8 Introduction
Since 1972, when the first such model was made, the amount of
available data has increased, and the data have become better,
due to advances in seismology, sea floor imaging, and marine
magnetic measurements. Similarly, the fit to the data has
improved (or the misfit reduced) due both to the higher data
quality and to improvements in the model, such as treating
India and Australia as separate plates. Similar patterns of
increased data and improved fit occur for many applications,
including seismic velocity structure in the earth.
Many of the same issues surface when considering the
models used to describe earth processes. For example, we will
see that there are various models for what occurs at the core–
mantle boundary or what causes earthquakes within downgoing plates at subduction zones. Such models assume that a
particular set of physical processes occur, and show that for
apparently plausible values of the (often unknown) relevant
physical parameters, some behavior like that observed might
be expected. Although these simple models attempt to reflect
key aspects of the complex natural system, we often have no
way of telling if and how well they succeed. Typically, various
plausible models are suggested, all of which may in part be true
and offer interesting insights into what may be occurring. The
data often do not allow discrimination between them, so the
model one prefers depends on one’s geological instincts and
prejudices, and models go in and out of vogue. A common
scenario is for a model to become the consensus of the small
group of researchers most interested in a problem, and then be
challenged by fresh ideas or data from the outside. Hence, critically examining conventional wisdom often leads to discarding
or modifying it, and so making progress in keeping with the
Number of data
1200
800
400
0
CH72
RM1
PO71
RM2
NUVEL-1
χ
2
misfit to NUVEL-1 data
4000
2000
1000
0
CH72
RM1
PO71
RM2
NUVEL-1
3000
slip vectors
transforms
rates
χ
Over the years this process leads to a better understanding
of how the earth works (Fig. 1.1-8). For example, Fig. 1.1-9
summarizes the development of global plate motion models,
discussed in Chapter 5, that give the motion of the dozen or so
major plates. The models are derived by inverting data consisting of the directions of plate motions along transform faults,
the directions of plate motions during earthquakes, and the
rates of plate motions shown by sea floor magnetic anomalies.
Fig. 1.1-8 Schematic illustration of how models of earth processes
advance with time due to additional data and improved model
parameterizations.
Inversion modeling
New data
Compare old and new model
predictions to new data,
not used in deriving either
Verify that improvement
is significant
(F-test)
Quantify improved fit
of new model to data
( χ
2 test)
Develop new model parameters
by reducing misfits to data
Identify and investigate
remaining misfits
New model
χ
Fig. 1.1-9 Evolution of successive global
plate motion models, as the amount of data
increases and the misfit is reduced. Left:
Number of data used to derive the models.
Three types of data are inverted: earthquake
slip vector azimuths, transform fault
azimuths, and spreading rates. Right: The
misfit to NUVEL-1 data for the various
models. The vertical bars showing total
misfit are separated into segments giving the
misfit to each type of data. (DeMets et al.,
1990. Geophys. J. Int., 101, 425–78.)
Since 1972, when the first such model was made, the amount of
available data has increased, and the data have become better,
due to advances in seismology, sea floor imaging, and marine
magnetic measurements. Similarly, the fit to the data has
improved (or the misfit reduced) due both to the higher data
quality and to improvements in the model, such as treating
India and Australia as separate plates. Similar patterns of
increased data and improved fit occur for many applications,
including seismic velocity structure in the earth.
Many of the same issues surface when considering the
models used to describe earth processes. For example, we will
see that there are various models for what occurs at the core–
mantle boundary or what causes earthquakes within downgoing plates at subduction zones. Such models assume that a
particular set of physical processes occur, and show that for
apparently plausible values of the (often unknown) relevant
physical parameters, some behavior like that observed might
be expected. Although these simple models attempt to reflect
key aspects of the complex natural system, we often have no
way of telling if and how well they succeed. Typically, various
plausible models are suggested, all of which may in part be true
and offer interesting insights into what may be occurring. The
data often do not allow discrimination between them, so the
model one prefers depends on one’s geological instincts and
prejudices, and models go in and out of vogue. A common
scenario is for a model to become the consensus of the small
group of researchers most interested in a problem, and then be
challenged by fresh ideas or data from the outside. Hence, critically examining conventional wisdom often leads to discarding
or modifying it, and so making progress in keeping with the
Number of data
1200
800
400
0
CH72
RM1
PO71
RM2
NUVEL-1
χ
2
misfit to NUVEL-1 data
4000
2000
1000
0
CH72
RM1
PO71
RM2
NUVEL-1
3000
slip vectors
transforms
rates
χ
Over the years this process leads to a better understanding
of how the earth works (Fig. 1.1-8). For example, Fig. 1.1-9
summarizes the development of global plate motion models,
discussed in Chapter 5, that give the motion of the dozen or so
major plates. The models are derived by inverting data consisting of the directions of plate motions along transform faults,
the directions of plate motions during earthquakes, and the
rates of plate motions shown by sea floor magnetic anomalies.
Fig. 1.1-8 Schematic illustration of how models of earth processes
advance with time due to additional data and improved model
parameterizations.
Inversion modeling
New data
Compare old and new model
predictions to new data,
not used in deriving either
Verify that improvement
is significant
(F-test)
Quantify improved fit
of new model to data
( χ
2 test)
Develop new model parameters
by reducing misfits to data
Identify and investigate
remaining misfits
New model
χ
Fig. 1.1-9 Evolution of successive global
plate motion models, as the amount of data
increases and the misfit is reduced. Left:
Number of data used to derive the models.
Three types of data are inverted: earthquake
slip vector azimuths, transform fault
azimuths, and spreading rates. Right: The
misfit to NUVEL-1 data for the various
models. The vertical bars showing total
misfit are separated into segments giving the
misfit to each type of data. (DeMets et al.,
1990. Geophys. J. Int., 101, 425–78.)