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TURNING DATA INTO EVIDENCE
Three Lectures on the Role of Theory in Science
1. CLOSING THE LOOP
Testing Newtonian Gravity, Then and Now
2. GETTING STARTED
Building Theories from Working Hypotheses
3. GAINING ACCESS
Using Seismology to Probe the Earth’s Insides
George E. Smith
Tufts University
THEORY-MEDIATED ACCESS
vs.
Theory-mediated measurement
vs.
“Theory-mediated observation”
Areas of science in which theory is indispensable to
having empirical access to the subject matter at all
Microphysics: atomic and subatomic
Internal structure of the Earth
THE QUESTION OF CORROBORATION
• Some historians and philosophers contend that science is a
construct constrained on its boundaries by observation
• What evidence is there then that unobserved “theoretical
entities” like electrons really exist – vs. mere constructs?
• Questions of this sort gain their maximum force when the
evidence for theory has to come from “data” that presuppose
the very theory in question
• Seismological research over the last century is no less an
example of this than research since 1850 in microphysics
• What sort of corroboration has there been for the conclusions
from seismology about the internal structure of the Earth?
OUTLINE
I.
Introduction: the issue
II.
Seismological research from 1900 to 1960
III.
Seismological research since 1960
A.
From 1960 to “Preliminary Reference Earth Model”
B. The years since “PREM”
IV.
Concluding remarks
Newton’s question:
How does density vary below the Earth’s surface?
“All these things will be so on the
hypothesis that the earth consists of
uniform matter…. If [, however,] the
excess of gravity in these northern
places over the gravity at the equator
is finally determined exactly by
experiments conducted with greater
diligence, and then its excess is everywhere taken in the ratio of the versed
sine of twice the latitude, then there
will be determined … the proportion
of the diameters of the earth and its
density at the center, on the hypothesis
that the density, as one goes to the
circumference, decreases uniformly.”
Isaac Newton, Principia, 1687
Gravity Measurements Underdetermine
Deviation of surface gravity
from Newton’s ideal variation
implies the value of (C-A)/Ma2
and hence a correction to the
difference (C-A) in the Earth’s
moments of inertia, and the
lunar-solar precession implies
the value of (C-A)/C and hence
a correction to the polar moment
C; these two corrected values
constrain the variation пЃІ(r) of
density inside the Earth by
implying it is notably greater
toward the center, but they do
not suffice to determine the
variation пЃІ(r) .
Hypothetical models of пЃІ(r):
• Legendre (1793)
• Laplace (1825)
• Roche (1848)
• G. Darwin (1884)
• Radau (1885)
• Wiechert (1897)
• Georg Kreisel (1949):
Gravity measurements at or
above the surface of the Earth
can never uniquely determine
the variation of density below
the surface.
NINETEENTH CENTURY BACKGROUND
Observational advances
Early pendulum seismometers
e.g. Palmieri (1856)
e.g. Ewing (1881)
Networks of observing stations
Italy
Japan
Increasing sensitivity
Milne (1892)
Wiechert (1903)
RICHARD DIXON OLDHAM
1899: Report on the great earthquake of 12 June 1897
1900: On the propagation of earthquake motion to great distances
1906: The constitution of the earth as revealed by earthquakes
NINETEENTH CENTURY BACKGROUND
Theoretical foundations
Transmission of compression (p)
and transverse shear (s) waves
Poisson (1829, 1831)
Stokes (1849)
Surface waves
Rayleigh (1885)
Love (1911)
Free oscillation modes of a sphere
Lamb (1882)
Love (1911)
Assumptions
elastic
linear
isotropic
2 stress-strain parameters
vs. as many as 21 in the
general case of anisotropy
homogeneous
….
EVIDENCE FOR THE THEORY
OF p AND s WAVES?
•
Poisson: Addition to Mémoire sur l’équilibre des
corps Г©lastiques
MГ©moire a classic in continuum mechanics
Mathematical consequences of Navier-Stokes equation
•
Basic equations of continuum mechanics
Fundamental principles of physics, e.g. F=ma
•
Constitituve equations for individual media
Solid vs. fluid, elastic vs. plastic, isotropic vs. ….
•
The question of evidence: Do the proposed
constitutive equations hold for the medium?
