scholarly journals Refraction tomography using a waveform-inversion back-propagation technique

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. R21-R30 ◽  
Author(s):  
Dong-Joo Min ◽  
Changsoo Shin
Keyword(s):  
Wave Equation ◽  
Waveform Inversion ◽  
Back Propagation ◽  
Angular Frequency ◽  
Damping Factor ◽  
Traveltime Tomography ◽  
Refraction Tomography ◽  
First Arrival ◽  
Propagation Technique ◽  
Tomography Method

One of the applications of refraction-traveltime tomography is to provide an initial model for waveform inversion and Kirchhoff prestack migration. For such applications, we need a refraction-traveltime tomography method that is robust for complicated and high-velocity-contrast models. Of the many refraction-traveltime tomography methods available, we believe wave-based algorithms to be best suited for dealing with complicated models. We developed a new wave-based, refraction-tomography algorithm using a damped wave equation and a waveform-inversion back-propagation technique. The imaginary part of a complex angular frequency, which is generally introduced in frequency-domain wave modeling, acts as a damping factor. By choosing an optimal damping factor from the numerical-dispersion relation, we can suppress the wavetrains following the first arrival. The objective function of our algorithm consists of residuals between the respective phases of first arrivals in field data and in forward-modeled data. The model-response, first-arrival phases can be obtained by taking the natural logarithm of damped wavefields at a single frequency low enough to yield unwrapped phases, whereas field-data phases are generated by multiplying picked first-arrival traveltimes by the same angular frequency used to compute model-response phases. To compute the steepest-descent direction, we apply a waveform-inversion back-propagation algorithm based on the symmetry of the Green’s function for the wave equation (i.e., the adjoint state of the wave equation), allowing us to avoid directly computing and saving sensitivities (Fréchet derivatives). From numerical examples of a block-anomaly model and the Marmousi-2 model, we confirm that traveltimes computed from a damped monochromatic wavefield are compatible with those picked from synthetic data, and our refraction-tomography method can provide initial models for Kirchhoff prestack depth migration.

Traveltime information-based wave-equation inversion

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCC27-WCC36 ◽  
Author(s):  
Yu Zhang ◽  
Daoliu Wang
Keyword(s):  
Wave Equation ◽  
Conventional Method ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Back Propagation ◽  
Velocity Model ◽  
Data Fitting ◽  
Inversion Method ◽  
New Wave ◽  
Seismic Record

We propose a new wave-equation inversion method that mainly depends on the traveltime information of the recorded seismic data. Unlike the conventional method, we first apply a [Formula: see text] transform to the seismic data to form the delayed-shot seismic record, back propagate the transformed data, and then invert the velocity model by maximizing the wavefield energy around the shooting time at the source locations. Data fitting is not enforced during the inversion, so the optimized velocity model is obtained by best focusing the source energy after a back propagation. Therefore, inversion accuracy depends only on the traveltime information embedded in the seismic data. This method may overcome some practical issues of waveform inversion; in particular, it relaxes the dependency of the seismic data amplitudes and the source wavelet.

scholarly journals Refraction traveltime tomography using damped monochromatic wavefield

Geophysics ◽  
2005 ◽  
Vol 70 (2) ◽  
pp. U1-U7 ◽  
Author(s):  
Sukjoon Pyun ◽  
Changsoo Shin ◽  
Dong-Joo Min ◽  
Taeyoung Ha
Keyword(s):  
Wave Equation ◽  
Frequency Domain ◽  
Computational Effort ◽  
Fréchet Derivative ◽  
Reciprocity Theorem ◽  
Damped Wave Equation ◽  
Traveltime Tomography ◽  
Frechet Derivatives ◽  
First Arrival ◽  
Fréchet Derivatives

