniques are employed by program AIJTRN to obtain stable spectral

estimates. First, the individual 128-word long data blocks are multiplied by

a Banning (cosine bell) function in the time domain. Second, the spectral

values at adjacent frequencies are averaged together to obtain the spectral

estimates. Third, the spectral estimates from independent blocks of data are

added together.

In geomagnetic variation studies, the usual quantity displayed is not the

transfer functions, but the in-phase and out-of-phase induction arrows which

are derived from them. Let the two transfer functions be given by

H. = hr.+ j hi. 2-17a

and

H2 " hr 2 + j hi 2 2"17b

where j is the square root of -1.

8

Transfer Functions

The magnitude of the in-phase and out-of-phase induction arrows are

2 2 1 /? Ai = (hr l + hr 2' 2~ 18a

and

A = (hi? + hi.) 1/2 2-18bO 1 L

respectively. The azimuths of these arrows with respect to the channel 1 (X)

direction are

6 i = tan~ 1 (hr 2/hr 1 ) 2-19a

and

00 = tan~ 1 (hi2 /hi 1 ) 2-19b

These quantities are also computed by program AUTRN. When induction arrows

are plotted, 180° is normally added to 0^ so that the in-phase arrows point in

the direction of current concentrations. This convention is used by program

PLTRF.

3. Program AUTRN

Purpose

Program AIJTRN is used to automatically compute geomagnetic transfer

functions. It uses a scheme similar to one developed by W. D. Stanley (oral

communication, 1979) to compute the transfer function over a wide range of

frequencies. The data set is divided into 128-point blocks, which are

analyzed. The data are then low-pass filtered and decimated, saving every

other data point. The new data sequence is now analyzed to obtain transfer

functions at periods twice as great as the previous analysis. This procedure

is called cascading, and is repeated up to seven times to obtain a maximum of

eight analysis-frequency sets. The longest input data set which can be

handled is 32,767 words. The advantage of this technique is that only short

data segments need to be handled.

Output from AIJTRN includes the stacked spectral matrix, the transfer

function, induction vectors, and error estimates. These data are stored in a

file and printed. Intermediate results, including plots of the original time

sequence, power spectra plots, the results of the analysis of individual data

blocks, and the stacked results every time they are updated, can be obtained

at the discretion of the user. Detailed descriptions of the user-supplied

input parameters are given in Appendix B.

Description

The program consists of a very short main program and eight segments

which are scheduled by the main program as needed via system EXEC calls. The

main program allocates most of the storage used by the segments. This storage

resides in a large common block. Control is returned to the main program by

means of GO TO statements that branch to labels which are in the common

block. In the main program these labels are assigned to statement numbers.

10

Program AUTRN

The labels are all named LOOPi where i is an integer between 1 and 8.

Figure 3.1 shows a flow diagram for AUTRN, which should be referred to

during the following discussion of the functioning of the main program. AUTRN

starts by initializing some parameters in the common block and then schedules

segment AUTR1. AUTR1 inputs the X, Y, and Z field data and creates work files

into which it places the data. The user provides some processing parameters

at this point. If any errors occur in AUTR1, flag ISTOP is set. Upon exiting

from AIJTR1, the main program checks to see if there were any errors. If there

were none, processing continues. If an error occurred the user is asked if

anymore data are to be processed.

AUTRN now enters a main processing loop and schedules AIJTR2. This

segment initializes some work buffers on all passes, and inputs some more

processing parameters only on the first time it is called. The next segment

scheduled, AUTR3, computes the Fourier transforms, spectral matrix, and the

quality factor for one block of data. The results of the individual block

analyses can be printed if desired. Stacking of the data takes place in

AUTR4. If the intermediate stacked data are to be printed and plotted, AUTR5

is scheduled, otherwise control transfers to LOOP5 in AUTRN and the next block

is processed.

When the last block has been processed, AIJTR6 is called to output the

results to a disk file. If stacking was based on the quality factor, and no

data were stacked and quality factor lowering is allowed, AUTR6 exits to LOOP2

and reprocesses the data for this decimation level with a lower quality factor

threshold for stacking results. The number of threshold lowerings allowed at

all decimation level are set by the user.

If the data are to be decimated, AIJTR7 is scheduled, which low-pass

filters and saves every other data point. Plots of the resulting time

11

Program AUTRN

Figure 3.1 Flow diagram of program AUTRN. The large circles refer to labels

in the main program. The double wide arrows indicate transfer

control to or from a program segment.

12

Figure 3-1 Continued

Program ADTRN

Caff yûr ^rfec*

call /VT«5

blocks

^/^/HJTK?Wo-ftosj, <fee,lu»fe; />/«f- c/»// Aimes

13

Program ACTTRN

sequences can be obtained if desired. The data are then processed to obtain

analyses at lower frequencies. When the last decimation level has been

reached, AUTR8 is scheduled. This segment writes a summary of the results on

the line printer, closes the result file, and purges the temporary work

files. AUTRN then asks if any more data are to be processed.

This completes the description of the overall functioning of AUTRN. Each

segment will now be discussed in detail.

AUTR1 opens files containing the X, Y, and Z components of the magnetic

field. These files are in Integer Format (see Appendix A). The data are

converted to floating point format and stored in Temporary Real Format files

named "..XX..", "..YY..", and "..ZZ.." respectively. If any of the input

files can not be opened or if the temporary work files cannot be created, all

open files are closed and any temporary work files are purged. The three

input files are checked to insure that they contain the same number of data

points, and have the same effective sample interval.

After all the temporary work files have been created, several parameters

that control processing are input. These include the number of decimation

levels the processing is to be carried through, and whether or not overlapping

of the input data sequence is to be used. If the former option is selected,

each analysis contains the last 64 data points of the previous data block plus

64 new data points. When this type of processing is used, the number of

degrees of freedom cannot be easily determined, but will be less than the

indicated value since some of the data are used twice. In the case of all

data being stacked, the degrees of freedom will be large by a factor of 2. A

consequence of this is that the transfer function error estimates will be

biased downward. After the question about overlapping is answered, control

transfers back to AUTRN.

14

Program AIJTRN

The next segment, AUTR2, requests more information from the user which

controls the processing. The user begins by supplying the name of the result

file. If the file cannot be created, the user is asked for another file name.

The transfer function analysis is carried out in 4 frequency bands at

each decimation level. Since there are 128 points used in the Fourier

analysis, there are 64 harmonics which can be used in the spectral

computations. Experience has shown that the harmonics above number 32 are

quite noisy and not well suited for analysis. AUTR2 displays the default

frequency averaging bands that are used unless a different set of harmonics is

selected.

The spectra from each block are considered for stacking only if the

quality factor (QF) exceeds a user-specified quality-factor cutoff (QFCUT).

Notice that a value of zero will result in all data being stacked. Simply

because a block's QF exceeds the cutoff value does not mean the data will be

stacked, but rather the process depends on the type of stack specified to

AUTR2. There are three types of stacks: (1) straight, (2) non-degrading, and

(3) non-degrading with QF lowering. For a straight stack, the data are

stacked if QF exceeds QFCUT. A non-degrading stack requires that the QF

exceed QFCUT, and that adding the data to the previously stacked data does not

lower the QF of the stacked data (QFSTK) below QFCUT-0.1. It is possible to

set QFCUT high enough that no data are stacked in any of the 4 frequency bands

at a given decimation level. If this occurs and a non-degrading with QF

lowering stack has been specified, QFCUT is lowered by 0.10 and the analysis

for this decimation level repeated. When this option is selected, the user

can specify how many lower ings of QFCUT are to be performed. When processing

of the current decimation level is completed, QFCUT is returned to its

original value.

15

Program AIJTRN

The user can also specify when the results of the individual block

analyses are reported. There are three choices: (1) report all results,

(2) report only results when data have been stacked, and (3) do not report any

results. Finally the user furnishes a parameter that determines when the

original data sequences are plotted. When the data sequence length is less

than or equal to the specified number of blocks, the X, Y, and Z time series

are plotted.

The input of processing control parameters by AUTR2 is done only before

the first cascade level is started. A second function of AUTR2 is to

initialize storage buffers. This function is performed at all cascade levels.

The "work horse" segment is AUTR3 which performs the spectral

computations. The three field components are read and a linear trend and mean

are removed. A cosine bell is applied to the data before the discrete Fourier

transform is computed. The spectral matrix is formed for the four harmonic

bands specified. From these quantities the ordinary coherence, residual cross

spectra, multiple coherence, partial coherencies, transfer functions, and

quality factor are computed. If the quality factor exceeds the threshold

value, the spectra are saved for possible stacking. These intermediate

results, called "BLOCK RESULTS" are printed if the "ALL DATA" print mode was

selected, or if the "STACK DATA" print mode was selected and QF exceeds

QFCUT. Control then returns to the main program.

Segment AUTR4 determines if the spectral matrix computed by AUTR3 should

be added to the stack. If the QF for a given frequency band exceeds the

threshold value, it is stacked. After a value is stacked, the QF of the stack

is computed. If a non-degrading stack has been called for, and the last

addition to the stack lowered QFSTK below QFCUT-0.1, the last addition is

removed. If the spectral values are removed, the coherencies, residual

16

Program AUTRN

spectra, and quality factor are recomputed.

The transfer function and error estimates of the stacked spectra are

computed. If additions were made to the spectral stack, and the "ALL DATA" or

"STACKED DATA" print modes were selected, then the "STACK RESULTS" are

printed. When stack results are printed, AUTR5 is also scheduled to plot the

X, Y, and Z data for this block as well as their power spectra.

When there are no more data blocks at this decimation level to process,

AUTR6 is scheduled. This segment checks to see if QF lowering is being

used. When it is, data must have been stacked in at least one of the four

frequency bands. If it wasn't, and the QF can still be lowered (by 0.1), it

is and the processing of this decimation level starts again. When QF lowering

is not being used or if some data were stacked, the results are written to the

output file for future use.

If more decimation levels are to be processed the data are now low-pass

filtered and decimated by segment AUTR7. This segment uses a 16-point filter,

which is convolved with the three input channels. The amplitude and phase

response of the filter are shown in Figure 3.2. The phase introduced by this

filter does not affect the calculations since we are only concerned about the

relative phase of the different channels.

