Zeroth‐order asymptotics: Waveform inversion of the lowest degree

Geophysics ◽  
2003 ◽  
Vol 68 (2) ◽  
pp. 614-628 ◽  
Author(s):  
D. W. Vasco ◽  
Henk Keers ◽  
John E. Peterson ◽  
Ernest Majer
Keyword(s):  
Asymptotic Solution ◽  
High Frequency ◽  
Perturbation Technique ◽  
Waveform Inversion ◽  
Time Derivative ◽  
Zero Order ◽  
Bacterial Transport ◽  
Forward Simulation ◽  
Inversion Algorithm ◽  
Transport Site

Sensitivity computation is an integral part of many waveform inversion algorithms. An accurate and efficient technique for sensitivity computation follows from the zero‐order asymptotic solution to the elastodynamic equation of motion. Given the particular form of the asymptotic solution, we show that perturbations in high‐frequency waveforms are primarily sensitive to perturbations in phase. The resulting expression for waveform sensitivity is the time derivative of the synthetic seismogram multiplied by the phase sensitivity. All of the necessary elements for a step in the waveform inversion algorithm result from a single forward simulation. A comparison with sensitivities calculated using a purely numerical perturbation technique demonstrates that zero‐order sensitivities are accurate. Based upon the methodology, we match 330 waveforms from a crosswell experiment at a bacterial transport site near Oyster, Virginia. Each iteration of the waveform inversion takes approximately 18 minutes of CPU time on a workstation, illustrating the efficiency of the approach.

High-frequency localized elastic full waveform inversion for time-lapse seismic surveys

Geophysics ◽  
2021 ◽  
pp. 1-55
Author(s):  
Shihao Yuan ◽  
Nobuaki Fuji ◽  
Satish C. Singh
Keyword(s):  
High Frequency ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Time Lapse ◽  
Target Area ◽  
Full Waveform Inversion ◽  
Inversion Algorithm ◽  
Elastic Parameters ◽  
Model Inversion ◽  
Full Waveform

Seismic full waveform inversion is a powerful method to estimate the elastic properties of the subsurface. To mitigate the non-linearity and cycle-skipping problems, in a hierarchical manner, one inverts first low-frequency contents to determine long- and medium-wavelength structures and then increases the frequency contents to obtain detailed information. However, the inversion of higher frequencies can be computationally very expensive, especially when the target of interest, such as oil/gas reservoirs and axial melt lens, is at a great depth, far away from source and receiver arrays. To address this problem, we present a localized full waveform inversion algorithm where iterative modeling is performed locally, allowing us to extend inversions for higher frequencies with little computation effort. Our method is particularly useful for time-lapse seismic, where the changes in elastic parameters are local due to fluid extraction and injection in the subsurface. In our method, both sources and receivers are extrapolated to a region close to the target area, allowing forward modeling and inversion to be performed locally after low-frequency full-model inversion for the background model, which by nature only represents long- to medium-wavelength features. Numerical tests show that the inversion of low-frequency data for the overburden is sufficient to provide an accurate high-frequency estimation of elastic parameters of the target region.

scholarly journals Application of an Improved Ultrasound Full-Waveform Inversion in Bone Quantitative Measurement

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 260
Author(s):  
Meng Suo ◽  
Dong Zhang ◽  
Yan Yang
Keyword(s):  
Nonlinear Equations ◽  
Waveform Inversion ◽  
Optimal Solution ◽  
Inversion Method ◽  
Full Waveform Inversion ◽  
Inversion Algorithm ◽  
Elastic Wave Equation ◽  
Full Waveform ◽  
Ultrasonic Propagation ◽  
Joint Velocity

Inspired by the large number of applications for symmetric nonlinear equations, an improved full waveform inversion algorithm is proposed in this paper in order to quantitatively measure the bone density and realize the early diagnosis of osteoporosis. The isotropic elastic wave equation is used to simulate ultrasonic propagation between bone and soft tissue, and the Gauss–Newton algorithm based on symmetric nonlinear equations is applied to solve the optimal solution in the inversion. In addition, the authors use several strategies including the frequency-grid multiscale method, the envelope inversion and the new joint velocity–density inversion to improve the result of conventional full-waveform inversion method. The effects of various inversion settings are also tested to find a balanced way of keeping good accuracy and high computational efficiency. Numerical inversion experiments showed that the improved full waveform inversion (FWI) method proposed in this paper shows superior inversion results as it can detect small velocity–density changes in bones, and the relative error of the numerical model is within 10%. This method can also avoid interference from small amounts of noise and satisfy the high precision requirements for quantitative ultrasound measurements of bone.

