►
From YouTube: PhD Presentation - Rowan Cockett
Description
A framework for geophysical inversions with application to vadose zone parameter estimation.
A
Thank
you
all
very
much
for
coming.
I
would
like
to
start
off
with
a
tiny
bit
of
context
for
the
research
that
I
completed.
So
this
is
a
picture
of
California
and
you
can
see
a
whole
bunch
of
agriculture
and
oak
this.
This
is
the
ocean
and
the
the
agriculture
is
about
200
meters,
and
so
this
is
this
is
in
the
Salinas
Valley
and
there's
about
10
billion
dollars
worth
of
agriculture
coming
out
of
here
every
year
and
because
they're
so
close
to
the
ocean.
A
And
this
up
here
is
a
managed,
Aquifer,
recharge
point,
and
so
California
gets
a
lot
of
rain
actually
in
the
winter
on
all
sort
of
at
once,
and
so
that,
but
comes
in,
and
so
you
want
to
capture
that
put
that
in
the
ponds
have
that
infiltrate
down
and
then
in
the
summer
recovery
that
water,
and
so
the
scientific
questions
here
are.
Where
does
that
water
go
and
sort
of?
How
does
it
move
in
the
subsurface?
A
And
so
that's
an
interdisciplinary
question
that
brings
together
geology,
hydrogeology
and
if
you
want
to
image
where
that
water
goes
also
geophysics,
and
so
this
this
was
a
study
that
I
was
involved
in
in
my
undergrad
on
where
we
used
a
geophysical
method
to
image
the
where
that
water
was
going.
What
was
sort
of
interesting
about
this
study
was
it
was
a
new
geophysical
probe
that
we
created
to
actually
get
a
lot
of
estimates,
both
spatially
and
temporally,
of
the
hydro
side
of
things.
A
And
so
all
of
these
disciplines
have
have
different
types
of
data
that
they're
collecting
and
those
data
are
used
to
inform
all
sorts
of
models
of
the
subsurface.
And
so
it's
it's
good
to
collect
these
different
data
data
sets
because
the
models
tell
you
something
different
about
the
subsurface,
and
so
the
data's
are
sensitive
to
either
different
physical
properties
or
different
sensitivities
of
those
physical
properties
and
so
sort
of
the.
A
Where
what
is
the
sensible
thing
to
do
and
sort
of
the
state
of
the
science,
and
so
there's
a
whole
bunch
of
PhDs
that
have
been
awarded
lots
of
papers
that
are
in
the
combining
of
two
different
types
of
methodologies?
Two
different
data
sets
into
a
coherent,
more
comprehensive
picture.
Image
of
the
subsurface,
and
so
I
would
I
want
to
jump
into
the
combination
of
Richards
equation
and
direct
current
resistivity,
and
so
this
this
is
in
the
context
of
beta
so
and
flow
and
a
geophysical
method.
A
So
bringing
in
that
context
that
I
was
talking
about
before
so
to
combine
these
two
methods
on.
If,
if
you
have
that
pond
and
there's
there's
sand
underneath
there-
and
you
are
raining
on
the
top
of
it,
so
you're
changing
the
boundary
condition
at
sort
of
the
top
of
your
model
and
that's
through
time,
and
so
you
have
some
infiltration
front
coming
down
through
through
the
subsurface
and
how
and
where
that
goes
is
dependent
on
the
hydraulic
properties
and
so
hydraulic
conductivity
sort
of
is
showing
where
that
goes
on
the
on
the
geophys
of
things.
A
A
Model,
an
image
of
and
I
that
is
it's
varying
through
time,
and
so,
if
we,
if
we
jump
back
to
Richard's
equation
or
this
this
infiltration
front,
a
wet
sand
is
much
more
electrically
conductive
than
a
dry
send,
and
so
there's
there's
the
empirical
relationship
between
these
two
models,
and
so
the
changing
in
time.
I
can
be
mapped
through
some
sort
of
empirical
relationship,
maybe
Archie's
equation
to
a
changing
electrical
conductivity
model.
A
Geology
side
of
things
in
the
hydrologic
estimate
and
what's
interesting
about
the
combination
of
these
two
disciplines,
is
that
we've
sort
of
vastly
opened
up
the
amount
of
data
that
we
can
collect.