AUTR7 also has a facility for plotting the input data sequences after

they have been low-pass filtered. The data are plotted whenever the total

number of blocks is less than or equal to the value specified by the user.

When the last decimation level has been processed, segment AUTR8 prints a

summary of the results including the stacked spectral matrix and the transfer

function.

17

Program AIJTRN

Figure 3.2 Amplitude and phase response if low-pass filter used by AUTR7.

F RE Q U E N C Y D 0 M HIN D R T R 1 a tfr

120 -

8

I H

Ti.

H | | j.

1 5 9 13F R E Q . I H T E R'.,' R L = .83125c R E Q . WIH D U W = 8 TO .5

F R E Q U c. M C Y D U M R I N D fl T R < M R G >

^ ^ p- i-4 1

F F: L i ' I N T E R '.-' R L = .931 M R X ',' RLUE - 6.38642E

18

Program AIJTRN

Special Requirements

Program AUTRN creates three temporary work files named "..XX..",

"..YY..", and "..ZZ..". Files with these names must not exist when AUTRN is

run or processing will be halted. Under normal operating conditions, AUTRN

purges these files when it is done using them. If AUTRN is abnormally

terminated with an "OFF" command, these files should be purged by the user

before the program is rerun.

Program Loading

The loading of program AUTRN can be accomplished by issuing the commands

shown in Figure 3.3. The first module, named %REPLC, is used to replace any

calls to software routines .LET and .SET with the corresponding hardware

commands. The percent signs in front of the module names indicate that they

are relocatable modules. The loader is called to do a temporary, background

program load with segments.

Program Operation

Before AUTRN can be run, temporary ID segments must be assigned to it and

its eight segments. This is easily accomplished by issuing the command

:TR,/AUTRN

which restores AUTRN and its segments by executing the commands in Figure

3.4. The program is then executed with the command

:RU,AUTRN

After execution of AUTRN is completed, the temporary ID segments can be

returned to the system with the command

:TR,\AUTRN

which executes the commands in file \AUTRN shown in Figure 3.4.

19

Program AIJTRN

Figure 3.3 Command sequence to load program AUTRN.

LDAUTR T-00003 IS ON CR00300 USING 00003 BLKS R»0000

0001

0003

0003

0004

0005

0006

0007

000S

0009

0010

0011

0013

0013

0014

0015

00160017.001S

0019

0030

0031003300330034003500360037003800390030

'LG, 10MR,&REPLCMR,&AUTRNMR,?sDSPLAMR, &AUTR1MR, SAUTR3MR , %AUTR3MR, &FOUR1MR , & A U T P 4MR,s:AUTRSM R % M 0 V EMR,?s2EROMR , ! I NDOTMR , %AUTR6MR,%AUTR7MR,?i2EROMR,?sIND-OTMR,&MOVEMR , ^sAUTRSRU , LOADR , SSP! AUTRN'SP. AUTR1SP', AUTR2SP, AUTR3SP, AUTR4SP, AUTR5SP . AUTR6SPi AUTR7SP, AUTRSTR

20

Program ADTRN

Figure 3.4 Command sequence contained in files /AUTBN and \AUTRN. File

/AUTRN is used to restore program AUTRN, and file \AUTRN is used

to off it.

/AUTRN 1-00003 is ON 0800300 USING 00001 BLKS R-00000001000200030004

0005

0006

0007

0008

0009

0010

RP,AUTRN RP.AUTR1 RP;AUTR2 RP.AUTR3 RP;AUTR4 RP,AUTRS RP . AUTR6 RP;AUTR7 RP,AUTR3 TR

\AUTRN T-00003 IS ON CR0'£300 USING 00001 BLKS R-0000

0001

0002

00030004

0005

©006

0007

000S

0009

0010

OF, AUTRNOF, AUTR1OF. AUTR2OF; AUTR3OF, AUTR4OF, AUTRSOF. AUTR-6OF'. AUTR7OF', AUTRSTR

21

Program AQTRN

Input to the program Is provided at the system console. AUTRN makes use

of the CPU display register to let the user know where It Is in the

computations. Bits 0-8 display the current block number being processed,

while bits 9-12 display the current decimation level.

22

4. Program STACK

Purpose

Program STACK is used to stack spectral matrices computed by program

AUTRN and compute the resulting transfer functions, error estimates, and

induction arrows. The stacked spectral matrix is formed by simply adding

together all of the spectra selected by the program.

Description

This program consists of a main program plus three segments which are

scheduled by STACK. Control is transferred back to the main program by the

same mechanism used in AIJTRN, _i .e_. , a branch to a label variable in a common

block that has been assigned to a numeric label in the main program. The main

program's function is to: (1) allocate a common storage block, (2) initialize

parameters, and (3) schedule the three segments.

The first segment, STAC1, is used to input the names of the transfer

function files to be stacked. Up to 16 files can be specified. The input

files are opened and read, and the frequency averaging bands and sample

intervals of the different decimation levels printed. After the last input

file is read, control returns to the main program which schedules segment

STAG2.

The user, after looking at the printer output, specifies the frequency

averaging bands to be used. The standard frequency bands used by program

AUTRN are used as default values if no changes are made. The user also

specifies the sample intervals to be used for stacking. There is one sample

interval for each decimation level computed by program AUTRN. Up to eight

values can be specified. In situations where more than eight sample intervals

are wanted, STACK must be used twice, producing two output files.

23

Program STACK

Once the stacking frequency bands and sample intervals have been

specified, stacking is performed by summing the selected spectral matrices.

When the stacking is complete, the quality factor, transfer function, error

estimates, and induction arrows are computed.

Control is now passed on to segment STAC3 by the main program. The user

specifies the name of the output file the results will be written to, and the

file is created. Any creation errors result in an error message and the user

is asked to again specify an output file name. The results are written to the

disk file and it is closed. A summary of the stacked data are printed. This

is similar to the summary given by program AUTRN including the stacked

spectral matrices, transfer function, error estimates, and induction arrows.

Additionally the names of the input files used in the stack are reported.

The user then specifies if any more files are to be stacked. A negative

response terminates the program, while a positive response starts execution of

segment STAC1 again.


Program STACK has no special requirements.

Program Loading

Program STACK and its three segments are loaded by executing the command

sequence shown in Figure 4-1. Binary relocatable modules are indicated by a

percent sign in front of their names. Module %REPLC serves the same function

as described in the section on the loading of program AUTRN.

Program Operation

Temporary ID segments are assigned to STACK and its three segments by

issuing the command

:TR,\STACK

which executes the commands contained in file \STACK shown in Figure 4.2. The

program is then run using the command

24

Program STACK

Figure 4.1 Command sequence to load program STACK.

LDSTAC T-00004 IS ON CR&0300 USING 00002 BLKS R-0012

000100020003000400050006

0009

00110012

<LG,10 'MR,XREPt.C

MR.XSTACi MR>STAC2

RU,LO^D'R.99,3,0, '

SP.STAC2

'TR

25

Program STACK

Figure 4.2 Command sequence contained in files /STACK and \STACK. File

\STACK is used to restore program STACK, and file \STACK Is used

to off it.

/STACK T-00004 IS ON CR-0>0300 USING 00001 BLKS R-000S

0001

0003 0003 0004 0005

RP, STACK RP,STAC1 .

RP^STACS TR

\STACK T-00004 IS ON CR0<0300 USING 00001 BLKS R-000S

0001 'OF,STACK0003 «OF,STA<C10003 'OF,STAC20004 »OF0005 <TR

26

Program STACK

:RU,STACK

After STACK has been run, and no more use is anticipated, the command

:TR,\STACK

is given to execute the commands shown in Figure 4.2, which returns the

temporary ID segments to the system.

27

5. Program LSTRF

Purpose

Program LSTRF is used to list the contents of transfer function files

created by programs AUTRN and STACK.

Program Description

This program is very straight forward in operation. The user is asked

for the name of the transfer function file to be listed. If the file exists,

a copy of the standard transfer function file summary like those printed by

programs AUTRN or STACK is printed. The files are then closed. If the

specified file cannot be opened, an error message is written. After either of

these actions, the user is asked if any more files are to be listed. An

affirmative response starts the whole process over, while a negative response

stops the program.


Program LSTRF has no special requirements.

Program Loading

This program is quite simple to load. The following commands are used:

:LG,2

:MR,%LSTRF

:RU,LOADR,99,6,0,0,2

:SP,LSTRF

Program Operation

Since LSTRF has no segments, it does not need an ID segment assigned to

it if it is run using a File Manager :RU command. The following command is

used to run the program:

:RU,LSTRF

No commands are necessary when the program completes execution.

28

6. Program PLTRF

Purpose

Program PLTRF is used to plot the induction arrows computed by programs

AUTRN and STACK. This provides an easy way to look at the results of the

transfer function analysis.

Description

The user supplies to PLTRF the name of the transfer file to be plotted.

If the file can be opened, processing continues, otherwise an error message is

displayed and the user asked if another file should be plotted. Once the

input field is opened, the user indicates the scaling factor for the plots,

the max imum-length induction arrow to plot, and the comment field that will

appear on the plot. The user can also indicate if more than one copy of the

plot is desired. The actual plotting procedure then begins.

The generation of a plot consists of three steps: (1) generation and

sorting (in blocks of 64) of plot vectors, (2) merging of the sorted plot

vectors, and (3) rasterizing and plotting of the sorted vectors. The first

function is carried out by PLTRF, while the last two functions are performed

by programs MERGE and PLOT respectively. The last two programs are described

in greater detail in D. V. Fitterman, Geomagnetic data utility programs for

the HP9640A, USGS Open-File Report 81-360, 1981.

PLTRF begins the plotting procedure by creating a file named "VECTRS" to

put the plot vectors into. Data from the first decimation level is read and

used in annotation of the plot. Dashed border lines to aid in trimming the

plots are drawn, as well as indicating the limits of the plotting area. Any

vectors which have an end point outside of this area are not plotted.

