Questioning Seismic Tomography

            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.