Seismic tomography: A window into deep Earth

Rawlinson, Nicholas; Pozgay, S.; Fishwick, Stewart

doi:10.1016/j.pepi.2009.10.002

Cited by 227 publications

(148 citation statements)

References 378 publications

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“…Most commonly, functional approaches with a set of basis functions or an a prior functional form, such as cells and grid nodes, have been adopted to represent the Earth's structure (e.g., Dziewonski, 1984;Aki and Lee, 1976;Thurber, 1983). Each approach has its own advantages and drawbacks (e.g., Zhao, 2009;Rawlinson et al, 2010). To guarantee accurate computation of synthetic seismograms and travel-time kernels and to adapt to local variations in data coverage, we use two sets of grid nodes (i.e., forward modeling grid and inversion grid) to parameterize the Earth's structure for forward modeling and inversion algorithms in this study.…”

Section: Model Parameterizationmentioning

confidence: 99%

“…However, because of scattering, wave front healing, and other finite-frequency effects, seismic measurements (such as travel-time and amplitude), especially those made on broadband recordings, are sensitive to three-dimensional (3-D) structures off the ray path (e.g., Marquering et al, 1999;Dahlen et al, 2000;Tape et al, 2007). Ray theory is actually only valid when the scale length of the variation of material properties is much larger than the seismic wavelength (Rawlinson et al, 2010). To take into account the sensitivity to off-ray structures, finite-frequency tomography methods that construct 2-D or 3-D travel-time and P. Tong et al: Part 1: Method amplitude sensitivity kernels are proposed, including those based on the paraxial approximation and dynamic ray tracing (e.g., Marquering et al, 1999;Dahlen et al, 2000;Tian et al, 2007;Tong et al, 2011) and those based on the normal mode theory (e.g., Zhao et al, 2000;Zhao and Jordan, 2006;To and Romanowicz, 2009).…”

Section: Introductionmentioning

confidence: 99%

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Wave-equation-based travel-time seismic tomography – Part 1: Method

et al. 2014

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Abstract. In this paper, we propose a wave-equation-based travel-time seismic tomography method with a detailed description of its step-by-step process. First, a linear relationship between the travel-time residual t = T obs − T syn and the relative velocity perturbation δc(x)/c(x) connected by a finite-frequency travel-time sensitivity kernel K(x) is theoretically derived using the adjoint method. To accurately calculate the travel-time residual t, two automatic arrivaltime picking techniques including the envelop energy ratio method and the combined ray and cross-correlation method are then developed to compute the arrival times T syn for synthetic seismograms. The arrival times T obs of observed seismograms are usually determined by manual hand picking in real applications. Travel-time sensitivity kernel K(x) is constructed by convolving a forward wavefield u(t, x) with an adjoint wavefield q(t, x). The calculations of synthetic seismograms and sensitivity kernels rely on forward modeling. To make it computationally feasible for tomographic problems involving a large number of seismic records, the forward problem is solved in the two-dimensional (2-D) vertical plane passing through the source and the receiver by a high-order central difference method. The final model is parameterized on 3-D regular grid (inversion) nodes with variable spacings, while model values on each 2-D forward modeling node are linearly interpolated by the values at its eight surrounding 3-D inversion grid nodes. Finally, the tomographic inverse problem is formulated as a regularized optimization problem, which can be iteratively solved by either the LSQR solver or a nonlinear conjugate-gradient method. To provide some insights into future 3-D tomographic inversions, Fréchet kernels for different seismic phases are also demonstrated in this study.

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Section: Model Parameterizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Wave-equation-based travel-time seismic tomography – Part 1: Method

et al. 2014

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“…Over the last three decades seismic tomography has produced a large number of models with a high degree of overlap as documented in many review articles (e.g., Woodhouse & Dziewonski, 1989;Ritzwoller & Lavely, 1995;Masters et al, 2000;Romanowicz, 2003;Rawlinson et al, 2010).…”

Section: Isotropic Velocity Tomographymentioning

confidence: 99%

“…Recent reviews provide extensive reference lists going back to the beginning of this research field in the 1970s (e.g., Romanowicz, 2003;Rawlinson et al, 2010). Sometimes, a collection of normal-mode frequencies is added to provide a global longwavelength constraint on the structure .…”

Section: Introductionmentioning

confidence: 99%

Global Imaging of the Earth's Deep Interior: Seismic Constraints on (An)isotropy, Density and Attenuation

Trampert

Fichtner

2013

Physics and Chemistry of the Deep Earth

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“…It is applied at all scales, from the local to the global scale (Romanowicz 2003), using signals from artificial sources and earthquakes (Rawlinson & Sambridge 2003;Rawlinson et al 2010;Liu & Gu 2012). Traditionally, the traveltime values 'picked' from the observed waveform signals (of seismic waves emerging from artificial sources or from earthquakes) are inverted for the distribution of the seismic velocity (or slowness) in the subsurface, either along 2-D profiles or in 3-D volumes (Thurber & Aki 1987).…”

Section: Introductionmentioning

confidence: 99%

Bayesian inversion of refraction seismic traveltime data

Ryberg

Haberland

2017

Geophysical Journal International

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S U M M A R YWe apply a Bayesian Markov chain Monte Carlo (McMC) formalism to the inversion of refraction seismic, traveltime data sets to derive 2-D velocity models below linear arrays (i.e. profiles) of sources and seismic receivers. Typical refraction data sets, especially when using the far-offset observations, are known as having experimental geometries which are very poor, highly ill-posed and far from being ideal. As a consequence, the structural resolution quickly degrades with depth. Conventional inversion techniques, based on regularization, potentially suffer from the choice of appropriate inversion parameters (i.e. number and distribution of cells, starting velocity models, damping and smoothing constraints, data noise level, etc.) and only local model space exploration. McMC techniques are used for exhaustive sampling of the model space without the need of prior knowledge (or assumptions) of inversion parameters, resulting in a large number of models fitting the observations. Statistical analysis of these models allows to derive an average (reference) solution and its standard deviation, thus providing uncertainty estimates of the inversion result. The highly non-linear character of the inversion problem, mainly caused by the experiment geometry, does not allow to derive a reference solution and error map by a simply averaging procedure. We present a modified averaging technique, which excludes parts of the prior distribution in the posterior values due to poor ray coverage, thus providing reliable estimates of inversion model properties even in those parts of the models. The model is discretized by a set of Voronoi polygons (with constant slowness cells) or a triangulated mesh (with interpolation within the triangles). Forward traveltime calculations are performed by a fast, finite-difference-based eikonal solver. The method is applied to a data set from a refraction seismic survey from Northern Namibia and compared to conventional tomography. An inversion test for a synthetic data set from a known model is also presented.

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Seismic tomography: A window into deep Earth

Cited by 227 publications

References 378 publications

Wave-equation-based travel-time seismic tomography – Part 1: Method

Wave-equation-based travel-time seismic tomography – Part 1: Method

Global Imaging of the Earth's Deep Interior: Seismic Constraints on (An)isotropy, Density and Attenuation

Bayesian inversion of refraction seismic traveltime data

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