Directional analysis of surface artefact distributions. A case study from the Murghab Delta, Turkmenistan

23 Pages·3.064 MB·English

by  Markofsky S., Bevan A.

Directional
 analysis
 of
 surface
 artefact
 distributions.
 A
 case
 study
 from
 the

Murghab
 Delta,
 Turkmenistan

Steven
 Markofsky
 and
 Andrew
 Bevan

Postprint
 of
 2011
 paper
 in
 Journal
 of
 Archaeological
 Science
 39.2:
 428-­‐439
 (doi:

10.1016/j.jas.2011.09.031).

Abstract

This
 paper
 investigates
 directional
 influences
 in
 the
 distribution
 of
 Bronze
 Age

surface
 pottery
 in
 the
 northern
 Murghab
 Delta,
 Turkmenistan.

 Drawing
 upon
 a

continuous
 dataset
 of
 pottery
 sherd
 counts
 obtained
 by
 intensive
 field
 survey,
 it

examines
 the
 degree
 to
 which
 we
 can
 make
 sense
 of
 the
 archaeological
 processes

at
 work
 in
 a
 heavily
 obstructed
 and
 dynamic
 landscape.

 In
 so
 doing,
 it
 makes
 use

of
  two
  analytical
  methods
  that
  have
  rarely
  been
  used
  in
  archaeology:
  a)

geostatistical
  analysis
  using
  variograms
  to
  investigate
  directional
  spatial

autocorrelation
 in
 recorded
 sherd
 counts,
 and
 b)
 angular
 wavelet
 analysis
 in

evaluating
  directional
  influences
  in
  the
  sherd
  distributions
  for
  particular

chronological
  periods.
  While
  some
  kinds
  of
  directional
  influence
  can
  be

identified
  visually,
  a
  quantitative
  approach
  is
  particularly
  useful
  in

deconstructing
 such
 patterns.

 In
 this
 particular
 dataset,
 distinct
 but
 related

directional
  processes
  can
  be
  identified
  and
  measured:
  a)
  the
  impact
  of
  the

complex
  system
  of
  watercourses
  in
  the
  delta
  on
  both
  settlement
  and
  post-­‐
depositional
 processes;
 and
 b)
 recovery
 bias
 in
 the
 observations
 made
 during

survey.

1.
 Introduction

Surface
  pottery,
  often
  the
  most
  accessible
  evidence
  of
  past
  archaeological

landscapes,
 constitutes
 an
 awkward
 analytical
 dataset.

 Rather
 than
 resulting

from
 any
 single
 archaeological
 or
 post-­‐depositional
 process,
 surface
 material

typically
 represents
 a
 palimpsest,
 the
 spatially
 and
 temporally
 averaged
 material

residue
  of
  a
  range
  of
  processes.

  Over
  the
  past
  several
  decades,
  increasing

recognition
 of
 this
 inherent
 dynamism
 in
 material
 distributions
 has
 fostered
 a

shift
 in
 survey
 methodology.

 Whereas
 traditional
 surveys
 focused
 primarily
 on

archaeological
 sites
 to
 explore
 settlement
 patterns
 (e.g.
 Adams,
 1965,
 Adams,

1981),
  more
  recent
  approaches
  have
  employed
  a
  broader
  range
  of

methodologies
 designed
 to
 address
 whole
 archaeological
 landscapes
 (e.g.
 Bintliff

and
 Snodgrass,
 1985,
 Wilkinson
 and
 Tucker,
 1995,
 Cleuziou,
 et
 al.,
 1998,
 Van

Leusen,
 2002).

A
  limitation
  of
  the
  analytical
  methods
  deployed
  by
  many
  recent
  surveys,

however,
 has
 been
 their
 tendency
 to
 consider
 rather
 simple
 isotropic
 spaces:
 that

is,
 ones
 in
 which
 distributional
 processes
 are
 assumed
 to
 have
 equal
 influences

in
 all
 directions
 and
 to
 exist
 in
 a
 uniform
 spatial
 environment
 (Longley
 and
 Batty,

2003:
  311).