Subroutine ARROW is used to plot the data from each decimation level, one

frequency band at a time. When the last decimation level has been plotted,

29

the input transfer function file and the vector file are closed. Program

MERGE is scheduled to merge the sorted vectors, and when it is done program

PLOT is scheduled to draw the plot. If more than one copy of the plot is

required, the sorted vectors are saved and PLOT outputs the plot again. When

the last copy of the plot has been made, file VECTRS is purged, control passed

back to PLTRF, and the user asked if another file is to be plotted.

We will now discuss the operation of subroutine ARROW. This routine

plots the in-phase and out-of-phase induction arrows. The sense of the in-

phase arrows is reversed 180 degrees, while the out-of-phase arrows are not.

The out-of-phase arrows are plotted with dashed lines and the in-phase arrows

are plotted with solid lines. If the X and Y component error estimates are

smaller than the maximum of the in-phase and out-of-phase induction arrows,

rectangular boxes centered on the ends of the induction arrows are plotted.

The period, quality factor, and number of data blocks in the stack are printed

beside the induction arrows.

The induction arrows and their error boxes are not plotted if either

arrow is greater than a user-specified maximum value. If no data were stacked

for a particular frequency band, ARROW will neither plot the small cross at

the arrow origin nor the values of T, QF, and NSTK.


The vectors generated by this program are written into a file called

"VECTRS". The user must be sure that another file by this name does not

exist. If it does, a creation error will result when PLTRF is run. Any other

programs that use the plotting programs MERGE and PLOT should not be run

concurrently with PLTRF as this will cause problems. Finally, programs MERGE

and PLOT should be restored before PLTRF is run. This procedure is described

in the Program Operation section below.

30

Program PLTRF

Program Loading

Program PLTRF uses some of the routines in the plotting library. These

routines are supplied after the loader pauses with undefined externals

specifying the needed routines. The procedure to use is as follows:

:LG,2

:MR,%PLTRF

:SYRU,LOADR,99,6,0,0,2

At this point the loader will print a list of the undefined externals and

suspend. Continue loading by issuing the command sequence below:

:MR,%PLTLB

:SYGO,LOADER,2,0,1

:SP,PLTRF

Program Operation

Before PLTRF is run, temporary ID segments must be assigned to program

MERGE and PLOT to prevent SC05 scheduling errors from occurring. This is

accomplished by issuing the command

:TR,\PLTRF

31

Program PLTRF

Figure 6.1 Command sequences contained in files /PLTRF and \PLTRF. File

/PLTRF is used to restore programs PLTRF, MERGE, and PLOT, and

file \PLTRF is used to off them.

/PLTRF T-00004 IS ON CR&0300 USING 00001 BLKS R-0004

0001 »RP,PLTRF0002 «RP,,MERGE0003 !RP,PLOT0004 . :TR

\PLTRF T-00004 IS ON CR33300 USING 00001 BLKS R-0004

0001

00030003

0004

'OF,PLTRF 'OF,MERGE OF, PLOT TR

32

7. Appendix A - Data Formats

There are three file formats used by the programs discussed in this

report that are described below. They are:

1. Integer Format - the form of input files for program AUTRN.

2. Temporary Real Format - used by program AIJTRN to store input

data during processing

3. Transfer Function Format - the form of output files from AUTRN

and STACK, and the form of input

files for STACK, LSTRF, and PLTRF.

Integer Format

Integer format files are created by program SLECT, which is described in

D. V. Fitterman, Geomagnetic data utility programs for the HP9640A, USGS Open-

File Report 81-360, 1981. These files consist of a 128-word header record,

followed 128-word data records. The data records contain 128, 16-bit integer

data words. The values of these data words should lie in the range of 0 to

4095. The units of the data are counts. Any unused data words at the end of

the last record are set to zero.

The header record has essentially the same format as Source Tape Files

produced by program TRANZ for the first 60 words. Additional information is

added to the remaining portion of the record by other processing programs (see

USGS Open-File Report 81-360). The header-record format is described in Table

7.1. Some of the parameters are not used by any of the programs described in

this report, but have been included for completeness.

33

Appendix A - Data Formats

Table 7.1 Integer Format file header record format

Word Contents

1 Transcription version number

2 Day of year of transcription

3 Year of transcription

4 Tape file number (0-32767)

5 1st and 2nd character of location code (ASCII)

6 3rd and 4th character of location code (ASCII)

7 Cassette ID number (0-99)

8 Instrument number (1-31)

9 Scanrate (0-7), NRATE (Original sample interval = 2** (NRATE-1)

seconds)

10 Channels per scan (1-7), NCHAN

11 Clock reset time, hours

12 Clock reset time, minutes

13 Clock reset time, day

14 Clock reset time, month

15 Clock reset time, year

16 Clock off time, hour

17 Clock off time, minute

18 Clock off time, day

19 Clock off time, month

20 Clock off time, year

21 Stop watch time, minute

22 Stop watch time, second

23 Stop watch time, tenths of second

24 Number of words per cassette record

25 Number of cassette records per disk record (always 32)

26 Number of words per tape record, NBUFL

27-51 Comment field (50 ASCII characters)

52 Number of words per subrecord, NWORD

(NWORD = NSCAN*NCHAN + 8)

53 Number of scans per subrecord, NSCAN (NSCAN = integer (24/NCHAN))

34


Table 7.1 Continued

Word Contents

54 Hx gain in nT/2048 counts (Value of 0 indicates a default value of

1000 nT/2048 counts.)

55 Hy gain

56 Hz gain

57 Ex gain, >0 north end (+), <0 south end (+)

58 Ey gain, >0 east end (+), <0 west end (+)

59 Ex line length in meters

60 Ey line length in meters

61 NHOUR (Starting time of data segment)

62 NMIN (Starting time of data segment)

63 NSEC (Starting time of data segment)

64 NDAY (Starting time of data segment)

65 NYEAR (Starting time of data segment)

66 Number of data points in data segment, (0-32767) Set to -1 when

greater than 32767. Then use FNPT in word 127 and 128.

67 Decimation number, NDEC. Equals 1 for no decimation.

68 Original sample interval in ticks (1 tick - 1/2 second)

69-71 Reserved

72-126 Not used.

127-128 Number of data points in floating point format.

35


Temporary Real Format

Program AUTRN creates three work files named "..XX..", "..YY..", and

"..ZZ.." that have Temporary Real format. The file contains only real data

records which are 128 words long. In each record there are 64 real data words

corresponding to the magnetic field component in nanoteslas (nT). Conversion

from the integer count data in an Integer Format file to the Temporary Real

Format is accomplished by using the formula

ngt -f «

H (nT) = |~| * (counts - 2048)

where the gain term is obtained from the Integer Format file header record.

Transfer Function Format

Files using the Transfer Function Format are created by programs AUTRN

and STACK. This type of file serves as input for programs STACK, LSTRF, and

PLTRF. The files contain 256-word records and no header record. The results

of one decimation level are stored in a record, and each record contains the

results of four frequency band averages. Table 7.2 gives the names,

descriptions, type, and address of the various data stored in the file. The

addresses are given for accessing the data in integer, read, and complex

mode. The addresses are those of data in the first frequency-averaging bin.

To access data in the next frequency bin add 64, 32, or 16 to the integer,

real, and complex data type addresses respectively.

36


Table 7.2 Transfer Function record format. The addresses are for the first

frequency-averaging band of a decimation level.

Variable

FREQ

DT

IDEC

NSTK

SXX

SYY

SZZ

SXY

SXZ

SYZ

HI

H2

El

E2

QFSTK

QFCUT

Al

ANGI

AO

ANGO

IFLO

IFH1

NDEGR

Type

r

r

i

i

r

r

r

c

c

c

c

c

r

r

r

r

r

r

r

r

i

i

i

iadr

1

3

5

6

7

9

11

13

17

21

25

29

33

35

37

39

41

43

44

47

48

49

50

radr

1

2

3

-

4

5

6

7

9

11

13

15

17

18

19

20

21

22

23

24

-

25

_

cadr

1

-

2

-

-

3

-

4

5

6

7

8

9

-

10

-

11

-

12

-

13

-

_

Description

frequency (hz)

sample interval (sec)

decimation level

# of blocks stacked

X power spectra

Y power spectra

Z power spectra

X, Y cross power spectra

X, Z cross power spectra

Y, Z cross power spectra

X, Z transfer function

Y, Z transfer function

X error estimate

Y error estimate

stacked spectra QF

cutoff QF

in-phase induction arrow

in-phase arrow azimuth

out-of-phase induction arrow

out-of-phase azimuth

low harmonic number of stack

high harmonic number of stack

number of degrees of freedom

per stacked block

37


Table 7.2 Continued

Locations 51-64 are not presently used, and are set to zero.

Type code: i - integer, r - real, c = complex

The data are stored in an integer array IBUF which is equivalent to a real

array RBUF and a complex array CBUF.

DIMENSION IBUF(64), RBUF(32), CBUF(16)k

COMPLEX CBUF

EQUIVALENCE (IBUF(l), RBUF(l), CBUF(l))

The data are then accessed by using the value of iadr, radr, or cadr

corresponding to the data type.

For example: IDEC = IBUF(5)

SXX = RBUF (4)

HI = CBUF(7)

38

8. Appendix B - User's Guide

This appendix gives examples of the terminal input and output, and

printer/plotter output for the operation of the programs described in this

report. The output are presented in figures. On the figures you will notice

circled numbers, which correspond to the description in the text.

Refer to Figure 8.1 for the following discussion.

1. This command transfers control to file /AUTRN which restores program AUTRN

and its eight segments.

2. Program AUTRN is run.

3. The three input files are specified. They each contain 2048 data points

or 16 blocks, the sample interval is 8 seconds, and a total of five levels

of output can be obtained.

4. Five levels of output are selected, no input data overlapping is desired,

and the output file is called "NRTEST". The list of standard spectral

harmonic averaging bands is chosen.

5. The stacking quality factor is set at 0.0, which will cause all blocks to

be used in the stack. The stack is to be a "straight" stack meaning all

data that exceeds the quality factor cutoff will be used. No reporting of

BLOCK or STACKED results will be printed, but plots of the original data

will be made whenever 16 or less blocks of data remain. One block of data

produces a plot 1.28" long.

