Computers & Geosciences 29 (2003) 961–969

SHEARCALC—a computer program for the calculation ofvolume change and mass transfer in a ductile shear zone$

Robert Sturm*

Institute of Physics and Biophysics, University of Salzburg, Hellbrunnerstrasse 34, A-5020 Salzburg, Austria

Received 1 November 2001; received in revised form 11 April 2003; accepted 16 April 2003

Abstract

SHEARCALC was created to automate mass balance calculations in an alteration zone. The program can be most

successfully applied to ductile shear zones, where an undeformed wall rock is transformed into a fine-grained mylonite

via several protomylonitic stages. The program was written in Visual Basic 6.0 and offers numerous features typical for

Windowst applications to increase the user friendliness. SHEARCALC consists of an input part for entering sample

names, specific weights and chemical data of the investigated rocks as well as for selecting immobile elements and

scaling factors for an appropriate display of the data in the isocon diagram. In the calculation part, the slope of the

isocon and related volume changes between two specific stages of alteration are computed. Additionally, gains and

losses of the main elements during deformation are expressed by respective mass transfer equations. As a special

feature, SHEARCALC contains an extensive diagram section, where the user can select between three chart types.

Besides the classical isocon diagram, mass changes of elements are also displayed in specific two- or three-dimensional

bar charts. Element behaviour along a transsect through the shear zone is documented by two- or three-dimensional

profile graphs. SHEARCALC is a stand-alone application adapted to modern Windowst operating systems and

therefore differs from many available programs in the geoscience which only run in DOS mode.

r 2003 Elsevier Ltd. All rights reserved.

Keywords: Shear zone; Mass balance; Windowst; Visual Basic; Isocon diagram

1. Introduction

Shear zones are outstanding examples of concentrated

deformation caused by the displacement of two adjacent

lithological blocks in the Earth’s crust. If imposed strain

rates are mainly accommodated by ductile processes,

shear zones are characterized by the development of

mylonites from unaltered wall rocks over scales of

centimetres to several 100m (e.g. White et al., 1980).

Due to their often very compact size, ductile shear zones

offer an excellent possibility to study the metamorphic

evolution as well as mechanical and chemical changes

along a predefined transsect of increasing deformation.

Recent investigations of these zones mainly include

questions concerning element mobility and related

volume changes during shearing and alteration processes

(e.g. O’Hara and Blackburn, 1989; Selverstone et al.,

1991; Simpson and de Paor, 1993; Ring, 1996; Hippertt,

1998; Yang et al., 1998). Based upon numerous

publications (see Selverstone et al., 1991 and references

cited therein), mylonitization may happen in the

following three ways (Fig. 1): (1) In ductile shear zones

marked by simple shear and the lack of metamorphic

fluids, mass transfer and volume change during defor-

mation may be regarded as almost negligible (isovolu-

metric shear zones). (2) If plane strain is combined with

transpression and affected rocks are infiltrated by

high amounts of metamorphic fluids, mylonitization

is accompanied by mass depletion and volume loss.

(3) In contrast, a combination of plain strain with

transtension may cause mass supply and volume gain

ARTICLE IN PRESS

$Code available from http://www.iamg.org/CGEditor.

index.htm

*Tel.: +43-662-8044-5709; fax: +43-662-8044-150.

E-mail address: robert.sturm@sbg.ac.at (R. Sturm).

0098-3004/03/$ - see front matter r 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/S0098-3004(03)00093-1

within the shear zone (e.g. formation of en echelon

veins). The quantitative description of volume gains

and losses during alteration processes has been intro-

duced in detail by Gresens (1967). A simple graphical

solution of Gresens’ mass transfer equation has been

described by Grant (1986). The results of both publica-

tions form the basis of the computer program presented

in this study.

Available computer programs concerning shear zones

mainly deal with the calculation of shear stress (Fares,

2000) or shear sense indicators (Zhang and Bjornerud,

1995; Jezek et al., 1999). The programs StrainCalculator

and GeoFryPlots by Rod Holcombe (University of

Queensland http://www.earthsiences.uq.edu.au/Brodh/

software) can also be assigned to this group. Computa-

tion of mass balances is limited to the Macintosh

program Mac Gresens (Potdevin, 1993), so far, while a

few other programs simulate comparable alterations in

the pedosphere due to weathering processes (e.g. Biddle

et al., 1998).

ARTICLE IN PRESS

Fig. 1. Types of mass transfer and volume change in ductile shear zones. Whereas ideal simple shear zones normally do not show any

mass transfer and volume change, subsimple convergent shear zones are characterized by an efflux of mass and respective volume loss.

