►
Description
Geophysical inversions are tools for constructing models of the subsurface (images) given a finite amount of data. SimPEG (http://simpeg.xyz) is an effort to synthesize geophysical forward and inverse methodologies into a consistent framework. We will show seven geophysical methods based around a diamond exploration case study, combining the results to drive a more informed decision. Slides may be found here: https://docs.google.com/presentation/d/1O6A85QwnnAibm7CsV2_VZ95HcRsnLyvPQIRYIz_K5xg/edit#slide=id.g15d5208fb1_2_246
A
A
So
as
geoscientists
were
we're
interested
in
what's
in
the
subsurface,
and
so
there's
a
couple
ways
to
do
that,
maybe
you
could
dig
it
up,
maybe
you
could
drill
it
both
of
those
are
expensive
methods
costing
millions
of
dollars
or
you
could
maybe
use
geophysics,
and
so
geophysics
is
using
some
sort
of
source.
Maybe
it's
electromagnetic,
maybe
it's
seismic
and
having
it
propagate
through
those
waves
propagate
through
the
subsurface
and
interact
with
the
physical
properties
down
there,
and
that
interaction
is
then
captured
in
the
data
which
are
you're
collecting
on
the
subsurface.
A
So
you
have
all
of
these
receivers
laid
out
and
those
are
capturing
some
of
the
information
about
the
physical
properties
in
the
subsurface,
and
so
the
world
is
in
in
in
3d
and
so
that
interaction
is
rather
complicated.
So
the
data
that
we're
collecting
isn't
necessarily
completely
like.
We
can't
just
draw
a
map
necessarily
and
drill
right
there.
A
But
I
think.
The
other
thing
that
we
are
always
keeping
in
mind
is
how
do
we
sort
of
interact
with
the
other
disciplines
in
our
Geoscience
colleagues?
How
do
we
interact
with
the
geologist
because
they
have
borehole
information
and
how
do
we
put
that
into
our
model
and
they
have
geologic
interpretations
and
they
know
things
that
us
geophysicists
do
not
know,
and
there
are
hydrogeologists
who
have
their
flow
models
and
their
own
techniques
of
figuring
out
what
the
subsurface
is,
and
so
really
we
want
all
of
these
methods
and
how
we
look
at
these
things.
A
But
really
there
are
lots
of
different
physical
properties
involved
in
there.
So
there
are
actually
these
these
methods,
it's
good
to
collect
them,
because
they
tell
you
different
things
about
that,
but
we
want
to
sort
of
collect
them
and
maybe
bring
a
few
together
to
get
more
information
about
about
reality
about
that
subsurface.
And
so
my
my
PhD
is
in
combining
sort
of
Vado
stone
flow
so
that
near
surface
the
top
unsaturated
zone
of
the
earth
with
direct
current
resistivity
methods,
and
so
that
was
sort
of
my
idea.
A
I
was
going
to
improve
it
and
integrate
all
the
things,
but
there's
this
PhD
size-two
barrier
between
all
of
these
different
methods,
and
so
that
that
is
perhaps
not
a
good
thing.
So
I
think.
Actually,
my
PhD
is
on
integrating
these
methods
and
sort
of
creating
a
framework
to
do
that
and
a
place
where
we
can
bring
multiple
people
into
the
same
place
to
do
all
of
these
methods
in
the
same
way,
so
that
we
have
the
opportunity
later,
when
these
are
all
sort
of
organized
and
optimized
to
do
it
better
and
communicate
those
results.
A
So
that's
sort
of
the
question
and
so
really
what
what
are
the
pieces
and
the
pieces?
We
have
these
inputs
to
here.
We
have
our
data,
we
have
our
uncertainty,
estimates
on
that
data.
We
have
the
governing
equations.
So
that's
our
physics,
and
we
have
this
prior
knowledge
and
assumptions
all
of
those
that
geologic
sort
of
soft
knowledge
is
it
flat.
Is
it
smooth?
We
don't
know,
but
maybe
we
do
and
then,
when
we
get
into
the
inversion
implementation,
we
really
need
two
bits
of
information
but
to
simulation
to
tools
at
our
disposal.
A
Think
speaking
back
to
what
we
want
to
do
as
scientists
is
we're
interested
in
what
we
can't
see,
and
so,
if
we
then
have
this
sort
of
opaque
layer
of
code
on
top
of
it
that
we
can't
see,
then
that's
probably
not
a
good
thing
so
making
everything
is
interactive
and
sort
of
modular
as
possible
so
that
we
can
jump
in
and
and
use
it.