For complicated earth models, wave-equation–based refraction-traveltime tomography is more accurate than ray-based tomography but requires more computational effort. Most of the computational effort in traveltime tomography comes from computing traveltimes and their Fréchet derivatives, which for ray-based methods can be computed directly. However, in most wave-equation traveltime-tomography algorithms, the steepest descent direction of the objective function is computed by the backprojection algorithm, without computing a Fréchet derivative directly. We propose a new wave-based refraction-traveltime–tomography procedure that computes Fréchet derivatives directly and efficiently. Our method involves solving a damped-wave equation using a frequency-domain, finite-element modeling algorithm at a single frequency and invoking the reciprocity theorem. A damping factor, which is commonly used to suppress wraparound effects in frequency-domain modeling, plays the role of suppressing multievent wavefields. By limiting the wavefield to a single first arrival, we are able to extract the first-arrival traveltime from the phase term without applying a time window. Computing the partial derivative of the damped wave-equation solution using the reciprocity theorem enables us to compute the Fréchet derivative of amplitude, as well as that of traveltime, with respect to subsurface parameters. Using the Marmousi-2 model, we demonstrate numerically that refraction traveltime tomography with large-offset data can be used to provide the smooth initial velocity model necessary for prestack depth migration.

Damped wave-equation-based first-arrival traveltime tomography using the embedded boundary method

Geophysics ◽  
2021 ◽  
pp. 1-91
Author(s):  
Yunhui Park ◽  
Sukjoon Pyun
Keyword(s):  
Wave Equation ◽  
Real Data ◽  
Damped Wave Equation ◽  
Traveltime Tomography ◽  
Velocity Models ◽  
Boundary Method ◽  
Embedded Boundary ◽  
First Arrival ◽  
Irregular Topography ◽  
Modeling Algorithm

First-arrival traveltime tomography (FATT) is used to delineate shallow velocity structures to identify static effects in oil exploration as well as to characterize the near surface for geotechnical purposes. Because FATT is generally used for land seismic data processing, it becomes necessary to consider irregular topography especially when performing wave-based tomography. However, the standard Cartesian finite-difference method cannot properly handle irregular topography. Hence, the embedded boundary method (EBM) is incorporated into the frequency-domain damped-wave equation in order to correctly describe irregular topography. The developed modeling algorithm is used to calculate first-arrival traveltimes and to perform FATT. The EBM-based modeling algorithm accurately describes the irregular surfaces of numerical velocity models on a regular mesh by exploiting the mirror image principle. The accuracy of the EBM-based traveltime calculation is validated by using two homogeneous velocity models with dipping and complex surfaces. The validation results demonstrate that the proposed algorithm is unaffected by the staircase approximation. The FATT is then applied to synthetic and real data to demonstrate the applicability of the developed algorithm to velocity models with complex topography. For the real data example, the inverted velocity model is used to apply static corrections. The processing results demonstrate an improvement in the continuity of seismic events, thus confirming the accuracy of the developed FATT 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.

Waveform tomography of field vibroseis data using an approximate 2D geometry leads to improved velocity models

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. R33-R43 ◽  
Author(s):  
Brendan R. Smithyman ◽  
Ronald M. Clowes
Keyword(s):  
Waveform Inversion ◽  
Velocity Model ◽  
Surface Velocity ◽  
Time Shift ◽  
Full Waveform Inversion ◽  
Near Surface ◽  
Traveltime Tomography ◽  
Full Waveform ◽  
First Arrival ◽  
Waveform Tomography