Subsimple divergent shear zones provide a mass influx with related volume gain.

R. Sturm / Computers & Geosciences 29 (2003) 961–969962

The present paper introduces a new computer

program, termed SHEARCALC (version 1.0), for a

comprehensive analysis of geochemical data obtained

from rocks within a ductile shear zone. SHEARCALC

exclusively calculates the mass transfer and related

volume changes in ductile shear zones and therefore

should help to overcome the lack of programs dealing

with this specific field. The program has been written

with Microsoftt Visual Basic 6.0 and is largely based on

the register form concept which enables the creation of a

clear and simply understandable structure. Besides an

extensive calculation block, the program offers numer-

ous diagrams for graphical presentation of the results.

The present contribution first describes all the theory

of mass and volume balancing employed in SHEAR-

CALC, and then explains the attributes and application

of the program.

2. Theoretical background

2.1. Formulation of mass transfer during alteration

processes

Gresens (1967) found a method for the analysis of

changes in volume and concentrations during an

alteration process, which has been applied in many

studies of hydrothermal and upper-grade metamorphic

alteration. Concerning an alteration of A to B; mass

transfer of each element i can be expressed by the

following basic formula:

Xi ¼ fVgB

gACB

i � CAi

� �a: ð1Þ

CAi and CB

i describe the concentrations of component

i in sample A and B; gA and gB are the respective specific

gravities, fv is the volume factor, and a denotes the

reference mass of the original sample (e.g. 100 g).

Equation (1) forms the basis of Gresens’ composition–

volume diagrams (Gresens, 1967; Fig. 3), in which for

each component i the relation between Xi and a set of

arbitrary values of fv is shown. Where the resulting lines

for one or more components intersect Xi ¼ 0; the

respective abscissa value for fv is taken as the volume

factor of alteration. After determination of fv; relativegains and losses of mobile elements can be directly read

from the graph.

Grant (1986) introduced a more effective graphical

method by applying Eq. (1). Instead of a volume ratio fv;the author considered a ratio of equivalent masses after

ðMBÞ and before alteration ðMAÞ; expressed by the

following simple formula:

MB

MA¼

VBgB

VAgA¼ fV

gB

gA: ð2Þ

Changes in mass with respect to the original rock

ðMAÞ can be determined for each component i according

to the equation

MBi ¼ MA

i þ DMi; ð3Þ

where DMi denotes the mass change of component i: Totransform mass units into concentration units, Eq. (3) is

normalized against MA and subsequently multiplied by

ðMA=MBÞ:

MBi

MB¼

MAMBi

MBMA¼

MA

MB

MAi

MAþDMi

MA

� �: ð4Þ

Eq. (4) can now be written with concentration units in

the following way:

CBi ¼

MA

MBðCA

i þ DCiÞ: ð5Þ

Eq. (5) represents the basic expression of Grant’s

approach and is used to define the so-called ‘isocon’ by

plotting the analytical data of CBi against CA

i and

drawing a line through those (immobile) components

characterized by DCi ¼ 0: The resulting line runs

through the origin of the graph and has the slope

ðMA=MBÞ: The obtained reference line offers an

excellent way to calculate relative gains and losses of

mobile components by simply checking the displace-

ments of respective data points from the isocon.

Mathematically this can be best determined by dividing

both sides of Eq. (5) by CAi :

CBi

CAi

¼MA

MB

CAi

CAi

þDCi

CAi

� �: ð6Þ

Rearrangement of Eq. (6) results in the following

expression:

DCi

CAi

¼MB

MA

� �CB

i

CAi

� �� 1: ð7Þ

Determination of volume changes during the altera-

tion process can be carried out by simply rearranging

Eq. (2) to

VB

VA¼

MB

MA

� �gA

gB

� �: ð8Þ

VB=VAo1 indicates volume loss, VB=VA > 1 volume

gain. If VB=VA ¼ 1; alteration has taken place iso-

volumetrically. The quantity of volume change can be

easily checked from Eq. (8) by setting VA ¼ 1 (or 100%)

and calculating the resulting value of VB:

2.2. Calculation of the isocon using linear regression

analysis

The slope MA=MB of the isocon is determined by

plotting oxide and element concentrations of the altered

rock against those of the wall rock and by fitting a

regression line through the data points representing

immobile elements. From a mathematical point of view,

ARTICLE IN PRESSR. Sturm / Computers & Geosciences 29 (2003) 961–969 963

MA=MB can be now expressed as follows (least-squares

method):