  This
  temptation
  to
  simplify
  can
  be
  analytically
  convenient,
  as

disregarding
  anisotropic
  (i.e.
  directionally
  varied)
  influences
  often
  makes
  it

easier
 to
 apply
 standard
 geographic
 methods
 such
 as
 Christaller
 hierarchies,

catchment
 models,
 buffers,
 networks
 or
 Voronoi/Thiessen
 tessellations
 (Evans
and
  Gould,
  1982,
  Conolly
  and
  Lake,
  2006:
  212).

  Even
  when
  directional

influences
 are
 obvious
 to
 the
 archaeologist,
 for
 example
 the
 inherent
 linearity

that
 may
 characterise
 the
 distribution
 of
 surface
 material
 along
 river
 channels,

roads
 or
 valleys,
 such
 factors
 tend
 to
 be
 addressed
 qualitatively
 and
 often
 as
 an

afterthought.

Because
  anisotropy
  has
  been
  seldom
  investigated
  formally
  in
  archaeological

research,
  a
  potentially
  informative
  body
  of
  data
  has
  been
  overlooked.

  For

example,
 in
 archaeological
 survey,
 directional
 influences
 may
 factor
 heavily
 in

the
 distribution
 of
 surface
 material,
 reflecting
 not
 only
 trajectories
 of
 artefact

deposition
 from
 settlement-­‐derived
 and
 post-­‐depositional
 processes,
 but
 also

recovery
 biases
 that
 may
 influence
 the
 interpretation
 of
 the
 surface
 distribution.

To
 an
 extent,
 such
 factors
 can
 be
 detected
 visually
 or
 with
 the
 help
 of
 GIS-­‐based

approaches.

 However,
 such
 methods
 only
 provide
 coarse
 data
 and
 may
 overlook

more
 subtle
 directional
 patterns,
 as
 well
 as
 ways
 in
 which
 they
 may
 be
 measured

or
 quantified.

In
 this
 paper,
 we
 investigate
 anisotropy
 in
 a
 carefully
 recovered
 distribution
 of

surface
  pottery
  from
  a
  dynamic
  fluvial
  environment.

  Using
  some
  analytical

approaches
 that
 have
 been
 rarely
 applied
 in
 archaeology,
 we
 seek
 not
 only
 to

identify
 directional
 trends
 in
 survey
 data
 that
 may
 not
 be
 readily
 apparent,
 but

also
 to
 measure
 and
 interpret
 these
 trends
 in
 the
 context
 of
 settlement
 dynamics,

post-­‐depositional
 processes
 and
 potential
 recovery
 biases.

2.
 Research
 Context

The
 survey
 data
 considered
 below
 is
 derived
 from
 the
 Northern
 Murghab
 Delta

Survey
  (NMDS),
  an
  intensive
  field-­‐walking
  project
  conducted
  by
  the

corresponding
 author
 in
 the
 Murghab
 river
 delta
 in
 southeastern
 Turkmenistan

from
  2007-­‐2009
  (Figure
  1).

  Since
  the
  1970s,
  the
  Murghab
  has
  been
  an

increasing
 focus
 of
 archaeological
 enquiry,
 prompted
 by
 the
 discoveries
 of
 major

Bronze
 Age
 sites
 dating
 to
 the
 late
 3rd
 and
 early
 2nd
 millennium
 BC
 (Kohl,
 1984,

Salvatori,
  1998),
  of
  which
  the
  best-­‐known
  is
  Gonur
  Depe
  (Sarianidi,
  1990,

Sarianidi,
  2005).

  Over
  the
  past
  two
  decades,
  researchers
  have
  identified

hundreds
 of
 new
 sites
 in
 the
 overall
 region
 through
 extensive
 surveys
 (Cattani

and
  Salvatori,
  2008,
  Salvatori,
  2008).

  These
  findings
  have
  led
  to
  a
  new

interpretation
 of
 the
 regional
 Bronze
 Age
 settlement
 pattern
 which,
 it
 has
 been

argued,
  was
  characterised
  by
  continuous
  and
  widespread
  occupation
  and

thought
 to
 be
 reflective
 of
 an
 integrated
 proto-­‐state
 structure.