Waveform tomography, a combination of traveltime tomography (or inversion) and waveform inversion, is applied to vibroseis first-arrival data to generate an interpretable model of P-wave velocity for a site in the Nechako Basin, south-central British Columbia, Canada. We use constrained 3D traveltime inversion followed by 2D full-waveform inversion to process long-offset (14.4 km) first-arrival refraction waveforms, resulting in a velocity model of significantly higher detail than a conventional refraction-statics model generated for a processing workflow. The crooked-line acquisition of the data set makes 2D full-waveform inversion difficult. Thus, a procedure that improves the tractability of waveform tomography processing of vibroseis data recorded on crooked roads is developed to generate a near-surface ([Formula: see text]) velocity model for the study area. The data waveforms are first static corrected using a time shift determined by 3D raytracing, which accounts for the crossline offsets produced by the crooked-line acquisition. The velocity model generated from waveform tomography exhibits substantial improvement when compared with a conventional refraction-statics model. It also shows improved resolution of sharp discontinuities and low-velocity regions when compared to the model from traveltime tomography alone, especially in regions where the geometry errors are moderate. Interpretation of the near-surface velocity model indicates possible subbasins in the Nechako Basin and delineates the Eocene volcanic rocks of the study area. This approach limits the ability of the full-waveform inversion to fit some propagation modes; however, the tractability of the inversion in the near-surface region is improved. This new development is especially useful in studies that do not warrant 3D seismic acquisition and processing.

Alternating first-arrival traveltime tomography and waveform inversion for near-surface imaging

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. R245-R257 ◽  
Author(s):  
Mengyao Sun ◽  
Jie Zhang ◽  
Wei Zhang
Keyword(s):  
High Efficiency ◽  
Joint Inversion ◽  
Waveform Inversion ◽  
Quality Data ◽  
Inversion Method ◽  
Multiscale Approach ◽  
Surface Imaging ◽  
Near Surface ◽  
Traveltime Tomography ◽  
First Arrival

Near-surface seismic imaging often plays a significant role in producing quality data processing results for the deep subsurface in land and shallow marine environments. First-arrival traveltime tomography is a common approach for near-surface imaging due to its high efficiency and simplicity. However, the method faces issues of missing hidden layers and resolving the structures with low resolution. On the other hand, waveform inversion should offer better solutions for dealing with these issues, but it may suffer from the cycle-skipping problem. We intend to use the advantages and reduce the disadvantages of the two methods by developing a new strategy of alternately applying traveltime tomography and waveform inversion through iterations. First-arrival traveltime tomography applies a wavefront raytracer and a nonlinear inversion approach. Waveform inversion is a multiscale approach in which a wavelet transform is applied in the data domain to better handle the cycle-skipping problem. By alternating the two inversions rather than performing a joint inversion, we reduce the memory requirements and avoid nonphysical scaling problems between the two approaches. Using one synthetic and two real data examples, we determine that alternating inversions minimize two separate objective functions at the same time and constrain the near-surface structures fairly well compared with the waveform inversion method alone. For the field examples, the new method avoids generating the obvious artifacts and provides results consistent with the geology analysis of those areas.

In-Process Monitoring and Estimation of Tool Wear on CNC Turning by Applying Multi-Sensor with Back Propagation Technique

2011 ◽  
Vol 291-294 ◽  
pp. 3036-3043 ◽  
Author(s):  
Somkiat Tangjitsitcharoen ◽  
Channarong Rungruang
Keyword(s):  
Acoustic Emission ◽  
Tool Wear ◽  
Monitoring System ◽  
Process Monitoring ◽  
Back Propagation ◽  
Force Sensor ◽  
Accelerometer Sensor ◽  
Cnc Turning ◽  
Propagation Technique ◽  
Cnc Turning Process

The aim of this research is to propose and develop the in-process monitoring system of the tool wear for the carbon steel (S45C) in CNC turning process by utilizing the multi-sensor which are the force sensor, the sound sensor, the accelerometer sensor and the acoustic emission sensor. The progress of the tool wear results in the larger cutting force, the higher amplitude of the acceleration signal, and the higher power spectrum densities of sound and acoustic emission signals. Hence, their signals have been integrated via the neural network with the back propagation technique to monitor the tool wear. The experimentally obtained results showed that the in-process monitoring system proposed and developed in this research can be effectively used to estimate the tool wear level with the higher accuracy and reliability.

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