SEISMIC WAVES AT ONE LOCATION
SEISMIC WAVE PROPAGATION
OLDHAM’S “BREAKTHROUGH”
“Of all regions of the earth none invites speculation more than that which lies
beneath our feet, and in none is speculation more dangerous; yet, apart from
speculation, it is little that we can say regarding the constitution of the interior of the earth….The object of this paper is not to introduce another
speculation, but to point out that the subject is, at least partly, removed
from the realm of speculation into that of knowledge by the instrument
of research which the modern seismograph has put in our hands.”
DISCONTINUITIES: A BRIEF HISTORY
•
Crust-mantle boundary
Mohorovičić 1909
•
Core
(Oldham 1906)
Gutenberg 1914
at 2900 km below surface
•
Core is liquid
Jeffreys 1926
•
Inner Core
Lehman 1936
THE PROJECT: 1900-1940 …
• from
Arrival times of seismic waves from earthquakes at
many locations around the Earth
• to
Travel times (О”t vs. О”Оё) for a spherically symmetric
Earth for p and s waves – reflected and diffracted as
well as refracted within a medium of varying density
• to
Velocity variation of p and s waves in a spherically
symmetric Earth, via ray theory and the HerglotzWiechart integral (1907) for an isotropic medium
DIFFICULTIES
Need to identify phases
(different pathways) of
waves reaching a single
point at different times
THE JEFFREYS-BULLEN TABLES, 1940
Assumptions:
• Arrival times of principal phases
distinguished from each other
• Times and source locations of
wave-origin identified, including
focal depth
• Systematic errors corrected for
– Ellipticity of Earth
– Double quakes
– Late readings due to weak p, pkp
• Averaging for spherical symmetry makes sense
THE JEFFREYS VELOCITIES, 1939
Assumptions:
• Fractional change in v gradient
over one wavelength small
compared to v
• Velocity increases slowly with
depth or
– Decreasing velocity zones
identified and provided for
• Numerical derivatives of Δt vs.
О”Оё are well behaved
• (Isotropic, linear elasticity with
continuous properties except at
identified discontinuities)
A FURTHER PROJECT: INFER DENSITY vs. RADIUS
P velocity in isotropic elastic medium п‚µ
пѓ–[(bulk-mod+4shear-mod/3)/density]
S velocity in isotropic elastic medium п‚µ
пѓ–(shear-mod/density)
Two equations in three unknowns:
(bulk-modulus/density)
(shear-modulus/density)
From gravity constraints, lab experiments
at high pressure, and assumptions
(equations of state), infer density
vs. radius in symmetric Earth
Bullen, 1940-42
THE QUESTION OF EVIDENCE
•
•
•
•
Precision: error bands?
Resolution: scale of detail?
Idealization: uniqueness?
Corroboration: assumptions?
Form of evidence: coherence,
as judged by magnitudes and
absence of systematicity in
residual discrepancies
Inference to best explanation
OUTLINE
I.
Introduction: the issue
II.
Seismological research from 1900 to 1960
III.
Seismological research since 1960
A.
From 1960 to “Preliminary Reference Earth Model”
B. The years since “PREM”
IV.
Concluding remarks
THE FIELD TRANSFORMS: 1950-1970
• Nuclear testing yields evidence supporting travel times
• Nuclear detection → U.S. finances open-data network
– World Wide Standardized Seismographic Network (1960)
– International Seismological Centre (1964)
• Advent of digital computers, of increasing power
• Satellites → improved values of mass, moments of inertia
• Improved and new instrumentation
– Including long period, electronic strain-based seismometers
– Fast Fourier transform: spectra (Cooley & Tukey, 1965)
• Burgeoning number of people entering the field
• Detection of natural modes of vibration of the Earth
– Proposed 1958, confirmed following Chile (1960), Alaska (1964)
– Initiating advanced efforts on “inverse methods” (late 1960s)
DETECTING FREE OSCILLATIONS
AN EXAMPLE: COLOMBIA, 1970
FREE OSCILLATIONS OF THE EARTH
Why so important
 New data, independent of
travel times (& ray theory)
 Each mode of oscillation
samples the whole Earth,
but differently
 Long period modes give
direct information about
density variations
 Conclusive evidence for
solid inner core
 Differing amplitudes give
information about action in
individual earthquakes
“INVERSE-THEORY”
Initial Earth model: densities & material properties
Calculate natural frequencies for model
Find array of discrepancies
vs. observed frequencies
Use array of discrepancies
to revise Earth model
FREE-OSCILLATION-BASED MODELS
“1066” inverse solution:
Start from two prior models
Use 1064 natural modes +
mass, moments of inertia
Obtain new Earth models
Results:
• Reconstruct two quakes
• Systematic discrepancies
between calculated and
traditional travel times
EMPIRICALLY DRIVEN REVISIONS TO
THE CONSTITUTIVE EQUATIONS
Low frequency waves more
highly attenuated, producing
anelastic wave dispersion
Outer mantle is anisotropic,
with different velocities
horizontally and vertically
PREM: Preliminary Reference Earth Model
(Dziewonski & Anderson, 1981)
• 1000 normal mode periods,
500 summary travel times,
100 normal mode Q-factors,
mass, moment of inertia
• Mantle includes anelastic
dispersion and anisotropy
(transversely isotropic,
yielding two velocities)
• In spite of other models and
known shortcomings, still
preferred as textbook model
WHY STILL “PRELIMINARY”?