 While
 not
 yet

broadly
 accepted,
 such
 an
 interpretation
 represents
 a
 substantial
 change
 from

previous
 ones
 that
 had
 envisioned
 settlement
 in
 a
 series
 of
 discrete
 ‘micro-­‐
oases’,
 each
 representing
 isolated
 groups
 (Hiebert,
 1994:
 39).
Figure
 1:
 Map
 of
 Central
 Asia
 (NASA
 Blue
 Marble)
 with
 the
 survey
 area
 indicated
 by
 small
 white

square
 in
 centre
 of
 image

This
 predominant
 focus
 on
 regional
 analysis
 and
 large
 sites
 in
 the
 interpretation

of
 Murghab
 settlement
 has
 however
 precluded
 a
 more
 refined
 understanding
 of

micro-­‐scale
 distributions
 of
 archaeological
 material.

 While
 a
 few
 small-­‐scale

intensive
 surveys
 have
 been
 conducted
 in
 the
 region
 (e.g.
 Cleuziou
 et
 al.
 1998;

Cerasetti
  pers.
  comm.),
  a
  continued
  under-­‐emphasis
  on
  local
  settlement

dynamics
 and
 material
 distributions
 has
 led
 to
 a
 rather
 lopsided
 interpretation

of
 Murghab
 settlement,
 drawn
 largely
 from excavation
 of
 a
 few
 large
 sites
 in
 the

context
 of
 regional
 surveys.

 This
 situation
 has
 only
 recently
 begun
 to
 change,

driven
  in
  part
  by
  the
  increasing
  interest
  in
  small
  sites
  in
  the
  context
  of

sedentary/nomadic
 relationships
 (e.g.
 Cattani
 et.
 al.
 2008).
 Compounding
 this

interpretative
  problem
  is
  the
  fact
  that,
  due
  to
  geomorphological
  and

anthropogenic
 processes,
 the
 recovery
 potential
 for
 archaeological
 sites
 is
 often

extremely
 poor.

 In
 some
 cases,
 sites
 have
 been
 completely
 destroyed
 as
 a
 result

of
 an
 explosion
 in
 urban
 and
 agricultural
 development
 over
 the
 past
 several

decades,
 associated
 with
 the
 construction
 of
 the
 Karakum
 Canal.

 Elsewhere,

particularly
 in
 the
 central
 and
 southern
 regions
 of
 the
 delta,
 aggrading
 silts
 have

resulted
  in
  alluvial
  deposition
  that
  may
  be
  several
  metres
  deep
  (Cremaschi,

1998).

 In
 the
 northernmost
 region
 of
 the
 palaeodelta,
 where
 alluvial
 deposits

are
 shallower
 and
 agriculture
 less
 pervasive,
 exposed
 sites
 are
 often
 severely

deflated,
  susceptible
  to
  desert
  winds
  and
  identifiable
  only
  as
  nebulous

aggregations
  of
  surface
  pottery.

  Intermittent
  but
  often
  heavy
  dune
  cover

obscures
  much
  of
  the
  landscape,
  presenting
  an
  additional
  barrier
  to

archaeological
 visibility
 and
 hindering
 effective
 interpretation.

The
 northern
 margin
 of
 this
 inland
 alluvial
 fan
 effectively
 constitutes
 a
 unique

geomorphology
 in
 which
 a
 transitional
 zone
 exists
 between
 delta
 and
 desert

(Figure
  2).

  Each
  of
  these
  regions
  may
  be
  seen
  to
  broadly
  exhibit
  certain

prevailing
 anisotropic
 trends.

 The
 desert
 morphology
 is
 represented
 in
 part
 by

dune
 ridges
 that
 tend
 to
 align
 north-­‐south,
 while
 the
 prevailing
 geomorphology

of
  the
  delta,
  by
  contrast,
  tends
  more
  towards
  the
  northwest.

  Where
  these

regions
 interact,
 however,
 these
 trends
 become
 much
 more
 complex,
 a
 situation
exacerbated
 by
 relict
 watercourses,
 roadways
 and
 gas
 pipelines.

 Each
 of
 these

myriad
  directional
  influences
  that
  exist
  in
  the
  landscape
  has
  potentially

influenced
 the
 present-­‐day
 orientation
 of
 surface
 pottery.