MA

MB¼

Pi CA

i CBiP

iðCAi Þ

2: ð9Þ

The goodness-of-fit can be best expressed by the

parameter r2; where r denotes the correlation coefficient

of the plotted concentration data:

r2 ¼P

iðCB0

i � CBðmÞÞ2PiðC

Bi � CBðmÞÞ2

: ð10Þ

In Eq. (10), CiB0

is the respective concentration point

of the immobile component i on the regression line,

CBðmÞ is the mean of all immobile component concen-

trations of B: Another parameter describing the quality

of the fitted regression line is the standard error of

estimation for the slope MA=MB which is represented by

the following equation:

MA

MBðerrÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

i CBi �

MA

MBCA

i

� �2

ðn � 2ÞP

iðCAi � CAðmÞÞ2

vuuuut : ð11Þ

The program algorithm of SHEARCALC is based on

the equations presented. Design and use of the program

will be described in detail in the next section.

3. Program description

3.1. Data processing

SHEARCALC computes the mass balance and

volume change between two rocks characterized by

different grades of alteration. The program can be best

applied to ductile shear zones, where a wall rock is

transformed into a high-grade mylonite by passing

through several protomylonitic stages. SHEARCALC

also offers the possibility to calculate losses or gains of

mass and volume between the intermediate stages of

alteration. Results of the calculations are presented on

specific forms and can be printed out optionally.

Additionally, the program includes an extensive diagram

section for a convenient graphical display of the results.

SHEARCALC was designed and programmed in Visual

Basic 6.0. This computer language allows to create very

user-friendly applications with the typical features of a

Windowst program (menu bar, symbol bar, etc.).

Although the design of SHEARCALC shows some

specificities like horizontal and vertical register bars, all

users familiar to any Windowst application should be

able to navigate successfully through the respective

forms, at once. The navigation is realized by simply

clicking on an element of the register bars or a button in

the symbol bar. Each active element or button is

characterized by a change of the mouse pointer into a

pointing hand symbol. SHEARCALC has the advan-

tage to run as a stand-alone application within the

Windowst operating system (Version 98 or 2000).

Many scientific programs written in other languages

than Visual Basic 6.0 (e.g. QuickBasic, Fortran,

TurboPascal, C) mainly run in the DOS environment

and therefore partly cause higher operating times or

conflicts with the Windowst operating system.

In general, the presented program can be subdivided

into six main parts, to which the user can navigate by

simply clicking on the respective elements of the vertical

register and the uppermost button of each symbol bar:

1. ENTRANCE: From here, the user can navigate to

the main parts of the program or leave SHEAR-

CALC, again. In this form, also first steps for a

successful use of the program as well as interesting

links in the world wide web are available (Fig. 2A).

2. INPUT: In this part of the program, sample names,

specific weights and chemical data (main and trace

element concentrations; mean values and standard

deviations SD) of an undeformed wall rock as well as

five different stages of deformation labelled with

mylonite 1–5 can be entered (Fig. 2B).

3. IMMOBILE ELEMENTS/SCALING FACTORS:

This part of SHEARCALC allows the selection of

elements considered as immobile during the process of

deformation (Fig. 2C). The input of scaling factors is

necessary for a convenient display of all selected

elements in the isocon diagram (Grant, 1986; Fig. 2D).

4. ISOCON: In this part, the isocons are calculated by

linear regression analysis for different transforma-

tions (e.g. transformation of wall rock into mylonite

5, etc.). The standard error of the isocon slopes,

goodness-of-fit (indicated by r2) as well as type and

relative quantity of volume change are computed

additionally (Fig. 2E).

5. MASS BALANCE: This part of SHEARCALC

provides the mass balance equations (Gresens, 1967)

for transitions between wall rock and mylonites as well

as between different mylonitic stages (Fig. 2F).

6. DIAGRAMS: In this part, the user can select

between three diagram types for a graphical dis-

play of the chemical data and calculation results

(Fig. 2G): (a) isocon diagrams; (b) bar charts to

visualize relative gains and losses of elements during

deformation; (c) line charts showing the behaviour of

elements throughout the zone of alteration.

Except for the ENTRANCE part, each form of

SHEARCALC contains a vertical register bar on the

right side for navigation to the main program sections

and a symbol bar on the left side for specific actions

useful in a Windowst program. As documented above,

within SHEARCALC the forms for data input and data

output are clearly separated. Therefore, the user is not

ARTICLE IN PRESSR. Sturm / Computers & Geosciences 29 (2003) 961–969964

able to manipulate any of the calculated results. After

each change of the input data, calculations have to be

carried out from the beginning and are not recalculated

automatically.

