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.

First-arrival picking with a U-net convolutional network

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. U45-U57 ◽  
Author(s):  
Lianlian Hu ◽  
Xiaodong Zheng ◽  
Yanting Duan ◽  
Xinfei Yan ◽  
Ying Hu ◽  
...  
Keyword(s):  
Seismic Data ◽  
Synthetic Data ◽  
Training Data ◽  
Convolutional Network ◽  
Data Set ◽  
Waveform Data ◽  
Near Surface ◽  
Arrival Times ◽  
Seismic Waveform ◽  
First Arrival

In exploration geophysics, the first arrivals on data acquired under complicated near-surface conditions are often characterized by significant static corrections, weak energy, low signal-to-noise ratio, and dramatic phase change, and they are difficult to pick accurately with traditional automatic procedures. We have approached this problem by using a U-shaped fully convolutional network (U-net) to first-arrival picking, which is formulated as a binary segmentation problem. U-net has the ability to recognize inherent patterns of the first arrivals by combining attributes of arrivals in space and time on data of varying quality. An effective workflow based on U-net is presented for fast and accurate picking. A set of seismic waveform data and their corresponding first-arrival times are used to train the network in a supervised learning approach, then the trained model is used to detect the first arrivals for other seismic data. Our method is applied on one synthetic data set and three field data sets of low quality to identify the first arrivals. Results indicate that U-net only needs a few annotated samples for learning and is able to efficiently detect first-arrival times with high precision on complicated seismic data from a large survey. With the increasing training data of various first arrivals, a trained U-net has the potential to directly identify the first arrivals on new seismic data.

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