Transcript Document

Magnetotelluric Method
Stephen Park
IGPP
UC Riverside
[email protected]
So, what is the magnetotelluric method?
The magnetotelluric (MT) method determines
the tensor electrical impedance of the earth
through measurement of naturally varying
EM fields, and then uses computer modeling
to find cross sections of electrical resistivity that
yield theoretical responses similar the observed
ones.
And why is it abbreviated “MT”?
1. It is the “empty” method because
of the long waiting times in the field
needed for data collection (MIT field
camp students, 1981).
2. It describes the look on the faces in the
audience when the above description is
given.
3. The initials stand for MagnetoTelluric
(Cagniard, 1953).
But seriously….. What can it tell
us about the Earth?
MT is one of the few
techniques capable
of sensing through
the Earth’s crust to
upper mantle.
IN THE CRUST…
Silicate minerals comprise 95% of the crust…
and silicate minerals are very resistive*
(< 10-6 S/m). Electrical currents do not like
resistors!
The observed finite conductivity (10-4 - 1 S/m)
of the crust is due to small fractions (ppm-10%)
of interconnected conductive material.
aMT cannot be used to determine mineralogy
but can be used to identify small fractions of:
aqueous fluids (0.1-10 S/m)
partial melt (2-10 S/m)
graphite (106 S/m)
metallic oxides and sulfides (104 S/m)
MT has been used successfully to locate:
• Underthrust sediments
• Regions of metamorphism and partial melting
• Fault zones (fractured, fluid-filled rock)
*At crustal temperatures!
IN THE MANTLE…
Temperatures are sufficiently high (> 800C)
that mobilities of crystal defects and impurities
are enhanced.
Ionic mobility   Electrical conductivity!
Enhanced mantle conductivity is caused by
higher temperatures
partial melt (> 0.01 S/m)
hydrogen (and carbon?) diffusion
MT has been used successfully to identify:
• partial melt
• variations in lithospheric temperature
• asthenosphere
What IS MT?….
ionosphere
Not all MT signals are from interactions
with the solar wind:
Micropulsations
Global
lightning
Range of frequencies
used to probe lower crust
Murphy’s law is hard at work!!
Let’s look at the governing equations
  E  jH
  H  E  J s
These break down into components:
E z E y
jH x 

y
z
jH y 
E x E z

z
x
H z H y
E x 

y
z
H x H z
E y 

z
x
H y
H x
E z 

x
y
jH z 
E y
x

E x
y
Consider a halfspace and a vertically incident
plane wave: Is there any difference between
one point and another 1 km away?
NO!
So, what terms vanish above?
jH x  
E y 
E y
jH y 
z
H x
z
Ex  
E x
z
H y
z
jH z  0
Ez  0
Note lack of vertical fields and similarity of
equations for (Hx,Ey) and (-Ex,Hy).
 2 Ey
z
2
 jE y  0
Assume solutions of form exp(jkz), and get
k=+/- (jωμσ)½ and final result of:
E y  Ae
 j t


j

e
2

H x  (1  j )
Ae jt e
2

e
2
z

2
z
z
j
e

2
z
Note that both of these contain an
undetermined constant, A, that is set
by the strength of the source field.
in order to get rid of this constant, we
examine the impedance of the Earth:
Z=E/H
1
2
Z yx 

H x (1  j ) 
Ey
Note that phase is constant at -45°
and amplitude is proportional to
frequency and resistivity (1/σ). This
leads to the concept of apparent
resistivity:
2
1
a 

Z xy
MT responses are represented by phase
and amplitude (apparent resistivity)
Assignment: Derive equations for Ex, Hy
and Zxy. What similarities or differences do
you see with Zyx?
E y
jH x  
E y 
jH y 
z
H x
z
Ex  
E x
z
H y
z
jH z  0
Ez  0
E y  Ae
 j t


j

e
2

 jt
H x  (1  j )
Ae e
2

e
2
z

2
1
2
Z yx 

H x (1  j ) 
Ey
a 
1

Z xy
2
z
z
j
e

2
z
 jt
Ex   Ae

e

2
z
j
e

 jt
H x  (1  j )
Ae e
2


2

2
z
z
j
e

2
z
Ex
1
2
Z xy 

Hy
(1  j ) 
SAME apparent resistivity and phase
is 135° (-1 is 180°) different from Zyx.
Summary
Layered halfspace characteristics:
apparent resistivity is independent of frequency
phase is either –45° or 135°
apparent resistivities for two modes (Ex,Hy
and (Ey,Hx) are equal
NO vertical fields.
Asssignment:
In a 1-D earth (layered geology) and a vertically
incident plane wave source, what terms can
be eliminated?
x
y
E z E y
jH x 
z
y
z
E x E z
jH y 