Figure 8.2 shows an example of some of the data plotted by the running of

AUTRN. Shown as the X, Y, and Z fields which will be used as input to the

third (IDEC=3) analysis level. The data have been low-pass filtered and

decimated twice. The new sample interval is 32 seconds. The scales are

always 50 nT/inch for Z and 100 nT/inch for Y and X. If the data exceeds the

plotting limits it folds over. An example of this can be seen on the Y

39

Appendix B - User's Guide

Figure 8.1 Terminal output for program AUTRN.

iTS./AUTRN

|RP,AUFR1:RP,AUTR2JRP,AUFR3 »RP,AUTR4 |RP,AUTR5 :RP,AUTR6 iRP,AUTR7 :RP,AUTR3 :TR :RU,AUTRM

42

X-COMPONENT FILE?-.N? RF20X Y-COMPOMENT FILE? MRF20Y Z-COMPOMEMT FILE? MRF20Z NPT= 2048 N3LK= 16 DT= 8.0 _J MAXIMUM NDEC= 5 DESIRED HD=C? 5 50% OVERLAPPING? (YE OR NO)

-NAME OF RESULT FILE? MRTEST SPECTRAL 3A/ID HARMONIC NUMBERS

BAND LO HI N 1 3 10

2 " 9 163 15 224 21 28

ANY CHANGES? (YE OR MO) NOQUALITY FACTOR CUTOFF? (3-1) 0STACK TYPE? (0=ST2AIGHT, 1=NCN-DEGRADIMG, 2=MDSPECTRAL REPORTING? (0«ALL, 1 =5T'\C;<ED, 2=NOME)DATA PLOTTING THRESHOLD? (<=3LOC^5) 16CONTINUE PROCESSING? (YE OR NO) YE

WITH 2

OF LOWERING) 0

40


Figure 8.2 Example of input data plotting by AUTRN.

NRTESTs IDEO3 DT- 32.0 (100*DT SEC/INCH) SCALECNT/INCH) 2« 50.00 Y-100.00 X-100.00

11111 M IT n i n 11111111 rn"i i rnrni \'\

I 1 M i I I I t I I II I I I I I I { I I III I I i I I I I I

41


channel. The name of the output transfer function file is printed for

identification.

While AUTRN is running, the user will notice that the CPU display

register lights are changing. The display contains the current decimation

level number in bits 9 through 12, and the current data block being processed

is shown by bits 0 through 8. Notice that the number of blocks processed at

each decimation level decreases by a factor of two from the previous level.

Figure 8.3 shows the summary printed by AUTRN when all of the input data have

been processed. It is the same data written into output file NRTEST. The

summary is divided into two parts: the first part contains the spectral

matrix, and the second part contains information about the transfer function.

1. Each section has a header which tells the name of the output file

(NRTEST), the cutoff quality factor value used (0.000), the percent

overlapping of the input data (0%), and the harmonic numbers of the four

frequency averaging bands (Bandl=3-10, etc.).

2. Each decimation level contains four lines of output, one for each

frequency band. Both parts of the summary contain the arithmetic average

frequency in hertz of the band (FREQ), the sample interval in seconds

(DT), the number of blocks stacked (NST), and the quality factor (QF) of

the stacked data. The number of degrees of freedom for the spectral

estimates is twice the number of harmonics in the stack multiplied by

NST. For example, for the first band of the first decimation level, this

is 2 * (10-3+1) * 16 = 256.

3. The marked columns contain the power spectral estimates (SXX, SYY, and

SZZ) and the cross power spectral estimates (SXY, SXZ, and SYZ). These

numbers have not been normalized by the length of the input data

sequences, the sample interval, or the number of data values in the stack

42


Figure 8.3 Example of summary printed by AUTRN.

SUMMARY OF RESULTS' FILE»NRTEST QFCUT-0.000 OVERLAP- 0* BAND1» 3-19 BAND2" 9-16 BAND3-15-22 BAN04-21-2S

FREQ(-306348

xCXl. 312207( 2>J,01S066^ 'I- 023926

.303174

.036104. 009033.011963

.001537

.003053

.004517. 00S9S1

.000793

.001526

'. 033991

. 900397,000763.001129. 001495

DT3.S.S,S.

16.16.16 .16 .

32.32.32.32.

64.64.64.64.

123.133.128,123,

0000

0

0

0

000

0

0

0

0

3

30

, 0

0

NST16161616

33S2

4444

223

2

1111

QF.53. 11.04.03

.56

.09

. 0a

. 11

.32

.30

. 12

.06

.64

.92

.60

.09

3789.'96

.65 \

SXX.305E+05.696E+04.439E+04. 151E+04

. 136E+0S

. 131E+04

. 123E+94

. 149E-I-04

. 102E+07

.383E+04

. S77E+03

.405E+03

.653E+06

.734E+04

.245E+04

. 146E+04

.672E+06

.952E+0S, 646E+04. 1S6E+04

SVY SZZ SXV. 303E+06 . 53SE+04 . 166E+0S .. S33E+04 . 366E+03 . 131E+04 .. 40SE+04 . 377E+03 . 199E+04 .. 149E+04 . d03E+03 . 686E+03 .

. 462E+06 . 1S1E + 05-. 136E+0S .

. 345E+04 . 97SE+02- . 258E+03- .1£ I7E + -'* 671E j*> ^2 . 243E + 02 .173E+04 .774E+02 . 537E+03 .

.247E+07 . 344E+0S- . 353E+06

.343E+04 . 106E+03-, 10SE+04. 103E+04 . 27SE+02-. 101E+03-.401E + 03 .351E-H33-. 131E+03-.

. 1S1E+07 . 901E+0S-, 246E+06 .

. 107E+05 . 400E+03-. S73E+03 .

.179E+04 . 694E-f02-. 437E + 03 .

.406E+03 , 263E+-02-. 107E+32-,

.166E+07 . 3S4E+05 . 740E+04 ,

.306E-I-06 . 110E + 05-.303E-I-05

.249E+05 .622E+03 . 233E+04

.251E+04 .S47E+02 . S43E+03

62SE+0S .301E+04 .367E+04-.623E+03-.

213E+06 .109E+04 .670E+03 .623E+03-.

133E+07 .793E+03 .37SE+-03 .207E+02 .

.740E+06 ,367E+04 .1S4E+03 ,513E+03 ,

.763E+06159E-I-06-333E+04, 11 1E+04

SXZ774E+04-S61E+01-130E+03-9S6E4-03-

3"33E-»-0S-131E+03436E *' 1?Sis0E+0a-2S4E+06-725E+03-160E+02-170E+02-

177E+063.89E+03-209E+03-,702E+0a-

133E+06246E+0S-.S13E+03-, 352E+03-

®

SUMMARY or RESULTS! FILE-NRTEST QFcuT-a.aoe OVERLAP" <&?.BANDl- 3-10 RAND2" 9-16 BAND3»lS-33 BAND4-21-23

FPEQT006343

fe. .012207(2V4.013066V> ' [_. 023926

.003174, 006104, 009033. 011963

.001537

. 003052

. 004517

.005931

. 000793

.001526. 003253. 003991

, 000397.000763. 001129001495

DTS,323

16 -161616

32323232

64646464

128133138133

,0

. 0

.0

.0

.3

.0

. 0

. 0

.0

.0

.0

. 0

.0

. 0

.0

.0

.0

.0

.0

,3

NSTIS161616

333g

4444

a3

22

1111

GIF.52. 11.04.03

.56

. 09 '

.02

. 1 1

.82

.30

. 12

.06

.64

.92

.60

.09

37!39. 96.65

HXR. 1065 -. 0344 -

- . 035.0 --.0714 -

. 1514

.0849

.0349 -

.0019 -

. 1773

. 0056 -

.0307 -,0303 -

. 1576, 1375 -.0738 -.0547 -

. 1413. 3065. 1327 -

. .0533 -

HXI HYP HVI EPX.0995 -.0904 -.0106 .0475.0564 -.0349 .0035 .0707.1239 -.0155 -.0016 .0519.0796 -.0145 -,0304 .1094

.0146 - 1332 .0059 ,0493

.0196 -.0309 -.0363 .1131

.0122 -.0247 .0017 ,1307

.0333 -,0901 -.0487 .1033

,0303 -.1359 -.0315 .0281.0759 -.0-657 .0226 .1370,0422 -,0669 -.0309 .2140.0993 -.0360 .0003 .3403

.3331 -.1699 -.0430 .1374

.0377 -.1139 .0333 .0649

.1049 -,0636 -.0-007 .3936

.0437 0273 -.0176 .1055

.0643 -.0374 -.0366 .1790

.1050 -.1773 .0023 .0405

.0953 -.1164 ,0033 ,0479

.1335 -.0493 .0040 .0834

EPV.0395. 3773. 9539. 1100

, 0313. 0964.1133.0959

. 0130

, 1446.1601. 3420

, 02410537.2439.2004

, 1139. 0226. 0344. 0657

M!. 1397. 0334. 0333 -.0723 -

.3016, 0904.04230901

. 2173,0659. 0736.0471

.2313

. 1703

. 1001

,0613

, 14673725

. 1765

. 0729

. 131E+05-

.643E+-03-

.S3SE+03-, 1S0E+03-

.257E+05-

.7SSE+02-, 157E+01-. 131E+03-

. 720E+05-

.370E+03-

.383E+01-

. 397E+03-

.705E+05-, 10SE+04-.369E+03-. 763E+02

. 143E+05-

. 133E+05-

. 163E+04-

. 367E+03-

<DANGI

-40 . 3-73.9156.116S.S

-41 . 3-20 . 0-35.2-3:3 . 3

-35.3-8.5 . 2-65 . 3-49 . 9

-47,3-41 . S-43.327.0

-14.3-40.7-41 . 3-43.4

SYZ.227E+05-..630E+03-.. 461E+03-. 120E + 03- .

.612E+05-.

. 119E+03-,, i3'2*$E'* |92 ,. 17SE + 03-.

