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

1
TURNING DATA INTO EVIDENCEThree Lectures on
the Role of Theory in Science1. CLOSING THE
LOOPTesting Newtonian Gravity, Then and Now2.
GETTING STARTEDBuilding Theories from Working
Hypotheses3. GAINING ACCESSUsing Seismology
to Probe the Earths Insides

• George E. Smith
• Tufts University

2
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

3
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?

4
OUTLINE

• Introduction the issue
• Seismological research from 1900 to 1960
• Seismological research since 1960
• A. From 1960 to Preliminary Reference Earth
  Model
• B. The years since PREM
• Concluding remarks

5
Newtons question How does density vary below
the Earths 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 every-where 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

6
Gravity Measurements Underdetermine

• Deviation of surface gravity from Newtons ideal
  variation implies the value of (C-A)/Ma2 and
  hence a correction to the difference (C-A) in the
  Earths 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 ?(r)
  of density inside the Earth by implying it is
  notably greater toward the center, but they do
  not suffice to determine the variation ?(r) .

• Hypothetical models of ?(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.

7
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)

8
RICHARD DIXON OLDHAM1899 Report on the great
earthquake of 12 June 18971900 On the
propagation of earthquake motion to great
distances1906 The constitution of the earth as
revealed by earthquakes
9
NINETEENTH CENTURY BACKGROUND

• Assumptions
• elastic
• linear
• isotropic
• 2 stress-strain parameters
• vs. as many as 21 in the
• general case of anisotropy
• homogeneous
• .

• 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)

10
EVIDENCE FOR THE THEORY OF p AND s WAVES?

• Poisson Addition to Mémoire sur léquilibre des
  corps élastiques
• Mémoire a classic in continuum mechanics
• Mathematical consequences of Navier-Stokes
  equation
• Basic equations of continuum mechanics
• Fundamental principles of physics, e.g. Fma
• 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?

11
SEISMIC WAVES AT ONE LOCATION
12
SEISMIC WAVE PROPAGATION
13
OLDHAMS 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
inter-ior 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.
14
(No Transcript)
15
DISCONTINUITIES A BRIEF HISTORY

• Crust-mantle boundary
• Mohorovicic 1909
• Core
• (Oldham 1906)
• Gutenberg 1914
• at 2900 km below surface
• Core is liquid
• Jeffreys 1926
• Inner Core
• Lehman 1936

16
THE PROJECT 1900-1940

• from
• Arrival times of seismic waves from
  earthquakes at many locations around the Earth
• to
• Travel times (?t vs. ??) 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 Herglotz-Wiechart integral (1907) for an
  isotropic medium

17
DIFFICULTIES

• Need to identify phases (different pathways) of
  waves reaching a single point at different times

18
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 symme-try makes sense

19
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 ?t vs. ?? are well
  behaved
• (Isotropic, linear elasticity with continuous
  properties except at identified discontinuities)

20
A FURTHER PROJECT INFER DENSITY vs. RADIUS

• P velocity in isotropic elastic medium ?
• ?(bulk-mod4shear-mod/3)/density
• S velocity in isotropic elastic medium ?
• ?(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
21
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

22
OUTLINE

• Introduction the issue
• Seismological research from 1900 to 1960
• Seismological research since 1960
• A. From 1960 to Preliminary Reference Earth
  Model
• B. The years since PREM
• Concluding remarks

23
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)

24
DETECTING FREE OSCILLATIONSAN EXAMPLE
COLOMBIA, 1970
25
(No Transcript)
26
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

27
INVERSE-THEORY

• Initial Earth model densi- ties material
  properties
• Calculate natural frequen- cies for model
• Find array of discrepancies vs. observed
  frequencies
• Use array of discrepancies to revise Earth
  model

28
(No Transcript)
29
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

30
EMPIRICALLY DRIVEN REVISIONS TO THE
CONSTITUTIVE EQUATIONS

• Outer mantle is anisotropic, with different
  velocities horizontally and vertically

• Low frequency waves more highly attenuated,
  producing anelastic wave dispersion

31
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

32
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

33
A QUESTION ANSWERED

• The early satellite results yielded
  anomalies that exceeded expecta-tions 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 tract-able.
• Lambeck, Geophysical Geodesy The
• Slow Deformations of the Earth, 1988
• Van der Hilst et al., 1997

34
TWO MORE RECENT EXAMPLES

• Inner Core Differential Motion Con-firmed 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 µgal

35
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

36
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
  Newtons 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.

37
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?

38
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?