We
can
collect
a
lot
of
direct
current
resistivity
data.
We
can't
necessarily
collect
a
lot
of
saturation
data
or
pressure
head
data,
at
least
in
a
dense
sense.
A
There's
quite
a
few
empirical
relations
that
describe
how
these
different
physical
properties
interact,
and
so
we
have
these
curves,
which
describes
describe
that
in
there,
and
so
this
this
is
a
nonlinear
differential
equation.
So
we
need
to
solve
it
with
the
appropriate
numerical
methods,
but
in
the
inverse
side
of
things
again,
this
is
going
from
something
that
we
know
to
describing
this
infiltration
front
through
time.
A
But
we
don't
actually
know
what
these
curves
are,
and
so,
if
we
sort
of
look
into
how
those
are
described
in
the
literature,
but
again
is
an
empirical
relation
with
maybe
five
parameters
that
we
want
to
estimate
everywhere
in
space
and
those
parameters
might
be
a
true
genius.
They
might
be
honest
and
isotropic,
and
so
it's
it's
a
difficult
inverse
problem
to
attack.
A
So
just
look
at
the
literature-
and
this
is
in
the
context
of
sort
of
the
hydro
geology
side
of
things,
not
the
hydrogen
physics
side
of
things.
What
people
are
typically
doing
is
laboratory
estimates
where
there
have
very
controlled
small
samples
and
they're
trying
to
estimate
these
these
parameters
of
those,
because
that
again
allows
you
to
simulate
in
the
fourth
sense,
and
so
there's
been
a
lot
of
work
done
on
sort
of
that
that
small
inverse
modeling
side
of
things
and
then
on
the
sort
of
large
hydro,
hydrologic,
modeling
side
of
things.
A
Sorry,
the
sparse
data,
which
is
like
a
very
good
estimate
to
a
dense
estimate
of
data.
Again,
we
don't
actually
have
all
of
the
such
saturation
or
water
content
side
of
things.
We
have
an
estimate
of
it
through
some
empirical
mapping
and
that
becomes
sort
of
a
big
inverse
problem,
and
so
the
models
that
we're
interested
in
are
much
bigger
and
so
I
in
that
2016
review
paper.
A
It
requires
formulation
of
Richards
equation
as
this
block
linear
system
through
time
and
there's
some
intricacies
there
due
to
the
non-linearity
and
also
model
dependence
in
sort
of
any
part
of
that
chain
of
of
how
the
two
methods
are
connected,
and
another
piece
is
if
we
actually
solve
this.
So
if
we
take
the
inverse
of
that
in
some
way
and
apply
it
to
the
right-hand
side.
A
A
So
a
brief
example
of
this.
This
is
sort
of
a
if
we're
thinking
about
the
context
of,
but
that
point
the
manege
Aquifer
recharge,
and
we
have
some
block
of
sediment
here
with
two
different
types
of
materials
and
loan
east,
and
then
we
can
infiltrate
from
the
top
and
if
we're
collecting
those
water
content
estimates,
we
hopefully
estimate
the
hydraulic
properties
and
so
on.
A
The
inverse
side
of
things.
In
this
example,
I've
only
estimated
for
a
single
hydraulic
property,
there
are
sort
of
five
distributed
in
space
at
each
point.
In
this
model,
I've
inverted
for
the
hydraulic
conductivity,
which
has
been
done
before
in
the
literature.
What
hasn't
been
done,
I,
don't
think
ever
before,
is
a
three-dimensional
inversion
for
distributed
hydraulic
conductivity,
and
so
this
is
probably
the
largest
inversion
for
Richards
equation.
A
Yeah,
it's
just
cool
so,
and
one
of
the
reasons
that
has
been
done
or
hasn't
been
done
is
because
makaan
text
of
the
problem
has
changed
because
we're
going
from
that
sparse
data
estimate
to
a
dense
model
estimate
everywhere.
We
can
expect
more
from
our
inverse
problems,
and
so
this,
the
dense
at
sensitivity
matrix
in
this
case,
has
half
a
billion
elements.