.249E+06-.

.295E+03 .

.6-05E+02-.

.163E+03 .

,3fi4E-t-05-.. 160E+04-., 174E + 03 .. 326E+02 .

. HSE-t-05-.

. 440E+05- ., 344E+04- ,.231E+03-.

104E+05156E+03153E+0355SE+03

298E+0S330E+01asaE+oa103E+03

33SE+0-6154E+03191E+02140E+02

351E+06943E+02313E+03213E+0.3

169E+0>63 5 1 E * 0'5120E+04166E+03

AO ANGO0901 -173.0565 176.1330 -179,0852 -159,

0157 33.0417 -61.0123 172,0537 -133,

0363 -310793 1630S23 -143,0998 179.

2354 -3,0923 1611049 -1790462 -157,

0740 -391050 10961 1751336 173

2531

0g29

. 4, 435

. 7,0

6, 6

!s, i. 3

43


since we are only concerned with ratios of the numbers for transfer

function analysis. Notice that the cross spectra are complex numbers.

4. The second part of the summary contains the real and imaginary parts of

the X and Y transfer functions (HXR, HXI, HYR, and HYI). The columns

labelled ERX and ERY are the 95% confidence limits on HXR and HXI, and HYR

and HYZ respectively. The quantities AI and ANGI give the magnitude and

phase of the vector made of HXR and HYR. It is the in-phase induction

arrow. When plotted by program PLTRF, its direction is changed by 180°.

The quantities AO and ANGO are the out-of-phase induction arrows magnitude

and phase derived from HXI and HYI. PLTRF does not change its direction

when it is plotted.

Figure 8.4 shows the input for another run of AUTRN.

1. This time the user has selected a different set of frequency averaging

bands.

2. The quality for accepting data has been set at 0.33. Also a non-degrading

stacking has been selected. This means that the analysis of any data

block must equal or exceed 0.33 before it is considered for stacking, and

the addition of this data to the previously stacked data cannot lower the

stacks of QF below 0.23 (0.33-0.10).

3. Only stacked results have been selected for reporting. This means that a

"BLOCK" and "STACK" summary will be printed whenever some data are

stacked.

Refer to Figure 8.5 for an example of a block and stack summary.

1. The first line of the block summary gives the decimation level (1), the

current block number (9), the cutoff quality factor (0.330), and the

sample interval (8.0).

44


Figure 8.4 Example of input to AUTBN showing user selected frequency bands.

CONTINUE PROCESSING? (YE OR MO) YE

X-COMPONENT FILE? MRF29X Y-COMPONENT FILE? NRF20Yz-COMPONENT FILE? NRF23ZNPT= 2,1548 N3LK= 16 DT= 8.0MAXIMUM NDEC= 5DESIRED NDEC? 450% OVERLAPPING? (YE 03 NO)NAME OF RESULT FILE? NRFTR2SPECTRAL BAND HARMONIC NUMBERS

NO

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2. The rest of the summary has two columns for each frequency-averaging

band. Numbers in the second column are the imaginary part of

complex quantities. The quantities displayed include: frequency, power

spectra, cross power spectra, residual cross spectra, various coherencies,

transfer functions, induction arrow estimates, and the quality factor.

The remaining portion of Figure 8.5 is called the stack summary and is

described below.

3. The first line gives the decimation level, block number, sample interval,

and number of blocks which have been stacked in each of the four bands

(band 1=9, band 2 = 4, band 3=1, and band 4=1).

4. As before, the results of each frequency band are given in two columns.

The results include: frequency, transfer function, error estimates,

induction arrow estimates, and the stack quality factor.

The last part of the stack summary contains plots of the data from the block

just stacked and their power spectra.

5. The first line gives the minimum (RMIN) and maximum (RMAX) value for all

three power spectra plots. Also printed are the full scale values of the

original data plots. In this example the end points of the scales go

between +5nT and -5nT on all three plots.

6. The power spectra plots are logarithmic in power (left to right) and

linear in harmonic number (top to bottom). Viewed from left to right the

spectra are of the Z, Y, and X channels. Along the harmonic number axis

are four vertical bars which show the limits of the four frequency

averaging bands. The harmonics run from one to 64.

7. The three plots to the right are the Z, Y, and X time series (going from

left to right). There are 128 points in on each plot. The scales are

automatically adjusted to keep the plot within the 1" allotted. The data

plotted have had a linear trend and average removed.

47


Refer to Figure 8.6 for an example of terminating AUTRN and starting STACK.

1. When the last data sequence has been processed the user types "NO" to the

query about continuing.

2. Program AIJTRN is shut down by issuing this command which automatically

causes the following 10 commands to be performed.

3. The stacking program is initialized with this command.

4. Program STACK is started running with this command.

5. The user specifies two files (NRTEST and NRFTR3) to be stacked.

At this point STACK prints the frequency bands and sample intervals of the

input transfer files (see Figure 8.7). The user needs this information to

decide on the harmonic bands and sample intervals to be selected for stacking.

Refer to Figure 8.8 for an example of inputting of stacking parameters.

1. The standard spectral harmonic bands are displayed.

2. The user decides not to use other spectral bands. The user can select

harmonic bands which do not exist in the input files, but no data will be

stacked.

3. Five sample intervals are selected for stacking. Each sample interval

corresponds to a decimation level.

4. An output file name of "NRFSTK" is selected, but the file already

exists. This causes a creation error. The user then selects an output

file name of "A".

5. No more data are to be stacked, so the program is stopped.

6. The user has decided that file NRFSTK should be purged, and file A renamed

to NRFSTK.

7. Program STACK is no longer needed so the command :TR, \STACK is given to

return its ID segments to the system. This causes the next five commands

to be executed.

48


Figure 8.6 Commands to terminate AUTRN and run STACK.

CONTINUE PROCESSING? (YE OR NO) NO AUTRN : STOP 3-303

:~TR, \AUTRN -'- OF, AUTRN Y<J

AULRN ABORTED :OF,AUfRl:OF,AUTH2 tOF,AUTR3:OF,AUTR4 «OF f AUTR5sOF,AUTR6 :OF,AUTR7:QF,AUTR8

:TR,/STACK sRP,STACK:RP,STAC1 tRP,STAC2*RP,STAC3

:RU, STACK

INPUT MAM55 OF FILES TO MAXIMUM NUMBER OF INPUT

3E STACKED FILES IS 16

TYPE 'STOP' TO TERMINATE INPUT

NFL123

NAME MRTESTNRFTR3 STOP

SEE SUMMARY ON LINE PRINTER

49


Figure 8.7 Summary of program STACK input files.

1 NRTEST BAND!* 3-10 BA;N.D2« 9-16 BAtfD3« 15-22 BANtr4«21-2:3DT« 3.0 16.0 32.@ 64,0 123.0

2 NRFTR3 BAND!" 3-10 BAMD2- 9-16 BANES-15-22DT- 8.0 16.0 32.0

50


Figure 8.8 Example of input of stacking parameters

SEE SUMMARY ON LIME PRINTER

SPECTRAL 3AMD HARMONIC MU'HERS3AMD LO HI

1 3132 9 163 15 224 21 2S

AMY CHANGES? (YE OR MO) MO

INPUT 1-8 DT VALUES TO STAC r< VALJcS '{J/ST LJ ." 1:1 ASCENDIMS OR3E3 USE MOM-POSITIVE VALUE TO STOP

DT 8

16 32 54 123

I123456 VOUTPUT FILE NAME? MRFSTFCCREATIOU ERROR: FILE-M-7F3TK IE.OUTPUT FILE MAME? ASTACK MORE FILES? CYE OR NO) NO

STACK s STOP :PU,MRFST[< :RM, <\ t N2FS' :TR,\5TAC;-C

:OF,ST\C;< STACK A-30RTED

sOF,5TACl«OF,3TAC2

-2(1

:TR :TR./PLTRF\

51


When program STACK finishes the stacking procedure, it prints a summary

similar to the one shown in Figure 8.3. The only difference is that at the

top of the summary a list of the input files is included.

The user now wants to print summaries and plots of some transfer function

files (see Figure 8.9).

1. Program LSTRF is run to list a file.

2. Files named NRFSTK and NRFTR2 are listed. The output for file NRFSTK is

shown in Figure 8.10. The output is similar in format to that of program

AUTRN described in Figure 8.3. After the last file to be listed is

printed, the user responds "NO" to the question "LIST ANOTHER FILE?" and

the program terminates.

3. Before program PLTRF can be run, it and programs MERGE and PLOT must be

restored by transferring to file \PLTRF.

4. Program PLTRF is run.

5. Transfer file NRFSTK is selected to have its induction arrows plotted. A

scale of 0.25 units/inch is chosen, and the maximum arrow length to be

plotted is 0.75 units, corresponding to a length of three inches. A

comment field which will appear near the top of the plot is input. The

user does not want multiple copies of the plot. The plot is now created

and printed.

6. The user does not want to plot any other files so an answer of "NO" is

given.

7. The ID segments of the three plotting programs are returned to the system

by transferring to file \PLTRF.

An example of part of an induction arrow plot made by program PLTRF is shown

in Figure 8.11. This figure has been reduced to fit onto a page.

1. The name of the input file and comment field are printed at the top.

52


Figure 8.9 Use of programs LSTRF and PLTRF.

:RU, LSTRF (T)

TRANSFER FILE NAME? MRFSTKLIST ANOTHER FILE? (YE OR MO) YE

TRANSFER FILE NAME? NRFTR2LIST ANOTHER FILE? (YE OR NO) NO

LSTRF : STOP 0339 :TR,/PLTRF

JRP,PLTRFsRP, MERGE»R?,PLOTsTR

:RU, PLTRF

TRANSFER FILE NAME? NRFSTK SCALE? (UNITS/IMCH) .25 LARGEST ARROW TO PLOT? (UNITS) .75 COMMENT FIELD? « = 53 CHARACTERS)

EXAMPLE OF TRANSFER FUNCTION PLOTTING MORE THAN ONE COPY OF OF PLOT? (YE OR MOY NO

PLOT : STOP 0077 ' PLOT ANOTHER FILE? (YE OR NO) YE

TRANSFER FILE NAME? NRFTR3SCALE? (UNITS/INCH) .25LARGEST ARROW TO PLOT? (UNITS) .75COMMENT FIELD? (<= 50 CHARACTERS)

EXAMPLE OF PLOTTING WITH NO 3AT\ STACKEDMORE THAN ONE COPY OF OF PLOT? (YE OR NO) NO

PLOT : STOP 3077PLOT ANOTHER FILE? (YE OR NO) MO

PLTRF J STOP 000:3 :TR, \PLTRF

«OF, PLTRF PLTRF ABORTED

MERGE ABORTED :OF.?T.or

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Figure 8.11 Example of an induction arrow plot.

