Multi-objective waveform inversion of shallow seismic wavefields

2019 ◽  
Vol 220 (3) ◽  
pp. 1619-1631 ◽  
Author(s):  
Yudi Pan ◽  
Lingli Gao ◽  
Renat Shigapov
Keyword(s):  
Objective Function ◽  
Waveform Inversion ◽  
Model Space ◽  
Earth Model ◽  
Near Surface ◽  
Multi Objective ◽  
Shallow Seismic ◽  
L2 Norm ◽  
Objective Space ◽  
Single Objective

SUMMARY It has been increasingly popular to use shallow-seismic full-waveform inversion (FWI) to reconstruct near-surface structures. Conventional FWI tries to resolve the earth model by minimizing the difference between observed and synthetic seismic data using a certain criterion (conventionally, l2-norm of waveform difference). In this paper, we propose a multi-objective waveform inversion (MOWI) in which the similarity of data is quantified and minimized using multiple criteria simultaneously. By doing so, we expand the dimensionality of objective space as well as the mapping from data space to objective space, which provides MOWI higher freedom in exploring the model space compared to single-objective FWI. We combine three different scalar-valued objective functions into a vector-valued multi-objective function which measures the similarity of the waveform, the waveform envelope, and the amplitude spectra of the data, respectively. This multi-objective function takes not only trace-based waveform and wave packet similarity but also the dispersion characteristics of surface waves into account. Furthermore, the uncertainty in the inversion result could be estimated and analysed quantitatively by the variance of the optimal models. We propose a modified ϵ-constraint algorithm to solve the multi-objective optimization problem. Two synthetic examples are used to show the advantages of using MOWI compared to single-objective FWI. We also test the efficiency of MOWI by using two synthetic shallow-seismic examples, which confirm that MOWI can converge to a better result compared to the conventional single-objective FWI.

3D elastic full-waveform inversion of surface waves in the presence of irregular topography using an envelope-based misfit function

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. R1-R11 ◽  
Author(s):  
Dmitry Borisov ◽  
Ryan Modrak ◽  
Fuchun Gao ◽  
Jeroen Tromp
Keyword(s):  
Surface Wave ◽  
Objective Function ◽  
Surface Waves ◽  
Large Scale ◽  
Body Wave ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Near Surface ◽  
Full Waveform

Full-waveform inversion (FWI) is a powerful method for estimating the earth’s material properties. We demonstrate that surface-wave-driven FWI is well-suited to recovering near-surface structures and effective at providing S-wave speed starting models for use in conventional body-wave FWI. Using a synthetic example based on the SEG Advanced Modeling phase II foothills model, we started with an envelope-based objective function to invert for shallow large-scale heterogeneities. Then we used a waveform-difference objective function to obtain a higher-resolution model. To accurately model surface waves in the presence of complex tomography, we used a spectral-element wave-propagation solver. Envelope misfit functions are found to be effective at minimizing cycle-skipping issues in surface-wave inversions, and surface waves themselves are found to be useful for constraining complex near-surface features.

scholarly journals Robust multi-objective calibration strategies – possibilities for improving flood forecasting

2012 ◽  
Vol 16 (10) ◽  
pp. 3579-3606 ◽  
Author(s):  
T. Krauße ◽  
J. Cullmann ◽  
P. Saile ◽  
G. H. Schmitz
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Model Performance ◽  
Data Depth ◽  
Automatic Calibration ◽  
Multi Objective ◽  
Robust Model ◽  
Robust Parameter ◽  
Robust Parameter Estimation ◽  
Single Objective

Abstract. Process-oriented rainfall-runoff models are designed to approximate the complex hydrologic processes within a specific catchment and in particular to simulate the discharge at the catchment outlet. Most of these models exhibit a high degree of complexity and require the determination of various parameters by calibration. Recently, automatic calibration methods became popular in order to identify parameter vectors with high corresponding model performance. The model performance is often assessed by a purpose-oriented objective function. Practical experience suggests that in many situations one single objective function cannot adequately describe the model's ability to represent any aspect of the catchment's behaviour. This is regardless of whether the objective is aggregated of several criteria that measure different (possibly opposite) aspects of the system behaviour. One strategy to circumvent this problem is to define multiple objective functions and to apply a multi-objective optimisation algorithm to identify the set of Pareto optimal or non-dominated solutions. Nonetheless, there is a major disadvantage of automatic calibration procedures that understand the problem of model calibration just as the solution of an optimisation problem: due to the complex-shaped response surface, the estimated solution of the optimisation problem can result in different near-optimum parameter vectors that can lead to a very different performance on the validation data. Bárdossy and Singh (2008) studied this problem for single-objective calibration problems using the example of hydrological models and proposed a geometrical sampling approach called Robust Parameter Estimation (ROPE). This approach applies the concept of data depth in order to overcome the shortcomings of automatic calibration procedures and find a set of robust parameter vectors. Recent studies confirmed the effectivity of this method. However, all ROPE approaches published so far just identify robust model parameter vectors with respect to one single objective. The consideration of multiple objectives is just possible by aggregation. In this paper, we present an approach that combines the principles of multi-objective optimisation and depth-based sampling, entitled Multi-Objective Robust Parameter Estimation (MOROPE). It applies a multi-objective optimisation algorithm in order to identify non-dominated robust model parameter vectors. Subsequently, it samples parameter vectors with high data depth using a further developed sampling algorithm presented in Krauße and Cullmann (2012a). We study the effectivity of the proposed method using synthetical test functions and for the calibration of a distributed hydrologic model with focus on flood events in a small, pre-alpine, and fast responding catchment in Switzerland.