Application of the variable projection scheme for frequency-domain full-waveform inversion

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. R249-R257 ◽  
Author(s):  
Maokun Li ◽  
James Rickett ◽  
Aria Abubakar
Keyword(s):  
Frequency Domain ◽  
Waveform Inversion ◽  
Simulated Data ◽  
Calibration Procedure ◽  
Full Waveform Inversion ◽  
Inversion Algorithm ◽  
Unknown Parameters ◽  
Variable Projection ◽  
Full Waveform ◽  
Data Calibration

We found a data calibration scheme for frequency-domain full-waveform inversion (FWI). The scheme is based on the variable projection technique. With this scheme, the FWI algorithm can incorporate the data calibration procedure into the inversion process without introducing additional unknown parameters. The calibration variable for each frequency is computed using a minimum norm solution between the measured and simulated data. This process is directly included in the data misfit cost function. Therefore, the inversion algorithm becomes source independent. Moreover, because all the data points are considered in the calibration process, this scheme increases the robustness of the algorithm. Numerical tests determined that the FWI algorithm can reconstruct velocity distributions accurately without the source waveform information.

Denoising for full-waveform inversion with expanded prediction-error filters

Geophysics ◽  
2021 ◽  
pp. 1-54
Author(s):  
Milad Bader ◽  
Robert G. Clapp ◽  
Biondo Biondi
Keyword(s):  
High Frequency ◽  
Prediction Error ◽  
Signal To Noise Ratio ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Full Waveform Inversion ◽  
Frequency Data ◽  
Signal To Noise ◽  
Frequency Signal ◽  
Full Waveform

Low-frequency data below 5 Hz are essential to the convergence of full-waveform inversion towards a useful solution. They help build the velocity model low wavenumbers and reduce the risk of cycle-skipping. In marine environments, low-frequency data are characterized by a low signal-to-noise ratio and can lead to erroneous models when inverted, especially if the noise contains coherent components. Often field data are high-pass filtered before any processing step, sacrificing weak but essential signal for full-waveform inversion. We propose to denoise the low-frequency data using prediction-error filters that we estimate from a high-frequency component with a high signal-to-noise ratio. The constructed filter captures the multi-dimensional spectrum of the high-frequency signal. We expand the filter's axes in the time-space domain to compress its spectrum towards the low frequencies and wavenumbers. The expanded filter becomes a predictor of the target low-frequency signal, and we incorporate it in a minimization scheme to attenuate noise. To account for data non-stationarity while retaining the simplicity of stationary filters, we divide the data into non-overlapping patches and linearly interpolate stationary filters at each data sample. We apply our method to synthetic stationary and non-stationary data, and we show it improves the full-waveform inversion results initialized at 2.5 Hz using the Marmousi model. We also demonstrate that the denoising attenuates non-stationary shear energy recorded by the vertical component of ocean-bottom nodes.

A generic 1-D imaging method for transient electromagnetic data

Geophysics ◽  
2002 ◽  
Vol 67 (2) ◽  
pp. 438-447 ◽  
Author(s):  
Niels Bøie Christensen
Keyword(s):  
Time Derivative ◽  
Step Response ◽  
Imaging Method ◽  
Nonlinear Inversion ◽  
Inversion Algorithm ◽  
Electromagnetic Data ◽  
Transient Electromagnetic ◽  
Dependent Part ◽  
Space Step ◽  
Forward Mapping

This paper presents a fast approximate 1-D inversion algorithm for transient electromagnetic (EM) data that can be applied for all measuring configurationsand transmitter waveforms and for all field components. The inversion is based on an approximate forward mapping in the adaptive Born approximation. The generality is obtained through a separation of the forward problem into a configuration-independent part, mapping layer conductivities into apparent conductivity, and a configuration-dependent part, the half-space step response. The EM response from any waveform can then be found by a convolution with the time derivative of the waveform. The approach does not involve inherently unstable deconvolution computations or nonunique transformations, and it is about 100 times faster than ordinary nonlinear inversion. Nonlinear model responses of the models obtained through the approximate inversion fit the data typically within 5%.

A New Underground Target Identification Method Based on Ground Penetrating Radar Map

2011 ◽  
Vol 58-60 ◽  
pp. 1926-1931
Author(s):  
Fei Yu Lian ◽  
Qing Li
Keyword(s):  
Dielectric Constant ◽  
Target Identification ◽  
Waveform Inversion ◽  
Homogeneous Medium ◽  
Main Idea ◽  
Comparison Method ◽  
Coarse Grained ◽  
Layer By Layer ◽  
Inversion Algorithm ◽  
Identification Method

In this paper, we proposed a punctuated target identification method for underground homogeneous medium based on dielectric constant inversion algorithm. Its main idea is that, initially, Hough transform is used to locate the target characterized by hyperbola in a radar profile map, then a layer-by-layer waveform inversion algorithm is used to invert the dielectric constant on the location where the target lies. To guarantee the correctness of inversion, the transmission beam method is adopted to obtain initial parameters and calibration factors required by inversion. Through numerical analysis of the dielectric constant of the target, the classification of multiple targets in an underground medium can be confirmed. This method not only overcomes the failure of the traditional phase-comparison method to distinguish different kinds of targets in the same region, but also overcomes the limitation of the image processing method, in which it only classifies the target in a coarse-grained manner. Experimental results show that this method has many advantages, such as fine-grained classification, high precision, and multiple target identification, in the identification of underground targets.

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