In the present contribution the program was tested on

chemical data from a shear zone described in detail by

Sturm and Steyrer (2003). The deformation zone is

located in the western part of the Tauern Window

(Eastern Alps, Austria) and has been formed under

medium- to deep-crustal P2T conditions. In general,

besides the wall rock (sample AS 14/92) five mylonitic

stages (samples 815A–E) could be distinguished. From

each deformation stage at least five samples have been

analysed chemically to recognize possible inhomogene-

ities in composition. Input data are listed in Table 1,

while selected results of calculation are shown in Figs. 2

and 3.

3.2. Graphics

SHEARCALC contains an extensive DIAGRAM

section for an appropriate visualization of input data

and results from diverse calculations. While chemical

data of the INPUT forms can be plotted in profiles

documenting chemical changes along a predefined

transsect, isocon diagrams help to describe the mobility

of certain elements within the investigated alteration or

shear zone. Mass transfers of the main elements between

two deformational stages are also presented graphically

in specific bar charts (Fig. 2G).

3.2.1. Isocon diagrams

Clicking on the isocon diagram button of the

DIAGRAM form opens a new window containing

several command buttons in the upper right corner

and an empty drawing area. After activation of the

DRAW button by a mouse click or with the TAB and

RETURN keys, the isocon diagram illustrating element

mobilities between two deformational stages of the shear

zone is drawn (Fig. 3A). Only those elements selected in

the SCALING form are plotted, and concentrations

(and standard deviations) are increased or decreased by

the respective scaling factors. The isocon, line of

constant mass, and line of constant volume are

ARTICLE IN PRESS

Table 1

Geochemical data from deep-crustal shear zone of western Tauern Window (Austria; Sturm and Steyrer, 2003)

Sample AS 14/92 815E 815D 815C 815B 815A

Rock Wall rock Mylonite 1 Mylonite 2 Mylonite 3 Mylonite 4 Mylonite 5

Conc. SD Conc. SD Conc. SD Conc. SD Conc. SD Conc. SD

Main elements (wt%)

SiO2 63.90 1.92 62.00 2.85 58.30 3.09 51.00 3.47 46.20 3.28 40.80 3.39

TiO2 0.66 0.02 0.76 0.03 0.82 0.04 0.83 0.06 0.72 0.05 0.80 0.07

Al2O3 17.00 0.51 16.60 0.76 18.50 0.98 19.00 1.29 20.60 1.46 19.80 1.64

Fe2O3 5.35 0.16 8.56 0.39 9.27 0.49 12.00 0.82 15.90 1.13 20.40 1.69

MgO 1.83 0.05 3.06 0.14 3.46 0.18 5.28 0.36 6.24 0.44 6.55 0.54

MnO 0.10 0.00 0.11 0.01 0.11 0.01 0.13 0.01 0.16 0.01 0.24 0.02

CaO 4.90 0.15 2.34 0.11 2.14 0.11 3.21 0.22 2.78 0.20 2.72 0.23

K2O 2.08 0.06 2.72 0.13 2.96 0.16 3.20 0.22 4.00 0.28 4.24 0.35

Na2O 4.00 0.12 2.13 0.10 2.20 0.12 3.06 0.21 1.80 0.13 0.84 0.07

P2O5 0.18 0.01 0.19 0.01 0.14 0.01 0.17 0.01 0.16 0.01 0.22 0.02

LOI 0.75 0.02 1.60 0.07 1.80 0.10 1.70 0.12 2.20 0.16 2.85 0.24

Total 100.75 100.07 99.70 99.58 100.76 99.46

Trace elements (ppm)

Nb 17 0.68 18 0.56 17 0.90 19 1.29 15 1.07 13 1.08

Zr 181 7.24 181 8.33 189 10.02 184 12.51 190 13.49 216 17.93

Y 11 0.34 18 0.64 22 1.17 29 1.97 17 1.21 17 1.41

Sr 315 12.60 164 7.54 174 9.22 163 11.08 110 7.81 98 8.13

Rb 88 3.52 97 4.46 103 5.46 102 6.94 148 10.51 164 13.61

Cr 11 0.44 18 0.83 14 0.74 12 0.82 11 0.78 10 0.83

Ni 6 0.24 7 0.32 10 0.53 13 0.88 8 0.57 8 0.66

Ba 442 17.68 513 23.60 380 20.14 240 16.32 350 24.85 518 42.99

Hf 4.8 0.19 5 0.23 4.9 0.26 5.4 0.37 4.5 0.32 4.2 0.35

Specific weight (g/cm3) 2.87 2.94 3.03 3.08 3.14 3.20

Data were used to test SHEARCALC. Grade of deformation is increased from Mylonite 1 to Mylonite 5.