Figure
 2:
 Landscapes
 of
 the
 northern
 Murghab:
a)
 Landscape
 of
 low
 dune
 ridges
 (left)
 and
 depressions
 (right),
 and

b)
 Sand
 begins
 to
 accumulate
 on
 an
 old
 trackway

A
 survey
 covering
 11
 km2
 of
 this
 landscape
 was
 investigated
 using
 intensive

methods
 in
 which
 surveyors,
 spaced
 20
 metres
 apart,
 collected
 information
 at

20m
 intervals
 along
 individual
 transects.

 This
 process
 has
 provided
 a
 dataset
 of

observations
 that
 are
 recorded
 on
 a
 20m
 x
 20m
 grid,
 each
 grid
 square
 of
 which

contains
 information
 such
 as
 the
 sherd
 counts
 for
 that
 square.

 For
 ease
 of

interpretation
 and
 discussion,
 the
 survey
 area
 is
 also
 divided
 into
 a
 coarser
 set
 of

analytical
  units,
  defined
  according
  to
  perceived
  similarity
  in
  geomorphology

and/or
 surface
 scatter
 (Figure
 3).

 This
 archaeological
 dataset
 is
 considered
 in

detail
 via
 the
 spatial
 analysis
 below.
Figure
 3.
 NMDS
 survey
 area:

a)
 NMDS
 survey
 boundary
 with
 analytical
 units,
 and

b)
 Directionality
 in
 the
 sherd
 distribution

3.
 Methodology

The
 objective
 of
 the
 following
 analysis
 is
 to
 ascertain
 the
 degree
 to
 which
 sherd

counts
  and
  other
  landscape
  surface
  phenomena
  exhibit
  continuity
  in
  some

directions
 more
 so
 than
 others
 (i.e.
 are
 anisotropic
 in
 nature).

 There
 are
 a
variety
 of
 methods
 for
 considering
 such
 anisotropy
 in
 spatial
 datasets,
 including

directional
 quadrat
 counts,
 nearest
 neighbour
 bearings,
 directional
 correlograms

and
 Fourier
 analysis

 (Patterson,
 1934,
 Bartlett,
 1964,
 Haynes
 and
 Enders,
 1975,

Rosenberg,
 2000),
 but
 rarely
 have
 these
 been
 considered
 in
 archaeology.

 Here

we
 use
 two
 methods
 for
 understanding
 possible
 directional
 effects
 within
 the

NMDS
  data.

  The
  first
  is
  an
  aspect
  of
  geostatistics
  that
  employs
  directional

variograms
 and
 variogram
 surfaces,which
 are
 graphical
 plots
 that
 can
 represent

spatial
 variation
 over
 multiple
 distances
 and
 in
 different
 directions.

 The
 second

method,
 angular
 wavelet
 analysis,
 examines
 angular
 variation
 between
 individual

point
 pairs
 (e.g.
 surface
 sherds).

 While
 geostatistics
 have
 seen
 some
 use
 in

archaeology
 and
 have
 recently
 been
 used
 for
 considering
 surface
 sherd
 counts

(Bevan
  and
  Conolly,
  2009:
  258-­‐9),
  angular
  wavelets
  have
  not
  yet
  been

considered
 in
 this
 context,
 despite
 having
 produced
 very
 promising
 results
 when

applied
 to
 ecological
 data
 (e.g.
 Rosenberg,
 2004).

To
  illustrate
  each

  method,
  we
  have
  created
  a
  hypothetical
  distribution
  of

material
 over
 a
 2km
 x
 2
 km
 grid
 in
 which
 anisotropy
 within
 the
 point
 patterns

(the
  heavy
  diagonal
  striping)
  has
  been
  exaggerated
  to
  better
  illustrate
  the

concept
 (Figure
 4).

 The
 following
 discussion
 will
 utilise
 this
 dataset,
 first
 in
 the

context
 of
 geostatistics
 and
 then
 of
 angular
 wavelet
 analysis,
 before
 applying
 the

methods
 to
 the
 actual
 NMDS
 survey
 data.