And
so
this
is
our
implementation
in
in
Python.
So
all
object-oriented,
and
so
one
of
the
separations
of
concerns
that
we've
sort
of
first
dealt
with
is
well.
A
What
is
our
survey
and
what
is
our
problem
and
those
are
the
the
names
that
we're
getting
to
it
so
that
we
can
potentially
use
the
same
physics
and
collect
a
different
simulation.
Sorry
different
receivers
and
a
different
acquisition
system
on
top
of
that
or
potentially
the
other
way
is.
Maybe
you
don't
want
to
simulate
all
of
your
physics
all
at
once.
Maybe
you
just
want
to
use
a
1d
problem
and
then
increase
your
dimensionality
over
time,
so
that
decoupling
of
these
two
things
is
turns
out
to
be
pretty
important.
A
We're
using
a
lot
of
finite
volume
techniques,
some-some
tensor
meshes
some
quadtree
and
octree,
and
some
logically
rectangular
meshes
that
were
aligning
to
surfaces
and
some
cylindrical
mesh
meshes
and
that's
mesh
again
is
an
object
and
it
has
things
on
it
like
your
differential
operators,
and
so
you
can
then
combine
those.
And
so
when
you
see
a
physical
equation
like
DC
resistivity,
it's
div
Sigma,
which
is
your
conductivity
grad
Phi,
which
is
your
potential
and
then
a
dipole
source.
You
can
just
write
that
down
and
you
can
have
div
Sigma
grat.
A
They
did
Sigma
Grad
equals
your
linear
operator
a
and
you
solve
it
kind
of
with
either
an
iterative
or
direct
method.
So
that's
an
implicit
multiplication
and
you
get
out
your
Phi
and
then
you
can
plot
it,
and
this
is
something
that
you
can
give
to
students
which
is
nice,
because
it's
a
simple
way
to
interact
with
it
and
there's
various
levels
of
abstraction
that
you
can
put
in
between
them
and
the
code.
A
But
it's
it's
a
little
bit
more
transparent
and
they
can
jump
in
one
more
step
which
is
nice,
and
so
we
can
get
to
more
complicated
things
like
time
domain
electromagnetics,
but
still
try
to
be
very
declarative
about
how
we're
writing
these
things.
So
this
looks
rather
similar
to
our
equation
over
here.
A
A
And
so
this
is
something
that
we've
tried
again
to
decouple
in
this
impact
framework
and
sort
of
allow
extensibility
so
that
you
can
define
your
own
model
and
so
that
that
can
sort
of
be
part
of
your
decision-making
process
and
that
it
can
inform
that
decision
directly.
So
maybe
your
parameterizing
a
layer
or
a
sphere,
but
you
still
need
to
get
that
all
the
way
back
to
the
physical
properties.
A
And
so
where
have
these
mapping
classes
that
you
can
compose
in
a
chain
and
then
evaluate
the
chain
rule
the
derivative
all
the
way
through
that,
and
so
we're
keeping
sort
of
a
close
tie
on
our
physics
and
our
optimization
all
the
way
through.
And
then
you
get
your
inversion
elements.
So
you
have
your
data
misfits.
There
are
many
models
that
could
fit
our
data,
and
so
we
need
to
regularize
in
some
way.
A
So
maybe
we
have
a
reference
model,
and
this
is
maybe
where
we
inject
smoothness
constraints
or
smallness
constraints,
and
then
we
combine
these
into
an
ingress
problem.
So
we
have
our
data
misfit
and
our
model
regularization,
and
we
put
them
together
with
some
sort
of
trade-off,
parameter
that
we're
saying
how
much
do
I
care
about
this
versus
this
and
that
changes
over
time
in
the
inversion.
A
A
So
you're
directing
your
inversion
to
where
you
want
to
go
and
that's
interpretation,
but
it's
quantitative,
so
you
can
share
it
with
someone
and
sort
of
at
at
the
end
of
the
day
you
get
a
green
box
that
really
you
want
people
to
play
in
and
so
soggy
and
the
rest
of
the
team
has
been
playing
in
this
box
and
has
been
doing
really
cool
stuff.
So
you
might
have
seen
some
of
their
posters
yesterday
about
diamond
exploration
and
Sagi
is
going
to
talk
more
about
that
now.
B
B
B
We're
gonna
use
that
case
study
as
an
example,
so
we're
gonna
generate
the
synthetic
model,
so
we're
gonna
build
upon
that
model,
and
so
we
know
the
answer
and
then
actually
the
question
here
is
where
the
diamonds
and
diamonds
in
the
kimberlite
pipe
right
this
guy
and
then
this
pipe
is
composed
of
different
geological
units
there.