R. Sturm / Computers & Geosciences 29 (2003) 961–969 965

displayed with different signatures (solid, dashed, and

dotted). Abscissa and ordinate of the diagram are

labelled with the rocks, whose element concentrations

and standard deviations are plotted in the graph. Scaling

of both x- and y-axis uniformly ranges from 0 to

50wt%. BACK and FORWARD buttons will navigate

ARTICLE IN PRESS

Fig. 2. (A–G) Entrance, input and calculation forms of SHEARCALC. Except for the ENTRANCE form, all forms are characterized

by their uniform organization with horizontal and vertical registers as well as a symbol bar on left side.

R. Sturm / Computers & Geosciences 29 (2003) 961–969966

ARTICLE IN PRESS

Fig. 3. Graphs produced by SHEARCALC: (A) isocon diagram (data points with SD rectangles), (B) two-dimensional mass transfer

diagram, (C) three-dimensional mass transfer diagram with autoscaling, (D) two-dimensional profile diagram, (E) three-dimensional

profile diagram with autoscaling.

R. Sturm / Computers & Geosciences 29 (2003) 961–969 967

through all possible isocon diagrams (up to 9), whereas

with the PRINT button a high-quality print of the graph

is produced.

3.2.2. Mass transfer diagrams

Activation of the medium button in the DIAGRAM

form opens a window that differs from the respective

isocon diagram window only in some details. Besides the

DRAW button, three input fields have been generated

which allow the determination of a minimum and

maximum ordinate value as well as the selection of

the distance between the major tics. After clicking the

DRAW button, a two-dimensional bar chart with

the specific properties entered above will be generated

(Fig. 3B). The topic of the diagram describes the

transition for which the mass balance equation was

calculated. As a further characteristic, respective results

can be also drawn in a three-dimensional graph. This is

realized by simply clicking on the 3D-GRAPH button.

After appearance of a new window containing a default

diagram, activation of the DRAW button generates the

desired chart (Fig. 3C). In each three-dimensional graph

five transition types are displayed. Scaling of the y-axis is

done automatically. The window of two-dimensional

diagrams can be activated again by clicking on the 2D-

GRAPH button.

3.2.3. Chemical profiles

As an additional feature of SHEARCALC, the user

can draw chemical profiles through the alteration zone.

This is realized by clicking the third button of the

DIAGRAM form. A window very similar to that of the

mass transfer diagram is opened. In the data fields, the

user can enter minimum and maximum values of the y-

axis as well as the distance between two major tics. After

clicking on the DRAW button, the desired graph is

displayed (Fig. 3D). For a better overview, each graph

only contains the profiles of five elements which are

listed in the legend on the right side. With the 3D-

GRAPH button a three-dimensional line chart can be

created, again. Similar to the mass transfer graph,

scaling of the ordinate is carried out automatically

(Fig. 3E).

3.3. Data output

By using the PRINT button, respective input data,

results of calculations, and graphs can be printed out,

optionally. Within the input and calculation forms, a

small menu is opened after clicking on the PRINT

command, where the user can select between printing the

activated form or a summary of computation containing

all raw data entered into the input section, the elements

assumed as immobile, the calculated isocons, the good-

ness-of-fit, the estimated volume changes, and the

related mass balance equations. Using the PRINT

button in the DIAGRAM forms results in printing out

the activated graph on a single sheet of paper.

Manipulation of a diagram is not possible at the

moment, but will be implemented in a future version

of SHEARCALC.

4. System requirements and availability of the program

SHEARCALC was programmed with the latest

version of MicrosoftTM Visual Basic. To take advantage

of the graphical layout of the program, a Pentium-IIt

computer with an SVGA graphic card is highly

recommended. Further, a newer version of Windowst

(98 or 2000) must be installed to guarantee a trouble-free

execution of the program. For execution of the program,

VBRUN.DLL must be included in the Windowst

system folder. Printing out of the charts should be done

either with a high-resolution inkjet printer or a laser

printer. Program files can be directly obtained from the

author via E-mail, or downloaded from the IAMG

server.

Acknowledgements

The author thanks the two anonymous reviewers, who

have helped to improve the paper significantly.

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