Making inferences based on data are ubiquitous
in science. Unfortunately, all too often the data is far from complete. The roads
of reason around that obstacle, are fraught with peril though. Perhaps as much
as in any field, Seismic Tomography has felt this cold hard truth. To
understand, imagine yourself standing in a large world full of craters,
valleys, hills, and deep pits, only that you are blind folded. Someone tells
you to find the lowest elevation on the planet. So what you do, is start
walking around and trying to find where the ground begins going downward. You
eventually find a place, where you know that no matter what direction you walk
in, you are going “up”. Alas, you conclude you have reached the lowest point.
As stupid as that conclusion is, it is quite similar to many “scientific” inference techniques. I am describing the way “altitude” corresponds
to the level of disagreement between the data and a theory, the error/misfit, in inverse theory.
You may say “well, why not get out of that valley, and go looking around for
the true lowest point, comparing each local lowest elevation to the previous
ones you have come across”. Alas, with the state of computational resources as
they are, for many problems involving huge data sets, this is truly is
analogous to telling a person blindfolded wanderer to make that search across that
large world on foot.
There are several categories of methods
used to tackle this difficulty in science, other than “just keep searching”.
The obvious method, is “just start out close to where you know the lowest
elevation is”, to continue the analogy. That is, explore scientific models and hypotheses
from a starting point that you think are close to the truth (mathematically,
start from an initial condition close to the global minimum). It works
terrific! At least, it does assuming where you start is actually close to the right
answer. Otherwise, it fails miserably. Even worse, due to noise and other lack
of ideality in the data obtained, the “true” answer may not even be the genuine
optimum solution.
Seismic Tomography, a method that
uses this type of search, uses observations of vibrations near the surface that
have travelled from a distant source, to infer how those vibrations travelled
inside the earth. Namely, it tells how fast waves travel at various places
inside the earth. It starts with a basic
model of the earth’s set of “speed limits” and proceeds to improve those
estimates from recorded travel times of waves. This has many issues.
Seismic waves are not laser beams, so why do many seismologists
keep pretending they are? Ray theory, that treats waves in the manner than
geometric optics treats light, is quite inaccurate in many respects, a fact
that is often masked through subtle omissions of certain details. If one were
to compare the travel time of an actual wave from a source to a quite distant receiver
to the prediction made by ray theory, they would find fair agreement often. The
missing fact though, is that the velocity model used to make that prediction
for ray theory, was constructed explicitly to make it agree with those observations,
not the actual velocity of the earth, which is to a large extent unknown. That
is one of the huge problems with not just Seismic Tomography, but any
discipline that uses very ill-posed inverse problems to attain models: since
the answer is horribly non-unique even qualitatively, it is possible to
generate quite dubious answers that fit the data exceptionally well, and even
allow for a fair amount of consistent extrapolation.
One way to address this issue with some math, would be to
simply analyze the uncertainties given by the scientists who made the ”answer”.
Unfortunately, Seismic Tomographers don’t really give error bars or any kind of
uncertainty measurements. In some cases,
depending on what the result is used for, it is slightly understandable.
However, all too often, it makes the issue not “is this good or bad science?”
but rather “is this even science?”. The issues don’t just stop at the accuracy
of the numbers, but what the numbers even mean is in question as well.
One of the perhaps dumbest and common assumptions in seismic
tomography, is isotropy (wave speeds being independent of direction of
propagation). In 1982, Don Anderson said “…we knew that our isotropic models
were not very good but we had no other choice. It is simply so far, computers
were not large enough to integrate the anisotropy parameter”. More recent
attempts to include anisotropy have relied on layer models or patches of
anisotropy. While this might seem like progress, it is not a full scale
inversion with respect to anisotropy, and could simply just be a means of
fixing errors produced by assuming isotropy everywhere else. To make matters worse, even a highly
anisotropic model input into a computer, can be modeled as an isotropic one. It
means that if you assume isotropic to start, you can find remarkable agreement
with data based on inverting for a model, even when the model is horribly
anisotropic.
The dejection of learning an imaged plume is a computational
artifact, the knowledge that the imaged subducting slab is questionable for
many reasons related to bias of incidence angles sampled and ignorance as to
the amount of thermal diffusion affecting imaged wavespeed, really makes you
wonder what you can and cannot trust in seismic tomography. Not to mention that
the vast majority of the other anomalies seen are beneath the floor of
systematic uncertainties in the answers.