Figure
 4.
 Sample
 data
 for
 a
 hypothetical
 2km
 x
 2km
 region:

a)
 sample
 pattern
 of
 40,000
 points,
 and

b)
 aggregated
 Point
 pattern.
 Legend
 indicates
 sherd
 counts
 per
 hypothetical
 unit

The
 first
 method,
 variogram
 analysis,
 falls
 within
 the
 discipline
 of
 geostatistics,
 a

body
 of
 related
 concepts
 and
 methods
 that
 explore
 spatial
 variation
 in
 attribute

values
 observed
 at
 different
 point,
 line
 or
 area
 locations,
 particularly
 with
 the

purpose
 of
 spatial
 prediction,
 simulation
 or
 sampling
 optimisation
 (Lloyd
 and

Atkinson,
 2004).

 Geostatistics
 typically
 assume
 an
 underlying
 continuous
 field
 of

variation
 that
 has
 been
 sampled
 at
 a
 limited
 number
 of
 locations.

 Each
 sample

point
 has
 a
 distinct
 attribute
 value
 as
 well
 as
 a
 location
 in
 space,
 and
 unknown

values
 may
 be
 predicted
 via
 the
 interpolation
 method
 known
 as
 kriging
 (a
 well-­‐
known
 example
 concerns
 the
 prediction
 of
 continuous
 geological
 phenomena
based
 on
 sparsely
 sampled
 borehole
 observations
 Journel,
 1974).

 The
 degree
 of

similarity
  between
  individually-­‐measured
  values
  is
  referred
  to
  as
  spatial

autocorrelation
 or
 spatial
 dependence
 (see
 Fortin
 and
 Dale,
 2005:
 6-­‐10
 for
 a

useful
 distinction
 between
 the
 two),
 and
 is
 a
 formal
 expression
 of
 ‘Tobler’s
 first

law
 of
 geography’(Tobler,
 1970)
 which
 states
 that
 the
 closer
 in
 space
 that
 two

measurements
 are,
 the
 more
 similar
 those
 measurements
 are
 likely
 to
 be.

We
 can
 explore
 this
 dependence
 by
 using
 experimental
 or
 empirical
 variograms:

graphical
 plots
 that
 summarise
 the
 average
 semi-­‐variance
 (half
 the
 variance)

between
 the
 attribute
 values
 (e.g.
 sherd
 counts)
 of
 sampled
 point-­‐pairs
 as
 a

function
 of
 the
 distance
 (or
 spatial
 lag)
 between
 these
 pairs.

 A
 model
 may
 then

be
 fitted
 to
 the
 plot
 in
 order
 to
 interpolate
 unknown
 values
 throughout
 the

underlying
 continuum.

 These
 fitted
 curves
 are
 commonly
 described
 in
 terms
 of

the
 range,
 sill
 and
 nugget.

 The
 range
 is
 the
 distance
 at
 which
 the
 semi-­‐variance

values
 reach
 a
 plateau,
 indicating
 that
 the
 observed
 point
 pairs
 have
 effectively

become
 spatially
 independent
 of
 each
 other,
 and
 the
 semi-­‐variance
 at
 this
 point

is
 referred
 to
 as
 the
 sill.

 The
 nugget
 effect
 is
 a
 non-­‐zero
 starting
 semi-­‐variance
 at

extremely
 short
 distances
 that
 reflects
 indeterminate
 local
 variability
 (Atkinson

and
  Tate,
  2000).

  Here,
  we
  are
  concerned
  with
  interpretation
  rather
  than

prediction
 and
 will
 focus
 on
 the
 empirical
 variogram,
 not
 the
 fitted
 model.

Variograms
 may
 be
 omnidirectional
 or
 directional.

 The
 first
 type
 considers
 only

the
  distance
  between
  point
  pairs
  (i.e.
  the
  range
  of
  spatial
  autocorrelation)

(Gringarten,
 2001).

 Directional
 variograms,
 however,
 examine
 specific
 angles

and
  can
  therefore
  identify
  directions
  that
  exhibit
  greater
  levels
  of
  spatial

autocorrelation
 than
 others
 (i.e.
 unusual
 continuity
 in
 values),
 and
 the
 spatial

scale
 at
 which
 these
 anisotropic
 influences
 come
 into
 play.