FiLE:NRFSTKEXflMPLE OF TRflNSFER FUNCTION PLOTTING

@QFCUT= .800 flRMflX= .75 ^ BflND 1 BflND £ B 1=1 N D 3 (3)3-10 .9-16 15-22

25 =

BflND 4 21-23

8

T » 158. QF* 63 NSTK« 17

T « 88. QF* .11 NSTK» 16

T = 55 QF' .04 NSTK* 16

T 42. QF= .08 NSTK« 17

I

T ' 111. QFt .08 NSTK« 3

T « QF' NSTK'

DT = 16

,. , QQF> .61 NSTK'

QF« N3TK

\

DT = 32

T * 338 QF> .30 NSTK«

T ' 231 . QF» iS NSTK =

T « QF'

167 .06

55


2. The first input file used in the stack had a value of 0.8 for QFCUT,

so this value is set in the output file. The maximum arrow length which

will be plotted is 0.75. The scale at the right shows the length of an

arrow with a value of 0.25.

3. The harmonic numbers used in the various stacking bands are shown above

the columns where the data are plotted.

4. This row of data is for the data with a sample interval of eight

seconds. The solid lines are the in-phase induction arrows (reversed

180°) and the dashed lines are the out-of-phase induction arrows. The

rectangular boxes are the 95% confidence limits. Notice that the data for

band 4 does not have an error box plotted since one of the errors

estimates is greater than the longest arrow length.

5. Each set of arrows is annotated with its period (T) in seconds, the

quality factor of the stack (QF), and the number of data blocks (NSTK) in

the stack.

56

9- Appendix C - Program Listings

This section contains listings of the programs described in this

report. They are presented in the order listed below. The list includes the

routine name, type of routine, and the language it is written in.

Page

1. AUTRN, main program, FORTRAN 58

a. DSPLA, subroutine, HP Assembly Language 62

2. AUTR1, segment, FORTRAN 65

a. FILLR, subroutine, FORTRAN 69



a. DTRMN, subroutine, FORTRAN 79

b. FOUR1, subroutine, FORTRAN 81


a. ADSTK, subroutine, FORTRAN 87

b. FTEST, subroutine, FORTRAN 88


a. FACTR, subroutine, FORTRAN 93

b. MOVE, subroutine, HP Assembly Language 95

c. ZERO, subroutine, HP Assembly Language 98

d. INDOT, subroutine, HP Assembly Language 101



a. IDEFL, subroutine, FORTRAN 111


10. REPLC, loader replacement module, HP Assembly Language 116

11. STACK, main program, FORTRAN 118

12. STAC1, segment, FORTRAN 120


a. FTEST, subroutine, FORTRAN 128


15. LSTRF, main program, FORTRAN 133

57a

Appendix C Program Listings

Page

16. PLTRF, main program, FORTRAN 136

a. ARROW, subroutine, FORTRAN 140

17. /AUTRN and \AUTRN transfer files 143

18. /STACK and \STACK transfer files 145

19. /PLTRF and \PLTRF transfer files 147

57b

PAGF OQ01 FJN. 10:10 AM MOM., 9 MAR., 19*1

0001 FIN,i0002 PROGPAM AUTRM,3,«00003 COQ04 C - PROGRAM TU AUTOMATICALLY COMPUTE TWO l^PI'I, OfiF OUTPUT0005 C TRANSFFR FUNCTION Fu^ GEOMAGNETIC DATA0006 C0007 C WRITTEN PY 0. V. F'TITEPMAN, n.S.G.S., FtPPUA^Y 1^7**0008 c MODIFIED ^n Â P C M 19790009 c0010 001 1 0012001 3 *LUTTY,LUPkT,TSTZF(?),MMF(9)0014 *TDCbCl /J 4),JDCbfl44),KDCb(l440015 *mG(4),TFHIf4),MDFG p (4),0016 *F(fl) r $(6f4),STK(6 r fl),rtSTK(0)0017 *HF(4),AIf4) , Ai-jHI C4) , A OC 4) , ANGUf4) ,TDATA(?304)0018 HOMPI. EV SrST*,!-10019 niWENSTON T3FGS(?4)00?0 DATA lSEGS/2HAU,?HTRr2Hl ,?hAU,2HT°,?H? ,2HAU,PhTh\, 2H300?1 *?riAu,2HTP,?h4 ,c M A !l ,?hTR f 2H5 ,?hAU,00?2 *?h7 ,2HAM,?hTK,2H8 /00?3 C00?4 C INITIALIZE COMMON RLOC* VAPJAbLES00?5 |,UTTY = 10026 I UPRT=600?7 ISIZF(?)=1?800?6 ^l cP = 12^00?9 no 10 1=1,°0030 10 MA MLCI)=?H..0031 00^200330034 C0035 C SET UP KFT"RM AOHRFSSES0036 ASSICi\ 30 Tu L n oPl0037 ASSIGN 60 TU LOOP20038 ASSIGN 80 Tu LOOP30039 ASSIGN 90 TU L nQP40040 ASSIGN 100 yo LOOPS0041 ASSIGN 110 TO LuOP6»0042 ASSIGN l?u TO LOOP70043 ASSIGN 140 TH LOOP80044 C0045 c SCHEDULE RFAD SEGMFNT - AOTRI0046 20 ISTUP=0004? TDFC=10048 CALL EXEC(P,I3FGS(1))0049 C00^0 C---- ChFCK FOP FRDfjRs00^1 30 TFflSTOp .Fu. 0) GO TU bO0052 C0053 C PROCESS SOME MORF FH t S?00^4 40 t*'RTTF(LUTTY,!000)00^5 1000 FyPMATf" CONTINUE PROCESSING? (YF OR NO) _"j

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PAGF 0003 AUTR? 10:1? AM MyM., 9 M A&.,

oni r0112 r---- T^PUT SPFCTRAL RFPPRTINQfU13 120 WKTTF(LUTTY,1100)0114 1100 FUPMATf" S p fcTTPAL P£ P U P T01 Ib PEADfU'fTY,*) TSW20116 TrflSw? .LT. 0 ,HR. T5 !"2 ,PT. ?) GH TU 1?00117 C0118 c---- T^PUT otrjMATinN PLO T TTNR THPtSHntn0119 WRTTFCLUTTY,1110)oi?o 1110 FoPMATf" uAr a PLPITJNG F^RFSMULD? f<=bLurK.^)01?1 PtADfLf'TTYf*) TS^'30122 nu TH tunp?oi?3 FNP

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74

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c SEGMFNT TU PFRFQPM SPECTPAIWRITTEN PY D. V. FITTERMAN,MUDIFIFD i? HCTUREP 1979

JANUARY 1979

r ToLKf TDFC , NOfcC , n T , uFCU \ ,

*TFlOf4),lFHIf4),i\iDFGP(4),*F(4),5f6,4l r ^TK(^,4),)\iSTK(*np f4) , Al f 4) , AJMRI (4) , AuC4) ,

STK,H r HT !XC25b),TYf25b), TZ r 256) , X (1 2P ) ,Yfl?8)r7(12«),

(lX(1) f xfl)rTDATA(l)),fiY( 1 ),Yri),T L,ATA(?b7)), *fl7(l)rZfl),TuATA(5l3))r(FX(1) ,sSPEC(1 )r

, fF7(1),SPEC(?57))

*2H1 , 2H2*?h f2Hh7

DATA PTiM/.04^08739/

READ x, Y, AMD z DATACALL RFADF(ir>CR,TEP,TX,25b,i,CALL RFAnFCjncR,T£ p ,TYf25d,i,IPDPT)CALL RFA n F<"Knc R fTEPfIZf256fI,IFDPr)

LTNFA P TRFNH AND CALL DTR^NCX,N&K.)CALL CALL

, TRANSFFR DATA TU FFT ARRAYS

FXf I)=CMPLX(3£LL*XU),0.0)

10 FZCI)=CMPLX(RELL*Z(I),0.0)

COMPUTFCALL FHUR1fFX,NdP,~l) CALL FHUR1(FY,N6R,-1) CALL FnuPirp7,

LOOP UVE P FRFul'ENCTE? TRPRT=n

75

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005000510052005300540055

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5

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SUBROUTINE FDUR1(DATA,NN,I

A RELATIVELY FAST, S M ALL FOUP1FR TRANSFORM SUBROUTINE

DATA=CONPLEX ARRAY OF FUNCTION TO BE TRANSFORMED. TWOCONSECUTIVE fcORDS OF ARRAY DATA ARE EXPECTED TO CONTAIN HEAL AND IMAGINARY PARTS RESPECTIVELY OF FACH COMPLEX POI M T.

Mh = NUwBh'P OF DATA POINTS IN ARRAY DATA = 1/2 NUMBER OF WORDS.f\N MuST bF A POÊP OF 2, I.F.f NN = 2**N

ISIGN=tl OR -1 INDICATING ThF DIRECTION OF TRANSFORMTO TRANSFORM ISJGN CAis, BE +1 OR -1. TO INVFRSE TRANSFORM, TSIGM MUST HAVF ThF OPPuSlTE SIGN.

NUTt: WHFh CONVERTING Tu FREQUENCY, MULTIPLY EACH DATA POINT BY 1/NN.

