Seismic Tomography and the Assessment of Uncertainty

Rawlinson, Nicholas; Fichtner, Andreas; Sambridge, Malcolm; Young, Malin M.

doi:10.1016/bs.agph.2014.08.001

Cited by 143 publications

(129 citation statements)

References 195 publications

Supporting

Mentioning

124

Contrasting

Order By: Relevance

“…Notions about prior model covariance are also used to precondition the inverse problem (e.g. Rawlinson et al 2014). The penalty term serves to deal with the underdetermined nature of the inverse problem, usually by trying to exclude models which exhibit levels of detail not required by the data.…”

Section: The Linearized Inverse Problem and The Resolution Matrixmentioning

confidence: 99%

“…Synthetic recovery tests are either noise free to assess optimal spatial resolution or include noise with a Gaussian distribution and standard deviation equal to that of noise estimates obtained from the data such as picking error (Rawlinson et al 2014). Spakman & Nolet (1988) advocate the addition of synthetic noise such that a data fit is obtained similar to that of the real data inversion.…”

Section: The Influence Of Data Noisementioning

confidence: 99%

“…This is despite rapid gains in computing power, and is out of balance with the significant theoretical and computational development of physically elaborate forward models leading to modern tomographic techniques such as full waveform inversion. This is part of the reason why, in most studies that use synthetic recovery tests to assess model robustness, the results are generally interpreted qualitatively (Rawlinson et al 2014); this can often be as simple as the qualitative description of detected resolution artefacts from a visual correlation between the input and output anomalies. The other reason is that sensitivity analysis principally leads to an implicit assessment of spatial resolution unless only one spike is used (Spakman & Nolet 1988).…”

Section: Colour Representationmentioning

confidence: 99%

“…Despite the massive increases in computing power and ongoing theoretical developments that have taken place since these seminal works, progress in the assessment of model robustness has been limited. As well as estimates of posterior covariance and uncertainty from linear theory, other methods that have been tried include synthetic reconstruction tests, jackknife and bootstrap methods and sampling strategies (for a review see Rawlinson et al 2014).…”

mentioning

confidence: 99%

See 3 more Smart Citations

On the use of sensitivity tests in seismic tomography

Rawlinson¹,

Spakman

2016

Geophys. J. Int.

159

View full text Add to dashboard Cite

S U M M A R YSensitivity analysis with synthetic models is widely used in seismic tomography as a means for assessing the spatial resolution of solutions produced by, in most cases, linear or iterative nonlinear inversion schemes. The most common type of synthetic reconstruction test is the so-called checkerboard resolution test in which the synthetic model comprises an alternating pattern of higher and lower wave speed (or some other seismic property such as attenuation) in 2-D or 3-D. Although originally introduced for application to large inverse problems for which formal resolution and covariance could not be computed, these tests have achieved popularity, even when resolution and covariance can be computed, by virtue of being simple to implement and providing rapid and intuitive insight into the reliability of the recovered model. However, checkerboard tests have a number of potential drawbacks, including (1) only providing indirect evidence of quantitative measures of reliability such as resolution and uncertainty, (2) giving a potentially misleading impression of the range of scale-lengths that can be resolved, and (3) not giving a true picture of the structural distortion or smearing that can be caused by the data coverage. The widespread use of synthetic reconstruction tests in seismic tomography is likely to continue for some time yet, so it is important to implement best practice where possible. The goal of this paper is to develop the underlying theory and carry out a series of numerical experiments in order to establish best practice and identify some common pitfalls. Based on our findings, we recommend (1) the use of a discrete spike test involving a sparse distribution of spikes, rather than the use of the conventional tightly spaced checkerboard; (2) using data coverage (e.g. ray-path geometry) inherited from the model constrained by the observations (i.e. the same forward operator or matrix), rather than the data coverage obtained by solving the forward problem through the synthetic model; (3) carrying out multiple tests using structures of different scale length; (4) taking special care with regard to what can be inferred when using synthetic structures that closely mimic what has been recovered in the observation-based model; (5) investigating the range of structural wavelengths that can be recovered using realistic levels of imposed data noise; and (6) where feasible, assessing the influence of model parametrization error, which arises from making a choice as to how structure is to be represented.

show abstract

Section: The Linearized Inverse Problem and The Resolution Matrixmentioning

confidence: 99%

Section: The Influence Of Data Noisementioning

confidence: 99%

Section: Colour Representationmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

On the use of sensitivity tests in seismic tomography

Rawlinson¹,

Spakman

2016

Geophys. J. Int.

159

View full text Add to dashboard Cite

show abstract

“…However, close to the edge the ray coverage and consequently the checkerboard pattern recovery is poor, thus interpretation must be made with caution. Furthermore, based on these tests the amplitude of an anomaly cannot be well determined, which is expected as usually calculated anomalies are lower than true anomalies (Rawlinson et al, 2014). Despite that, it is possible to reliably obtain the signs (positive or negative) of the anomalies compared to the average group velocity of the studied area.…”

Section: Resultsmentioning

confidence: 96%

Ambient Seismic Noise Tomography of a Loess High Bank at Dunaszekcső (Hungary)

Szanyi

Gráczer

Győri

et al. 2016

Pure Appl. Geophys.

View full text Add to dashboard Cite

show abstract

Resolution analysis by random probing

Fichtner

Leeuwen

2015

JGR Solid Earth

Self Cite

View full text Add to dashboard Cite

We develop and apply methods for resolution analysis in tomography, based on stochastic probing of the Hessian or resolution operators. Key properties of our methods are (i) low algorithmic complexity and easy implementation, (ii) applicability to any tomographic technique, including full‐waveform inversion and linearized ray tomography, (iii) applicability in any spatial dimension and to inversions with a large number of model parameters, (iv) low computational costs that are mostly a fraction of those required for synthetic recovery tests, and (v) the ability to quantify both spatial resolution and interparameter trade‐offs. Using synthetic full‐waveform inversions as benchmarks, we demonstrate that autocorrelations of random‐model applications to the Hessian yield various resolution measures, including direction‐ and position‐dependent resolution lengths and the strength of interparameter mappings. We observe that the required number of random test models is around five in one, two, and three dimensions. This means that the proposed resolution analyses are not only more meaningful than recovery tests but also computationally less expensive. We demonstrate the applicability of our method in a 3‐D real‐data full‐waveform inversion for the western Mediterranean. In addition to tomographic problems, resolution analysis by random probing may be used in other inverse methods that constrain continuously distributed properties, including electromagnetic and potential‐field inversions, as well as recently emerging geodynamic data assimilation.

show abstract

Seismic Tomography and the Assessment of Uncertainty

Cited by 143 publications

References 195 publications

On the use of sensitivity tests in seismic tomography

On the use of sensitivity tests in seismic tomography

Ambient Seismic Noise Tomography of a Loess High Bank at Dunaszekcső (Hungary)

Resolution analysis by random probing

Contact Info

Product

Resources

About