scholarly journals Bayesian Full-waveform Inversion with Realistic Priors

Geophysics ◽  
2021 ◽  
pp. 1-20
Author(s):  
Xin Zhang ◽  
Andrew Curtis
Keyword(s):  
Prior Information ◽  
Velocity Structure ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Reflection Seismic ◽  
Variational Bayesian Inference ◽  
Full Waveform ◽  
Highly Nonlinear ◽  
Seismic Acquisition ◽  
Using Data

Seismic full-waveform inversion (FWI) uses full seismic records to estimate the subsurface velocity structure. This requires a highly nonlinear and nonunique inverse problem to be solved, so Bayesian methods have been used to quantify uncertainties in the solution. Variational Bayesian inference uses optimization to provide solutions efficiently. However, previously the method has only been applied to a transmission FWI problem, and with strong prior information imposed on the velocity such as is never available in practice. We show that the method works well in a seismic reflection setting, and with realistically weak prior information, representing the type of problem that occurs in reality. We conclude that the method can produce high-resolution images and reliable uncertainties using data from standard reflection seismic acquisition geometry, realistic nonlinearity, and practically achievable prior information.

scholarly journals Adding Prior Information in FWI through Relative Entropy

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 599
Author(s):  
Danilo Cruz ◽  
João de Araújo ◽  
Carlos da Costa ◽  
Carlos da Silva
Keyword(s):  
Inverse Problem ◽  
Relative Entropy ◽  
Global Minimum ◽  
Prior Information ◽  
Waveform Inversion ◽  
Petroleum Industry ◽  
Synthetic Data ◽  
Full Waveform Inversion ◽  
Full Waveform

Full waveform inversion is an advantageous technique for obtaining high-resolution subsurface information. In the petroleum industry, mainly in reservoir characterisation, it is common to use information from wells as previous information to decrease the ambiguity of the obtained results. For this, we propose adding a relative entropy term to the formalism of the full waveform inversion. In this context, entropy will be just a nomenclature for regularisation and will have the role of helping the converge to the global minimum. The application of entropy in inverse problems usually involves formulating the problem, so that it is possible to use statistical concepts. To avoid this step, we propose a deterministic application to the full waveform inversion. We will discuss some aspects of relative entropy and show three different ways of using them to add prior information through entropy in the inverse problem. We use a dynamic weighting scheme to add prior information through entropy. The idea is that the prior information can help to find the path of the global minimum at the beginning of the inversion process. In all cases, the prior information can be incorporated very quickly into the full waveform inversion and lead the inversion to the desired solution. When we include the logarithmic weighting that constitutes entropy to the inverse problem, we will suppress the low-intensity ripples and sharpen the point events. Thus, the addition of entropy relative to full waveform inversion can provide a result with better resolution. In regions where salt is present in the BP 2004 model, we obtained a significant improvement by adding prior information through the relative entropy for synthetic data. We will show that the prior information added through entropy in full-waveform inversion formalism will prove to be a way to avoid local minimums.

Introduction to this special section: Seismic acquisition

2022 ◽  
Vol 41 (1) ◽  
pp. 8-8
Author(s):  
Keith Millis ◽  
Guillaume Richard ◽  
Chengbo Li
Keyword(s):  
Special Section ◽  
Waveform Inversion ◽  
Environmental Concerns ◽  
Full Potential ◽  
Full Waveform Inversion ◽  
Low Frequencies ◽  
Seismic Surveys ◽  
Operational Risks ◽  
Full Waveform ◽  
Seismic Acquisition

In the life cycle of a seismic product, the lion's share of the budget and personnel hours is spent on acquisition. In most modern seismic surveys, acquisition involves hundreds of specialized personnel working for months or years. Seismic acquisition also must overcome potential liabilities and health, safety, and environmental concerns that rival facility, pipeline, construction, and other operational risks. As only properly acquired data can contribute effectively to processing and interpretation strategies, a great deal of importance is placed on acquisition quality. Arguably, many of the advances the seismic industry has experienced find their origin arising from advances in acquisition techniques. Full-waveform inversion (FWI), for example, can reach its full potential only when seismic acquisition has provided both low frequencies and long offsets.

Source estimation for wavefield-reconstruction inversion

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. R345-R359 ◽  
Author(s):  
Zhilong Fang ◽  
Rongrong Wang ◽  
Felix J. Herrmann
Keyword(s):  
Objective Function ◽  
Prior Information ◽  
Additional Data ◽  
Waveform Inversion ◽  
Search Space ◽  
Full Waveform Inversion ◽  
Auxiliary Variables ◽  
Full Waveform ◽  
Source Estimation ◽  
Exact Data

Source estimation is essential for all wave-equation-based seismic inversions, including full-waveform inversion (FWI) and the recently proposed wavefield-reconstruction inversion (WRI). When the source estimation is inaccurate, errors will propagate into the predicted data and introduce additional data misfit. As a consequence, inversion results that minimize this data misfit may become erroneous. To mitigate the errors introduced by the incorrect and preestimated sources, an embedded procedure that updates sources along with medium parameters is necessary for the inversion. So far, such a procedure is still missing in the context of WRI, a method that is, in many situations, less prone to local minima related to so-called cycle skipping, compared with FWI through exact data fitting. Although WRI indeed helps to mitigate issues related to cycle skipping by extending the search space with wavefields as auxiliary variables, it relies on having access to the correct source functions. To remove the requirement of having the accurate source functions, we have developed a source-estimation technique specifically designed for WRI. To achieve this task, we consider the source functions as unknown variables and arrive at an objective function that depends on the medium parameters, wavefields, and source functions. During each iteration, we apply the so-called variable projection method to simultaneously project out the source functions and wavefields. After the projection, we obtain a reduced objective function that only depends on the medium parameters and invert for the unknown medium parameters by minimizing this reduced objective. Numerical experiments illustrate that this approach can produce accurate estimates of the unknown medium parameters without any prior information of the source functions.

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