J DATAfl)

J=JDO 5 I=1,N,2 TFCI-J) If?f2

1 TtMpR=DATACJ)TEMPT=OATA(J+1) DATACJ)=DATA(I)

DATACI+I)=TEMPT

7,10,10

nTHETA=S?PI/FLOAT(MMAX) THFTA=0.0DO 9 H= 1, MM AX, 2

WI=SINCTHETA)DO 6 l=MfNf ISTFPJ=T+ MMAX

J ) - *D AT A ( J+

DATA(J)=DATA(I)-TEMPP DATACJt 1)=DATACItn-TEMPI DATA(i)=DATAU)tTEMpP

8 DATACI+l)=DATA(I+l)+TEMpI9 ThETA=THFTAtDTHETA

GO TO 6

81

PAGE 0002 FUUR1 9:b2 AM TUF.r 4 NUV., 1980

0056 10 RETURN0057 FNO

FTN4 COMPILE": HP92060-160^2 KFV. 1913 (790206)

** MU WARNINGS *^ NU EPRDR-S **r PPURRAM = 00356 COMMON = 00000

82

PAGE OQ03 FTN. 9:5? AM TUE., 4 MUV., 19«0

0058

83

PAGF 0001 F]M. 10:13 AH 9 *'AP., 19*1

0001000200030004000500060007000800090010001 100120013001400150016001700180019oo?o00?100?200?300?400?500?600?700?800?900300031003200330034003500360037003800390040004100420043004400450046004700480049005000510052005300540055

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MAN, U.S.H.S., JANUARY 1979 i960

, L nUP3,LPUP4,LPQP5,LPOP6

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OETEPMTNF TF n U 10 .1=1,4 TSAVF=0 TFCQF(J) .LT. HpTUT) GO TU 10

SET SAVE FLAP TSAVF=1

STACK PESULFSCALL AOSTKfJ,STK,3rP

STACK

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STACKFD

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SY=RFAL(STK(4,J)) SZ=RFAL(STK(6 f J))

, J))/3X/?Y ,J))/3y/SZ , J))/S V /SZ

S2?l=SY*(1.0-bl2) SVY1=S7*(1 .0-GYp

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Oil 1 CALL wPlTFfinCPr ThP,T&UFU^9), 12P,.TpTR)0112 CALL ftRiTf jncR,T£R, JbnFfl59), 12*, JPTR)0113 CALL KPlTF(KncP,TtR,KbUF(l59),12«, JPTR)0114 JPTR=JPTRtt0115 JJ=00116 C0117 c SHIFT LAST i* HATA POINTS f3n WORDS) TO FKPUT PFona eo CALL MOVFCTBMF, i?a, iRuF,0,300119 CALL MovF(,TbHF, i?a, jPuF,o,3(n0120 CALL MPVFCKBMF,i?8,KRuF,o,3u)01?1 C0122 c no K*E?oi?3 TFdRL* .C;F. N&LK2) RU m QQ01?4 Coi?s c RL-AD RFCHNDS0126 CALL RFADFUncPf TtR,T6HFf31) . 1?6, J.,iP]P)01?7 CALL RFAHFCjncPfTtP,JDUFC3l)rl?8fl,iPTP)0128 CALL RFAnF(Knc°, f TER, KbUF^l) , 1?«J, i , IP FP)01?9 IPTR=lPTRf101300131 HO TO SO0132 C0133 c SKTP IF0134 90 Tf-fN^LK .UT. ISA'3) GO TU 110ons c0136 C TICK MARKS0137 CALL EXET(3, UOOR+LUPRT, 1 j0138 CALL ZFRO(TPLT,30)0139 CALL MOvF(MASK4,0,TPLTfOr 30)oiô no 100 1=1,100141 100 CALL LVEC(?,1.00b + LHpPl r 1PLT,30)0142 CALL MOVF(MASK3,0,TPLT,0,30)0143 CALL EX£C(? f 1OOb+LUpRTf1PLT,30)0144 CALL EXECC*, 1 IOQR+LUPRT,?)0145 C0146 C HOME FTLTEFiMG AND DFCIMATTNG0147 C ClJMpMTF FFFECTTVF FILEOH8 1 100149 Coiso c RE.WINU V-0151 CALL0152 CM! L KWNPFfJHCP)0153 TALL RWNOFCKHCP)0154 CO TO LOOP70155

FFN4 COMPILER: riP9?OftO-160 c>2 RFy. 1913 (790^06)

** MO FARMINGS ** MO ERRORS ** PROGRAM = Q0846 rU MMHN =

110

PAGF 0004 FT*1 . 10:20 A M MQM., 9 MAR., 19*1

0156 FUNCTION IDEFL(X,SCALE)0157 C01^8 C - COMPUTES MnuULAK DFFI.ECTTUN01S9 COiAO C SCALF = NlJMtjFR OF MMTS PEP 100 .^TYLTifl INCH)0161 T*=IFIY(100.*X/SCAL£)0162 TDFpt =Mun(TX + ISlPN(50,TX),100)-ISinu(50,TX)01630164

FTN4 CHMPILfcP; HP9PQ60-160^2 KFV. 1913

** MO MANNINGS ** NU EPKHRS ** RPU^RAM = 00039 CU M UHN = 00000

111

PAGF 0005 FT*'. io:ao AM MQM., 9 MAP., 19*1

0165

112

PAGF 0001 F]M. 10:21 AM MCJN.,

000100020003 C0004 c SESMFNT TU I/VPJTE RFSULTS/ CLDSF OUTPUT0005 c AND PUPGF WU P K FTLFS0006 C0007 c WKTTTEM PY u. v. FTTTEPMAN, u.s.n.s., FEPRNAPY i°7°oooe c MODIFIFQ 21 AUGUST 19790009 c0010 COMMC(hi LHuP0011 *TRPPT,!SW1,00120013 *LUTTY,LUPRT,0014 *!DCB(144) , JDCBC144) ,KDCbM44) ,LDCU(J. 44) ,0015 *!FL.U(4), TFHIf 4) f MDFGP(4) ,001600170016 DIMENSION LA R EI (?) r LPuF(?b6),t>UFi ci2«)0019 FyMIVALENCF (LRUF ( 1 ) f tfllFI C1) )oo?o COMPLEX S,STK,H00?1 r»ATA LABEL/2H50 f ?n O/00?2 Coo?3 c---- PEÎÛ U'ITPU T FILE00?4 CALL00?5 C00?6 C ^RINT00?7 CALL EXEC(3 f 1lOORtLU p RT f ?)00?8 WRTTFCLUPRT, 1 005) TFTLF f PFCUT , I. AÊL ( TS^! 1) ,00?9 *(lFLn(T) f IFHT(!),!=1,4)0030 1005 FQPMAT <"2?X / "SUMMARY OF0031 *" QFCI'l=" f F"5.3," uVEPLAp = " f A?,"%"/0032 *?2X f "bANni = " f I?, "-" f T2r " PAMD?=" , I'd , "-" r J ?/0033 *T2r"-%l?r" ttA}-jD4 = ",i?f "-", T210034 r Al L EXEC(3r1100R + 1 UPRTr 1)0035 w K TTF(LuPRT,10101

0037 *"SYY"f 6Xr "PZ7" f bX f "yvy'1 , 1 5X, "3XZ" , 1 5X f "SY/" )0038 HO 10 T=1,NDFC0039 C0040 c PEAD KFSULT0041 CALL0042 IuFFI=-640043 TyFFP=-3?0044 HO 20 J=l f 4004500460047 20 WHTTF(LUPHT f 10?0) nyFL(inpFR^11 f RuFLfIHFFRf21r0048 *Lb"F(inFFJ4b) , PUFLf10FFR+1^) , (RUFL(1HFFR+K1 r K=0049 1020 F"{J p MAT n* f Ffc.6f lX f F6. 1 r IX,0050 10 CALL EX£C(3 f 1 IOOR-KLUPRT, 1)

0052 c PEWJND OUTPUT FILE0053 CALL0054 C0055 C PRINT

113

PA&F 0002 AUTR« 10:21 AM 9 M AP., 19*1

005600570058005900600061006200630064006500660067006800690070007100720073007400750076007700780079 00*0 00*1 00*2 00*3 00*4 0085 00*6 00*7 00*8 00*9 00^0

1030

CC

TALL EYECC?, iWKTTF(LUPRT,1005) TF II.F , *FCUT , I AREU TSW 1 ) , f iFl_n(T),IFHT(T), 1=1,4)CALL txtro, 1 ioo»tt UPRT, n WKTTFCLUPRT, 10^0)

r 5X r "OT " , 3X , "NS 1" , 3X , " CF W r

Du 30

CALLFILE

RFAHFfL^CRr TEPrl

40 J=

TUFF D =TQFFPt32 40 WRTTFCLuPRT, 1 040)

*LbUF(IOFFl+6)fRUFLf( IHFFR+1 ) , RUFL f IPFFk+2 )

, IRUFL r 1PFFR + K) ,K

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30 CALLCALL

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, 1

FTLFTALL ci

PUPGFCALL PHRGf, ( CALL PURniCCALL PURGE r nu TO LUOP*

FTLFS

FTN4 HP9P060-16Q92 RFV. 1913 ( 7 90206)

MQ = 00911

114

PAGF 0003 FIN. 10:21 AH MQM.r 9 MAR., 19*1

0091

115

PAGF 0001 0001

S 1057635? 105764

** MO EPRHRS PASS*1 **NTE ASMR

116

PAGF 0002 #010001 ASMBfLfT 0002*0003* ROUITIMF TO RFPLACE j DT AND .SPT ENTRY POINTS WITH0004* MICRO-COPE INSTRUCTIONS. TO USE MOVF RELOCAPL^0005* Munyi. E %PEPLT TO THE LOAO-AMP-RU (LG) ARFA P1 FRONT0006* OF AIL OTHFR RFLOCATAbLE0007* THF LOADFR.0008*0009* WRITTEN PY D. V. FTTTERÂNr U.S.R.S., JUtY 0010* MUDIFIFD 2^ JULY 1^7^001 1*0012 ooooo MAW0013 FNT0014 10^763 S .LPT P PI,0015 1057MS .SPT PPL0016 F Nn** NO ERRORS *TOTAL **R T E ASHR 7609?a**