So
it's
not
a
single
unit.
B
There
are
multiple
geological
unit
that
we're
interested
and
then
we're
interested
in
more
interesting,
specific
unit
which
is
diamond
rich
and
it
has
a
feature
and
then
the
what
we're
seeing
is
a
physical
property.
So
that
feature
is
like
something
like
that:
we
have
lower
density,
moderate
susceptibility
and
high
conductivity.
So
that's
sort
of
a
target
that
we
are
finding
and
we're
gonna
use
like
a
geophysical
methodologist
to
find
that
physical
property
distribution
in
the
earth,
the
first
one
is
gravity,
so
that
was
actually
done
by
Dominic
and
so
gravity.
B
It's
like
we're
living
in
the
earth,
there's
a
vertical
gravitational
field
coming
and
then,
if
there's
a
density
contrast
in
the
earth,
that'll
generate
some
enormous
graph
gravity
fields.
So
if
the
and
then
say
like
that's
the
data
on
plan
view
map,
so
let's
say:
we've
run
an
airborne
gravity
survey
and
the
data
looks
like
that.
So
and
then
look
at
the
data.
So
it's
there's
a
minus
acceleration,
which
means
negative
gravity
field
so
in
the
earth.
They're,
probably
less
dense
material
than
the
background,
and
that
looks
like
that.
B
But
well
so
we
could
see
something
and
then
so
there's
a
some
reflectivity
of
Earth.
But
it's
not
enough.
That's
2d
view,
but
I'm
interested
in
3d
distribution
of
density.
So
what
we
do
we
do
a
geophysical
inversion,
so
we
are
kind
of
moving
from
2d
space
to
three
space
and
we're
using
inversion
to
do
that.
So
we
fit
the
data
and
then
we
find
model
which
explains
our
data.
B
So
we
fit
it
and
that's
what
we
recover
so
and
then
this
is
the
vertical
section
of
the
3d
density
and
as
we
expect
it,
we
kind
of
recover
some
lower
density
volume
in
the
earth,
and
we
know
that
kimberlite
usually
less
dense
than
then
the
background.
And
then
we
can
interpret
that
as
like.
This
pick
a
contour
and
we
can
interpret
that
as
something
certain
rock
model.
So
there
are,
there
are
probably
some
kimberlites
and
then
we're
moving
on
to
magnetics.
B
That
was
also
done
by
dominic
and
now
we're
the
magnetic
field
is
also
in
the
earth.
But
it's
not
vertical,
depending
on
where
you
are
so
in
Canada,
is
almost
vertical
and
that
that
generates,
if
there's
a
some
susceptible
body
magnetic
body
that
will
generate
secondary
magnetic
fields
and
also
we
can
measure
that
on
the
surface
by
using
some
airborne
magnetic
survey-
and
if
you
do
that,
that
looks
like
that,
okay
and
from
compared
to
gravity
it's
actually
different.
So
pick
is
the
different
at
least,
and
that
means
we're
seeing
different
part
of
the
Earth's.
B
So
we're
sensing
the
different
part
of
the
earth
by
using
different
geophysical
methodology.
So
there's
more
information
and
by
inverting
that
we
can
recover
3d
susceptibility
model,
and
that
works
like
that.
So
we
can
make
a
to
contour
here
now.
So
we
have
a
big
kind
of
hot,
really
high
susceptibility
volume
and
then
moderate
susceptibility
volume.
We
can
put
that
into
our
model-
that's
possibly
enough,
but
not
for
me.
So
what
we
could
do,
there's
another
physical
property
that
we
can
consider
is
electrical
conductivity
and
kind
of
popular
methodologies
called
direct
current.
B
What
we
do
we
have
a
giant
battery
we're
putting
the
inject
we're,
injecting
the
current
to
the
earth,
and
if
there
is
some
conductor
or
resistor
that'll,
make
some
potential
difference
that
we
can
measure
on
the
earth
and
if
you
look
at
the
data
that
we
measured
it's
lower,
so
we
have
lower
anomaly.
That
means
like
we
have
low
potentials.
That
means
like,
if
there's
a
conductor,
then
it's
really
like
the
currency
is
really
easy
to
pass
through.
So
you're
gonna
get
less
potential
than
the
background,
so
we
can
what
we
can
expect.
B
There
might
be
some
conductor
in
the
ground,
so
we
do
the
inversion.