z
x
H x H z
E y 

z
x
H z H y
E x 

y
z
H y
H x
E z 

x
y
jH z 
E y
x

E x
y
In a 2-D earth (variations in conductivity in
x and z only) and a vertically incident plane
wave source, what terms can be eliminated?
x
y
z
| 0 Z1|
| -Z1 0 |
| 0 Z1|
| Z2 0 |
| Z1 Z2|
| Z3 Z4|
T
When we have multiple sites, we plot a
pseudosection:
Interpretation:
1. 1-D modeling, inversion – fast, easy,
readily available, almost always WRONG!
2. 2-D modeling, inversion – slower, more
difficult, programs usually available, may
have 3-D effects in data.
3. 3-D modeling – used to verify 2-D results,
programs available but only simple models
possible. Inversion not yet available.
2-D inversion is standard tool for
interpretation.
A system of equations for Ex, Ez, and Hy
(called the TM mode):
H y
  Ez
x
H y

  Ex
z
Ez Ex

  jHy
x
z
and a system of equations for Hx, Hz, and
Ey (called the TE mode):
Ey
  jHz
x
Ey
 jHx
z
Hz Hx

 Ey
x
z
Note similarities in equations if E, H
switched
and , -j switched. This leads to some
simplifications in programming the forward
solution! Each mode is simply excited by an
equivalent current sheet in the appropriate
direction at the surface (Jx for the TM mode
These sources lead to problems in solving
both sets of equations with one forward
solution!
In EM, basic boundary conditions at
Interfaces are:
1)continuity of tangential fields
2)continuity of normal current density
Consider the TM case (with Jx source):
Jx
Because Jx at the surface must be
continuous both across the air-Earth
interface and between the adjacent prisms,
Jx is constant everywhere on the surface
and therefore is a equivalent to an MT
source with a uniform plane wave. Thus,
the current sheet is placed at z=0.
Consider the TE case (with Jy source):
Ey1 Ey2
Jy
Continuity of tangential E at the surface
requires that Ey be continuous across
the air-Earth interface AND at the edges
of the prisms. Because Jy = Ey, Jy must
be DIScontinuous at the edges of the prism.
This means that Jy varies in the x direction
across the model and does NOT represent
a uniform source!
SOLUTION: Add air layers to top of model
to a sufficient height that Jy is once again
uniform (typically 8-10 layers to a height
of ~100 km or more).
Typical steps for interpretation:
1. Identify TE, TM modes based on
a. comparison to geologic strike
b. decomposition of impedance tensor
c. similarity of Hz with Hhorizontal
TE mode:
Induction
arrows
Hhorizontal
H
I
Hz
2. Design starting model based on
a. geologic structure
b. other geophysical data
c. guesses
3. Run inversion and try to fit data
4. Perform sensitivity analysis to determine
which bounds on modeled structure.
MT can provide resistivity sections at many
scales from the uppermost crust…
High resolution MT profile in Krygyzstan to determine neotectonic structure
to the entire crust….
MT profile across Sierra Nevada and
eastern California:
37N
KVF
K
OV
DP
105112 115 DV
123
HS
118
128
1 3 10 15
22
6
Isabella
anomaly
GV
SN
Scale
T=100 s
120W
.1
118
35
116
MT modeling and inversion are regional problems!
Data in the Sierra Nevada are affected by the highly
conductive Pacific Ocean (and all of the structure
in between). Mackie et al. (1996) showed with
a 3-D model of California that the Transverse
Ranges resistivity affected electric field levels
in Death Valley.
W
GV
3 10
1 6
15
HS DP PV DV
22
25
E
112 118 128
106 117 123
130
0 SL
<100
Depth, km
>100
<30
>100
100
>100
>300
<30
200
300
Some sensitivity to depths
up to 400 km
0
100
200
Distance, km
0
1
2
Log10()
300
3
4
However, what you really need not
electrical resistivity…..