 A
 further
 measure
 of

the
 strength
 of
 anisotropy
 may
 be
 obtained
 by
 calculating
 the
 ratio
 of
 the
 ranges

for
  the
  primary
  direction
  (major
  axis)
  of
  anisotropy
  and
  the
  perpendicular

direction
 (minor
 axis),
 and
 typically
 this
 is
 one
 of
 the
 parameters
 that
 is
 fitted
 as

part
 of
 a
 model
 variogram
 and
 for
 subsequent
 prediction
 purposes
 (e.g.
 Atkinson

and
 Lloyd,
 2009:
 135,163).

 However,
 the
 original
 empirical
 variogram
 retains

more
 information
 about
 the
 spatial
 range
 and
 character
 of
 the
 anisotropy
 so
 we

prefer
 it
 below.

Referring
 to
 our
 sample
 data,
 the
 omnidirectional
 variogram
 (Figure
 5a)
 shows

decreasing
 spatial
 dependence
 as
 the
 distance
 between
 observations
 increases,

reaching
  a
  plateau
  around
  400m,
  the
  distance
  at
  which
  point
  pairs
  become

spatially
 independent
 of
 each
 other.

 Also
 visible
 is
 a
 ‘hole-­‐effect’,
 a
 characteristic

dip
 in
 the
 plot
 that
 can
 indicate
 heterogeneity
 and/or
 periodicity
 in
 the
 data

(Pyrcz
 and
 Deutsch,
 2003).

 The
 omni-­‐directional
 variogram,
 however,
 provides

little
 information
 about
 anisotropy.

 This
 is
 reflected
 more
 clearly
 in
 the
 45°

directional
 variogram
 (Figure
 5c,
 bottom
 right),
 in
 which
 the
 semi-­‐variance
 is

much
 lower
 than
 in
 the
 omni-­‐directional
 variogram,
 indicating
 continuity
 in
 that

direction.

  Also
  potentially
  useful,
  and
  sometimes
  easier
  to
  interpret,
  are

variogram
 maps,
 in
 which
 the
 direction
 of
 maximum
 anisotropy
 corresponds

with
 the
 major
 axis
 of
 the
 observed
 ellipse
 (in
 Figure
 5d,
 this
 appears
 linear

because
 of
 the
 prominence
 of
 the
 35°-­‐45°
 direction).
The
 second
 analytical
 method
 used
 in
 this
 paper
 is
 angular
 wavelet
 analysis

(Rosenberg,
 2004).

 More
 commonly
 used
 in
 fields
 such
 as
 mathematics
 and

engineering,
 for
 example
 in
 the
 context
 of
 signal
 processing,
 the
 procedure
 has

been
  recently
  applied
  in
  ecological
  contexts
  to
  identify
  spatial
  patterning
  in

different
 types
 of
 vegetation.

 An
 advantage
 of
 wavelet
 approaches
 is
 that
 they

are
 useful
 for
 recovering
 patterns
 in
 the
 presence
 of
 noise,
 for
 example
 of
 the

kind
  produced
  by
  time-­‐averaged,
  post-­‐depositionally
  transformed
  and

imperfectly
 recovered
 archaeological
 datasets.

Figure
 5.
 Variograms
 for
 sample
 dataset:
 a)
 omnidirectional
 empirical
 variogram,
 b)

omnidirectional
 empirical
 variogram
 (as
 points
 only)
 with
 fitted
 spherical
 model
 (as
 grey
 line),

c)
 directional
 variograms
 (0°
 indicates
 the
 N-­‐S
 direction)
 shown
 as
 black
 points
 alongside
 the

omnidirectional
 variogram
 shown
 as
 a
 grey
 line,
 and
 d)
 a
 variogram
 map.

The
  method
  differs
  from
  geostatistical
  approaches
  in
  that
  it
  considers
  non-­‐
valued,
 or
 unmarked
 point
 patterns
 where
 each
 point
 has
 no
 intrinsic
 value
 and

is
 merely
 identified
 by
 its
 location
 in
 space.

