scholarly journals An adjoint state method for three-dimensional transmission traveltime tomography using first-arrivals

2006 ◽  
Vol 4 (1) ◽  
pp. 249-266 ◽  
Author(s):  
Shingyu Leung ◽  
Jianliang Qian
Keyword(s):  
Three Dimensional ◽  
Traveltime Tomography ◽  
Adjoint State ◽  
State Method ◽  
Adjoint State Method

First-arrival traveltime tomography based on the adjoint-state method

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCB1-WCB10 ◽  
Author(s):  
Cédric Taillandier ◽  
Mark Noble ◽  
Hervé Chauris ◽  
Henri Calandra
Keyword(s):  
Synthetic Data ◽  
Point Of View ◽  
Data Set ◽  
Near Surface ◽  
Traveltime Tomography ◽  
Adjoint State ◽  
Gradient Based ◽  
First Arrival ◽  
State Method ◽  
Adjoint State Method

Classical algorithms used for traveltime tomography are not necessarily well suited for handling very large seismic data sets or for taking advantage of current supercomputers. The classical approach of first-arrival traveltime tomography was revisited with the proposal of a simple gradient-based approach that avoids ray tracing and estimation of the Fréchet derivative matrix. The key point becomes the derivation of the gradient of the misfit function obtained by the adjoint-state technique. The adjoint-state method is very attractive from a numerical point of view because the associated cost is equivalent to the solution of the forward-modeling problem, whatever the size of the input data and the number of unknown velocity parameters. An application on a 2D synthetic data set demonstrated the ability of the algorithm to image near-surface velocities with strong vertical and lateral variations and revealed the potential of the method.

scholarly journals First-arrival traveltime tomography for anisotropic media using the adjoint-state method

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. R147-R155 ◽  
Author(s):  
Umair bin Waheed ◽  
Garret Flagg ◽  
Can Evren Yarman
Keyword(s):  
Waveform Inversion ◽  
Surface Model ◽  
Model Parameters ◽  
Mathematical Framework ◽  
Near Surface ◽  
Traveltime Tomography ◽  
Adjoint State ◽  
First Arrival ◽  
State Method ◽  
Adjoint State Method

Traveltime tomography using transmission data has been widely used for static corrections and for obtaining near-surface models for seismic depth imaging. More recently, it is also being used to build initial models for full-waveform inversion. The classic traveltime tomography approach based on ray tracing has difficulties in handling large data sets arising from current seismic acquisition surveys. Some of these difficulties can be addressed using the adjoint-state method, due to its low memory requirement and numerical efficiency. By coupling the gradient computation to nonlinear optimization, it avoids the need for explicit computation of the Fréchet derivative matrix. Furthermore, its cost is equivalent to twice the solution of the forward-modeling problem, irrespective of the size of the input data. The presence of anisotropy in the subsurface has been well established during the past few decades. The improved seismic images obtained by incorporating anisotropy into the seismic processing workflow justify the effort. However, previous literature on the adjoint-state method has only addressed the isotropic approximation of the subsurface. We have extended the adjoint-state technique for first-arrival traveltime tomography to vertical transversely isotropic (VTI) media. Because [Formula: see text] is weakly resolvable from surface seismic alone, we have developed the mathematical framework and procedure to invert for [Formula: see text] and [Formula: see text]. Our numerical tests on the VTI SEAM model demonstrate the ability of the algorithm to invert for near-surface model parameters and reveal the accuracy achievable by the algorithm.

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