So
we
have
some
expectation
and
recovered
some
conductive
body
at
some
depth.
So
we
can
make
a
similar
contour
to
tarrant
our
interpretation
now
we're
narrowing
down
for
our
target
by
using
different
physical
properties.
But
we
could
do
another
thing,
so
they
actually
DC
was
done
by
Mike.
B
Now,
what
we
could
the
DC's,
as
it
says,
is
as
once
one
like
there's
no
time
dependency,
it's
a
static
problem,
but
in
the
earth
there's
a
electromagnetic
wave
coming
from
the
universe
and
then
getting
down
to
the
earth.
So
it
has
some
time
dependency.
It
has
a
certain
frequency
band
that
we
can
use.
B
That
means
we
have
more
information
about
the
earth
and
the
methodology
we're
going
to
use
magnetics
that
was
done
by
Roland,
Lindsey,
Tebow
and
goodne,
and
let's
pick
up
the
two
frequency
that
we
measured
and
it's
thousand
Hertz,
and
this
is
20,000
Hertz
lower
the
frequency
we're
seeing
the
deeper
part
of
the
earth
higher
the
frequency
we're
seeing
the
near
the
shallower
part
of
the
earth
so
thousand
Hertz
and
20,000
Hertz.
They
show
different
data.
That
also
means
we're
seeing
the
different
information
of
the
earth
in
terms
of
the
conductivity
okay.
So
we
could.
B
We
have
more
information,
it's
more
kind
of
expensive
to
do
the
inversion,
because
it's
more
complicated
to
physics
and
then,
but
we
do
it,
we
recover
the
3d
conductivity,
it's
pretty
expensive,
then
that's
what
we
recovered.
Now
what
we
see
we
have
much
better
resolution
on
top
part,
now
we're
seeing
the
boundary
between
some
sedimentary
layer
and
possibly
the
kimberlite,
and
we
can
put
that
into
a
rock
model.
So
now
we
got
four
different
models
and
simply
what
we
want
to
do.
B
We
want
to
interpret
so,
let's
do
really
simple
thing
and
what
we
know
is
like
what
we're
target
is
low
density,
moderate
susceptibility,
not
a
high
susceptibility,
but
high
conductivity,
and
so
this
guy
is
a
low
density,
so
that
gives
sort
of
a
big
volume
of
kimberlites
over
a
volume
of
kimberlites.
And
then
this
modular
susceptibility
is
here
and
then
high
conductivity
is
there.
So
what
we
could
do
something
like
that?
B
B
A
kimberlite
unit
called
like
a
pyroclastic,
and
that
was
the
most
diamond
for
us
unit,
and
so
what
we
did
is
okay,
but
more
importantly,
important
thing
is:
there
are
four
open
source
packages
developed
in
a
single
framework
and
as
a
community,
that's
and
that
like
what
as
a
practitioner,
what
I
am
excited.
So
actually,
my
PhD
work
is
mostly
on
conductivity
part,
but
now
as
a
community
that
in
it
like
using
these
tools
and
in
it
like
by
being
in
this
community,
enable
me
to
do
a
lot
of
different
things.
B
B
A
A
Think,
like
the
first
part,
is
I,
think
that's
sort
of
an
open
question
in
the
research
community
and
there's
a
lot
of
people
doing
some
stuff.
One
of
the
things
that
I
know
something
about
is
that,
like
you,
can
use
clustering
algorithm,
so
you
know
like
physical
properties
like
the
kimberlite
pipe.
It
has
low
density,
moderate
stability,
something
else
and,
and
you
can
create
that
space
and
then
regularize
towards
that
space
in
your
and
if
you
know
like
a
few
different.
B
B
Yeah
I
I
think
the
sort
of
point
is
it's
a
start.
I
think
we're
not
saying
where
we
solve
the
problem,
put
a
stack
on
it,
but
I
think
to
to
do
that.
I
I.
Think
the
starting
point
is
having
stuff
in
that
in
a
single
framework,
so
that
sort
of
things
that
what
we
wanted
to
emphasize
yeah
yeah
exactly.
B
That
yeah
yeah-
that's
that's
really
well!
Okay,
assuming
that
I
did
a
really
okay
job
for
mashing
things
mashing
in
time,
mashing
in
like
3d
space
well,
I
think
that's
pretty
fairly
accurate,
depending
on
like
the
assuming
that
the
problem
that
we
are
dealing
with,
I'm,
not
exactly
sure
about
for
other
other
applications,.