If
we're
going
to
use
something
like
pest,
which
is
a
finite
difference,
external
method
that
would
take
a
very
long
time
to
actually
compute
the
sensitivity
in
this
method.
A
So
if
we
go
back
to
the
the
context
of
where
we're
looking,
we
have
a
whole
bunch
of
questions.
So
now
it
might
be
possible
to
on
that
these
two
together,
because
this
is
that
sort
of
the
same
a
model
scale
that
we're
expecting
from
the
data.
But
there
are
a
massive
amount
of
questions
along
the
way
about
how
to
actually
tie
these
things
together
and
those
are
sort
of
by
their
nature.
A
So
when
one
of
the
papers
that
I
read
early
on
with
was
talking
about
these
problems
and
they
showed
that
the
the
coupling
of
these
two
methods
had
sort
of
these
direct
advantages,
but
it
forced
the
hydrogeologist
and
the
geophysicist
to
formulate
a
consistent
framework
and
that
had
like
all
sorts
of
advantages,
but
it
was
also
because
of
sort
of
its
difficulty.
It's
the
the
primary
limit
to
routine
implementation
of
these
style
of
inversions,
and
if
it's
the
primary
limit,
then
we
can't
actually
ask
lots
of
questions.
A
We
can
ask,
maybe
one
questions
and
a
year
implementing
it
and
then
and
move
on,
and
so
that's
sort
of
the
style
of
things
that
has
been
happening
in
the
literature.
And
so
my
research
has
been
sort
of
into
this.
This
framework
idea
that
might
lower
the
barrier
to
entry
to
address
the
primary
limit
to
this
to
this
problem.
A
And
so,
if
we
look
back
at
the
discipline
before
I
was
saying
that,
if
you
combine
and
in
two
of
these
methods,
there's
a
PhD
sort
of
at
the
end
of
it.
And
so
there
are
these
PhD
sized
barriers
between
the
geophysical
methods
and
there
are
large
large
barriers
between
going
outside
of
our
field
as
well,
and
so
you
might
not
actually
be
able
to
implement.
The
word
solve
the
scientific
question
that
you're
you're
after.
A
So
a
computational
science
framework
lays
out
a
set
of
standards
that
allows
multiple
researchers
to
write
units
of
software.
These
components,
in
this
case
geophysical
inversions
with
the
confidence
that
those
components
work
with
other
components.
In
that
same
very
much,
and
so
it's
it's.
It's
an
its
systematic
approach
to
that
interdisciplinary
problem
in
in
our
case,
we
need
to
be
able
to
simulate
physics,
compute
sensitivities,
efficiently,
regularize
and
optimize,
and
that's
a
lot
of
the
research
that's
done
in
this
discipline.
A
We
also
need
to
be
able
to
capture
in
virtual
heuristics
and
couple
enjoying
them
in
some
way,
and
so
the
questions
are:
what
are
those
components
and
what
are
the
interfaces
of
those
components?
And
we
know
a
lot
about
that
in
the
discipline
of
geophysics,
and
so
what
I've
sort
of
been
doing
is
studying
that
such
that
it
can
be
exposed
externally
to
our
discipline
and
also
potentially,
if
you're,
organizing
these
things
appropriately.
A
That
can
allow
you
to
ask
new
questions
inside
your
discipline
as
well,
and
so
this
is
the
that
the
framework
that
I'm
proposing
and
I'm
just
going
to
walk
through
it
very
briefly
to
get
you
give
you
a
flavor
of
it.
You
need
to
be
able
to
discretize
your
problem
in
some
way,
I'm
using
a
lot
of
finite
volume
techniques
and
aligning
those
measures
to
interfaces
or
refining
the
areas
of
interest.
A
Once
you
have
that
you
need
to
be
able
to
use
simulate
physics,
so
there
are
differential
operators
on
those
meshes
which
you
can
combine
in
a
sensible
way
to
simulate
physics,
to
go
from
the
equations
to
the
code,
to
the
physics
in
a
smooth
way,
and
then
you
need
to
Ford
stimulate.
So
this
is
going
from
your
model
going
to
your
physical
properties.
Your
physics
fields
are
your
sources
and
your
receivers,
and
the
way
that
this
is
laid
out
is
that
these
are
all
sort
of
combinatorial
so
that
you
can
go
from
one
switch.