 To
 visualise
 the
 method,
 consider
 a

spoked
 wheel
 placed
 over
 a
 distribution
 of
 points,
 and
 centred
 on
 one
 of
 these

points.

  Along
  each
  angular
  transect
  (i.e.
  1°
  spoke),
  a
  scalable
  window,
  or

‘wavelet’,
 is
 fitted
 that
 measures
 the
 average
 variance
 in
 the
 angles
 between
point-­‐pairs
 (Rosenberg
 2004:
 278-­‐9).

 Statistical
 significance
 is
 derived
 using

Monte
 Carlo
 simulation,
 which
 also
 allows
 for
 the
 investigation
 of
 irregularly

shaped
 datasets.

 The
 method
 can
 be
 applied
 either
 to
 a
 single
 point,
 effectively

assessing
 local
 anisotropy,
 or
 can
 be
 applied
 to
 multiple
 points
 simultaneously
 to

examine
 directional
 patterns
 more
 globally.

 Plotted
 results
 represent
 variance

as
 a
 function
 of
 angle
 measurement
 (as
 opposed
 to
 distance)
 and
 peaks
 in
 the

graph
 indicate
 the
 direction
 of
 maximum
 anisotropy.

Returning
 to
 our
 sample
 data,
 we
 can
 see
 that
 the
 graph
 of
 observed
 variance

(dark
 line)
 rises
 above
 the
 expected
 variance
 (dashed
 line)
 by
 a
 statistically

significant
 margin
 from
 about
 10°
 (N-­‐S
 is
 0°),
 and
 peaks
 around
 45°
 (Figure
 6).

This
 suggests
 that
 although
 the
 anisotropy
 is
 the
 strongest
 in
 a
 SW-­‐NE
 direction,

several
 trends
 are
 present,
 although
 the
 noise
 in
 the
 data,
 and
 the
 similar
 bearing

of
 each
 ‘line’
 of
 points,
 obscures
 each
 individual
 trend.

 It
 is
 worth
 noting
 an

individual
 spike
 towards
 50°
 as
 well,
 which
 is
 not
 so
 apparent
 visually
 but
 may

reflect
 additional
 influence
 in
 the
 right-­‐most
 diagonal
 line.

 Spikes
 in
 the
 eight

cardinal
 and
 intermediate
 directions
 (i.e.
 N,
 NE,
 etc.)
 are
 artefacts
 of
 the
 gridded

pattern
 (i.e.
 at
 shorter
 distances,
 fewer
 angles
 are
 possible
 between
 points).

Figure
 6.
 Angular
 wavelet
 graph
 for
 the
 sample
 dataset.

The
 above
 dummy
 example
 suggests
 that
 each
 analytical
 method
 may
 provide

useful
 insights
 and
 might
 be
 deployed
 to
 make
 sense
 of
 far
 more
 noisy,
 real

world
 datasets.
 The
 following
 analysis
 proceeds
 by
 highlighting
 the
 directional

trends
  that
  may
  be
  perceived
  by-­‐eye,
  first
  examining
  the
  underlying

geomorphology
 and
 subsequently
 the
 distribution
 of
 surface
 material.

 Once

these
 have
 been
 articulated,
 the
 two
 methods
 discussed
 above
 will
 be
 used
 to

provide
 an
 integrated
 assessment
 of
 anisotropy
 in
 the
 Murghab
 archaeological

landscape.

4.
 Data
 Analysis
 and
 Results

4.1
 Variography

A
 visual
 assessment
 of
 the
 northern
 Murghab
 landscape
 reveals
 two
 prevailing

directional
 trends.

 The
 first
 is
 the
 ridged
 topography
 of
 the
 sand
 dunes,
 broadly

orientated
 north-­‐south.

 A
 second
 is
 the
 geomorphology
 of
 the
 palaeodelta
 itself,

which
 tends
 more
 towards
 the
 northwest.

 Relict
 channels
 often,
 but
 not
 always,

follow
 a
 SSE-­‐NNW
 trajectory,
 influenced
 by—but
 not
 directly
 following—this

underlying
 geomorphology
 of
 the
 delta
 fan.

 A
 third
 anisotropic
 influence
 is