• Multiple spherically
symmetric models
• Question: What exactly
do they represent?
• Interest turns to details,
including tomography
using compact arrays of
seismometers to identify
lateral density variations
A QUESTION ANSWERED
“The early satellite results yielded
anomalies that exceeded expectations and led to the conclusion that
significant lateral variations in the
density of the mantle occurred.
These departures from isostatic and
hydrostatic equilibrium imply either
a finite strength for the mantle or
convection within it. With the finite
strength interpretation, the gravity
field reflects a long-past condition
of the planet, while the convection
interpretation implies an on-going
evolutionary process. The inability
to distinguish between two extreme
alternative hypotheses emphasizes
once again that Earth models based
on gravity observations alone are no
better than the assumptions made to
render a non-unique problem tractable.”
Lambeck, Geophysical Geodesy: The
Slow Deformations of the Earth, 1988
Van der Hilst et al., 1997
TWO MORE RECENT EXAMPLES
Inner Core Differential Motion Confirmed by Earthquake Waveform
Doublets, Zhang et al., 2005
Crustal Dilatation Observed by GRACE
After the 2004 Sumatra-Andaman
Earthquake, Han, et al., 2006
Gravity changes in Ојgal
SOURCES OF CORROBORATION
• The highly redundant data have been sufficiently well-behaved
to be yielding reasonably unequivocal answers to questions
• Systematic discrepancies between observation and theoretical
models have proved informative, e.g. in answering questions
• Complementary sources of data have converged on the same
conclusions rather than opposing one another
• Theoretical models have enabled advanced research to develop
evidence for details that reach well beyond those models
PRIMARY CONCLUSIONS
• Without the theoretical basis supplied by continuum mechanics,
seismology would not have given us empirical access to the
interior of the Earth
• While this theoretical basis has been indispensable to turning
seismographic data into evidence, that basis has itself been tested
in the process, providing corroborative evidence
• Seismology has given us, in particular, an enormously more
strongly confirmed answer to Newton’s question about the
density variation than we had in 1900
• Seismology has done this even though the constitutive equations
it used throughout much of the last century were over-simplified
and hence were made “more exact or liable to exceptions.”
THE QUESTION OF THEORETICAL ENTITIES
• Theory-mediated measurements vs. theoretical entities
– Do electrons really exist?
– Does the Earth really have a liquid outer core 2891 km below its
surface and an anisotropic solid inner core of radius 1221.5 km?
• The evidence for these entities consists of gross differences
we have concluded that they make in our measurements
• For which is the evidence stronger, that we should take
electrons to exist or that we should take the liquid outer
and solid inner core to exist?
The nature, scope, and limits of the knowledge
attained in individual sciences when they at least
seem to be most successful in marshaling evidence
• Science viewed from inside is an endeavor to turn data into
compelling evidence, something that is difficult to do and for
which theory is invariably needed
• Success in doing so has generally presupposed theoretical
claims that were first adopted when little evidence was
available for their truth
• Knowledge pursued is not merely theory, but also, even more
so, which details in the domain make a difference and what
differences they make
• How, if at all, has the theory presupposed in turning data
into evidence while establishing such details itself been
tested in the process?
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