A
On
the
inverse
side
of
things,
there's
a
lot
of
work
in
our
discipline
about
data
mesfets,
different
types
of
regularization,
z'
and
being
able
to
combine
those
in
a
sensible
way
and
in
a
sensible
way.
Sort
of
means
is,
is
the
difference
between
optimization
and
the
inversion
discipline,
and
so
there's
all
sorts
of
workflows
that
are
created
in
the
literature
that
are
specific
to
geophysics
and
hydro
geophysics,
which
needs
to
reach
into
every
single
component
in
this
to
actually
make
it
work.
A
And
so
what
what
this
is
sort
of
under
the
hood
is
a
whole
lot
of
written.
But
they
just
thought
just
like
put
down
it's
the
process
of
creating
structure
from
that,
and
so
thinking
about
the
interfaces
and
and
the
sensible
components
that
are
appropriate
for
this
discipline.
And
so
there's
a
lot
of
of
structure
and
organization
and
thought
that's
gone
into
this.
A
So
this
framework
we've
published
in
a
couple
places
what
about
the
geophysical
inversion
methodology
sort
of
at
a
general
sign
of
things,
but
talking
about
sort
of
those
components
in
those
databases
and
how
they
fit
together
and
then
about
the
foreign
simulation
framework
in
the
context
of
electromagnetics
and
we've
also
sort
of
been
doing
a
lot
of
case
studies
so
proving
to
ourselves
that
this
framework
is
appropriate
to
the
the
various
case.
Studies
that
we
have
in
front
of
us,
and
so
that's
I,
had
a
couple.
A
Svg
abstracts
about
imaging
hydraulic
fracturing
using
a
joint
inversion
without
imaging
seawater,
infusions
with
electromagnetics
and
modeling
electro
magnetics
in
the
presence
of
cased
wells,
and
so
this
is
demonstrating
sort
of
the
utility
of
the
frame
are
going
to
and
again
sort
of
proving
that
to
ourselves.
But
in
some
sense
you
need
to
like
the
point
of
a
framework
is
that
it
allows
multiple
scientists
to
work
together
and
provide
those
standards
such
that
they
can,
and
so
there's
some
groundwork
to
do
to
get
there.
A
And
that's
really
in
the
implementation
side
of
things
and
then
doing
that
sort
of
like
exposing
that
in
an
appropriate
way,
and
so
that
means
having
software
testing
and
documentation
and
sort
of
all
of
the
engineering
aspects.
But
the
point
of
that
is
that
we
can
have
a
conversation
as
a
discipline
about
these
things.
And
so
we
started
that
conversation.
We
hosted
an
international
workshop.
A
That's
like
we
started
talking
about
that
standards
and
and
making
sure
that
it
is
appropriate
for
the
discipline
and
that's
yeah.
But
it's
like
the
components
and
interfaces
that
people
can
use
to
solve
their
own
problems,
and
that
has
started
to
be
happening
and
so
that
the
software
framework
was
published
in
2015
and
there's
a
whole
bunch
of
work.
That's
taking
those
and
building
upon
it
and
really
having
other
scientists.
A
A
In
summary,
the
the
two
sort
of
contributions
of
this
work
are
this
computationally
scalable
in
the
in
the
context
of
Richards
equation
and
direct
current
resistivity
and
putting
those
together
in
a
way
that
attacks
this
3d
application.
And
then
the
second
side
of
things
was
trying
to
attack
this.
This
primary
limit
to
the
routine
implementation
of
integrated,
Geoscience,
inversions
and
and
I
did
how
to
do.
A
That
is
to
look
out
to
the
disciplinary
community
and
ask
how
how
they
build
these
things,
and
that
is
through
the
definitions
of
frameworks
and
the
standards
of
the
components
and
the
interfaces
and
one
of
the
things
that
this
author
said,
who
was
that
it
dark
selector
in
2016
on
is
that
requires
an
uncommon
level
of
collaboration
during
scientific
analysis
and
what
a
framework
hopefully
addresses
is
that
that
becomes
much
more
common,
because
the
the
future
Geoscience
problems
are
bigger
than
any
one
domain.
So
thank
you
very
much.