117

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0056 c THFC* FUR0057 TFUFR % Eu. -i?) GO TU 600056 C00^9 c SAVE DT0060 NuFc=Nntr + i0061 DTfNnEC)=bllFT(?)0062 C0063 r TF FTKST TTMF PHTNT FILE NAME AND RAND*0064 TFfNHEC .EH. 1) rt*UTE CLUPPT , I 070 ) h»FL , ( TF TLF ( J ,MFL ) r J= 1 , 3) ,0065 *riBUF(J + fl8),Tt>UFCj.mP) ,J=1, 193,6«)0066 1070 FUPMATf2V,T2, IX, 3 A?, t X , "R A^D 1 =" , T2 , " -" , I ? , " RANO? = B r T 2 , "-" f 10067 *" RAND3 = ",T2r "-",!?," R AMO /I = " , T 2, " -" , 1 ? )0066 HU TP 500069 CGOTO c WKTIF HT'S0071 60 'A/KTTFCLUPRT, 10BO) fOT ( J) , J= 1 , NDfcC )0072 1080 FQPMATf 1 2X , "Hf =» , 8 CF 6 . 1 f 1X) )0073 C0074 c AUVAMCF PAPER0075 CA! L EXECC?, UOORtLUPRT,!)0076 H0077 c CLDSF FILE0078 CALL CLUSEfincR)0079 TFfNFL .LT. MKIMX) GH Tu 10OOPO Ru TP PO00-n l C0082 c REDUCE NFL i..v HNF0083 70 NFL=WFL-I0084 C0085 C EJFCT PAPEP0086 80 CALL E*£C O, 11 nOPtLUPKT, SO)0087 C0088 C WRTTF MESSAyF0089 WRTTFCI UTTY, 1Q90)0090 1090 FU°MAT(/" .ÊF SUMMARY HN LTIMF0091 no jn i.unp?0092 Fun

FTN4 COMPILER: HP9P060-160°2 RFV. 1913 (79020 0 )

** NO EARNINGS ** MU EPRHRS ** PPOPRAM = 005^3 PU^MHiM = 0?o60

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OOS6OOS700^8OOS900600061006200630064006500660067006800690070007100720073007400750076007700780079

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HTLSTsO.nWRTIFUUTTY, luSO)FQRhATf/" INPUT 1-8 HT VALUES TO STACK"/

*" VALUFS MUST RE IN ASCENDING nRDtP"/*" USF ^QN-PuSlTiVt VALUt TH STOP"//* " T n T " )WHTTFUUTTY, 1060) TFuRMATClX, Ti, " _")READ f LUTTY f *) n i ( i )

CHFCK FUR PT PHSTITVFTFfDT(I) J.t. . n .O) GH TU 70

CHFCK FUR Asct. M uTfjn OHDERTFfDT(T) ,IE. HTI ST) GO TU 50NuT=NQTt 1HTLSTrP F f I ^

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,TRT = JpTt64,.TpTR = JPTRt?2q UFJ(JPrP + ?) = l»T(T)R UFJfJPTR+l) = PIUAl(IFHT(«T) <<-IFLn(J)')/nTri

JyUF(JPTtbO)=IFHT(.T)T = Tt1TFffvHT .l.T. P0 GO TO 50

START STACKING LHQPLOOP UVER FILESHO 80 T=1,NFL

npFfsi FTLFCAl L OPEMCTuCBf lFR,lFHE(l f l),?)

PEAD A RFCHRHCALL RFAnFCincR,TE p rTbLiF/2Sb)

CHFCK FUR FUFTKflFR .Fy. -l?) GH TO 1^0

CHFCK FOP S1ACKARLF OTJ = 0JPT=-2^6JpTR=-128

J=JttJpT=JPTt?56JPTR=JPTRt128TFCbUFTC?) .FQ. D]fJ)) Gn TU 110TFf J .LT . 8) GO TU 100

MQ MATCH UM n TR u T n 9o

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PAGF 00^3 STAG? 10:2? AH MJJM., 9 W A P., 1981

Oni r ruFC* FU P PRHPFR HARMONIC LIMITS0112 110 TpT=-b4

0113 TpTR=-32^114 nu i?o J = i,40115 IPTsIPTtM0116 TpTRrlPTPf320117 TFfI*UF(TPT + 49) .NF. lF|_n(J) .OR. TtfMFfIPJ+bO) .Nfc;. TFHI(J))0118 *CU JH 1200119 KpT=JPT+TpT01?0 KpTRrlPTPt.TPTRoi?i r01 ?2 C DO STACKING DPFRATTQM01?3 C FRFQUtMC v01?^4 RUFJCKPJP-l-1 )=b!»FT (TPTR+n01?5 C01?6 C SAMPLE01?701?8 C0129 C nECI M ATinN LFVFL0130 JBUF(KPT-»-5)=TbMFriPT+b)om r0132 C NuMbFR UF STACKS0133 Jd"FCKPT-»-t>)=Ja!IFCKPT-«-6)tT D IIFf 1PT + 6")0134 C0135 C SpFCTRAL VAL"tS0136 DO 130 K=4,l?0137 130 RUFjCKPTPtK)=bMF-HKpTR-«.K)tf1 uFl(IPTPtK)0136 T0139 r QFCUT0140 RUFJfKPTPt01/11 Coia2 c DEGREES DF01430144 1200145 Gu TO PO0146 C0147 r CLOSF INPUT FILEoi48 140 CALL CLuSf_(i n CB)0149 80 CijNTTNUEoiso r0151 r roMP"TF THAN.SFFR FMNCTTQW AND FRPUP0152 ,TPT = -640153 JpTR=-320154 JPTC=-160155 C0156 C LLIHP UVEP SAMPLE IMTFRX/ALS0157 HO 150 1=1,NO!0158 T0159 C l.onp UV£P FRFQMEMCY RAÛS0160 D(j 150 J = l,40161 JpT = -JPTt640162 TpTR=JPTPt320163 JpTC=JPTC-Hb0164 C0165 C ChFC* FOP NO DATA STACKED

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0195 c ROUTTNF TU PLOT INDUCTTU M ARROWS AND RANOOM01^6 C0197 niMEMSTQN NOTAT(4) ,IRUF(?56) ,b!IFI(128)0196 C.0199 C CHFCK FOR NO DATA0200 TFCIPUF(TPTI*b> .LF. 0) RETUP.M0201 C0202 c PLPT A CPUSS AT THP PRTGTN0203 CALL LTNFCTXPQS-^,TYPOS,TXPOS+'VTYPOS)0204 TALL LTNE(TX n OS,TYPOS-*:,TXPO$,TYPOStS)0205 r0206 C - ThFCH' FOR ARPQWS [HO L n NH TO PLOT0207 TFfbUFT(TpTR + 21 ) - r-T. ARM A Y .OP. BMPT(TPTR+23) . r. T . WAX)0208 *RETORN0209 C0210 r---- ruMpuiF ARPO W co^P 10211 ^ P-tVEPSF Ê K! L' OF TN021202130214 C021.5 C NuN-P-EVEPSFu SFNSE F'PR OUT OF PHASF0216 IDXO=-IFTX(bUFTCTPTK+lft)/sr)021 7 TDYO=IF1X(RUFI (IPTRtM)/SC)0218 C.0219 c PLOT IN PHAS P ARPQW WITH SPLTD LTNF02?0 CALL LTNF(Tx p oS,TYPUS,TxPUStTDXI,0221 C0222 c---- USF DASHFD LT[S»F FOR PUT PF PHASE02?3 TALL ULlNE(lXpns,lYpnSrlXpns+inxn,TYP(jStTDYu,7,3)02?4 C02?5 c CHFCK FOR FRRuR TOP LAPGF TO PLOT CRFLATTVF FRPU D > ioo/0 i02?6 c CHFCK PEU\TI\/E EPR^H OF I.APGFST VE^TPR02?7 AH = A M AX1 railFT (TpTR + 21 ) roUFT CTPTR + 23) )02?8 TF fBl'PT (IPTK+1«) .GT. Ah .PR. PuF I (iPTR 11 71 .bT. A M ) bP T 0 1002?9 C0230 r COMPUTF FRPOR0231 TE p X = MAXO( 1, Tl0232 TERY=MAXO(1 f TFIX CtJUFT (IPTR+17)/SC) )0233 C0234 C -- PEP] £RR n R0235 CALL0236 *0237 PALL L>PO Y (TXPOS + TDXO+IFRY,TXPOS + TQXU-IFRX,02380239 C0240 c DETEPHTNF ANNPTATTUW PLOTTING0241 10 MOTEX= C;O0242 TpfjnxT .GF. 0) KJOTEX = -500243 MOT£Y=750244 TFTIHYT .GF. o) ôT£Y=-7^0245 Tpf inYH*ÔTEY .GT. 0) M|JTF,Y = -i\m F i02460247

140

PAGF 0006 ARPQW 10:2"* AM MQN., 9 ÂP., 19R1

0248 C0249 C ANNOTATE0250 PE P =1.0/RUFif0251 TALL0252 WR!T0253 10QO FuPhATf'T =",FS.O)0254 CALL CHA^SfNnTPXfNnTFYriMnTATf 8 f lf-t)0255 MOTtY=NUTtY-100256 C02^7 C ANNOTATE uF02S8 CALL COpF02^9 WRTTF(MUTAT r 1010) BUFICIPTR+J9)0260 1010 FURMAT( w nF= n rF4.?)02^1 CALL LHAPSfNnTFXfi\jnrFYn>jnTATr7r lf-1)0262 MOTfc.YsNOTEY-100263 C0264 C P|_ni NUMRtR n F0265 CALL CODF0266 WHITFCÛTAT, io?u)0267 1020 FQPMATf0268 TALL C02690270

FTN4 C^MPILEP: hP9?06()-160 <'2 RFV. 1913 (790206)

= 00465

141

PAGF 0007 FT.N. 10:23 AM MUM., 9 ÂP., 19M

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Computation of Geomagnetic Transfer Functions Using … derivation of this analysis can be found in Bendat and Piersol (Random Data: ... The following description uses notation similar