Tackling cycle skipping in full-waveform inversion with intermediate data

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. R411-R427 ◽  
Author(s):  
Gang Yao ◽  
Nuno V. da Silva ◽  
Michael Warner ◽  
Di Wu ◽  
Chenhao Yang
Keyword(s):  
Objective Function ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Intermediate Data ◽  
Full Waveform ◽  
L2 Norm ◽  
Recorded Data

Full-waveform inversion (FWI) is a promising technique for recovering the earth models for exploration geophysics and global seismology. FWI is generally formulated as the minimization of an objective function, defined as the L2-norm of the data residuals. The nonconvex nature of this objective function is one of the main obstacles for the successful application of FWI. A key manifestation of this nonconvexity is cycle skipping, which happens if the predicted data are more than half a cycle away from the recorded data. We have developed the concept of intermediate data for tackling cycle skipping. This intermediate data set is created to sit between predicted and recorded data, and it is less than half a cycle away from the predicted data. Inverting the intermediate data rather than the cycle-skipped recorded data can then circumvent cycle skipping. We applied this concept to invert cycle-skipped first arrivals. First, we picked up the first breaks of the predicted data and the recorded data. Second, we linearly scaled down the time difference between the two first breaks of each shot into a series of time shifts, the maximum of which was less than half a cycle, for each trace in this shot. Third, we moved the predicted data with the corresponding time shifts to create the intermediate data. Finally, we inverted the intermediate data rather than the recorded data. Because the intermediate data are not cycle-skipped and contain the traveltime information of the recorded data, FWI with intermediate data updates the background velocity model in the correct direction. Thus, it produces a background velocity model accurate enough for carrying out conventional FWI to rebuild the intermediate- and short-wavelength components of the velocity model. Our numerical examples using synthetic data validate the intermediate-data concept for tackling cycle skipping and demonstrate its effectiveness for the application to first arrivals.

Random objective waveform inversion of surface waves

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. EN49-EN61
Author(s):  
Yudi Pan ◽  
Lingli Gao
Keyword(s):  
Objective Function ◽  
Surface Waves ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Initial Model ◽  
S Wave ◽  
Data Set ◽  
Near Surface ◽  
Synthetic Test ◽  
Ground Penetrating

Full-waveform inversion (FWI) of surface waves is becoming increasingly popular among shallow-seismic methods. Due to a huge amount of data and the high nonlinearity of the objective function, FWI usually requires heavy computational costs and may converge toward a local minimum. To mitigate these problems, we have reformulated FWI under a multiobjective framework and adopted a random objective waveform inversion (ROWI) method for surface-wave characterization. Three different measure functions were used, whereas the combination of one measure function with one shot independently provided one of the [Formula: see text] objective functions ([Formula: see text] is the total number of shots). We have randomly chose and optimized one objective function at each iteration. We performed a synthetic test to compare the performance of the ROWI and conventional FWI approaches, which showed that the convergence of ROWI is faster and more robust compared with conventional FWI approaches. We also applied ROWI to a field data set acquired in Rheinstetten, Germany. ROWI successfully reconstructed the main geologic feature, a refilled trench, in the final result. The comparison between the ROWI result and a migrated ground-penetrating radar profile further proved the effectiveness of ROWI in reconstructing the near-surface S-wave velocity model. We also ran the same field example by using a poor initial model. In this case, conventional FWI failed whereas ROWI still reconstructed the subsurface model to a fairly good level, which highlighted the relatively low dependency of ROWI on the initial model.

The Research of Multi-Resource Equilibrium Optimization in Schedule Management

2012 ◽  
Vol 209-211 ◽  
pp. 1406-1410
Author(s):  
Yun Ning Zhang ◽  
Wei Wei Chen
Keyword(s):  
Objective Function ◽  
Basic Principle ◽  
Comprehensive Evaluation ◽  
Fuzzy Comprehensive Evaluation ◽  
Equilibrium Theory ◽  
Typical Problem ◽  
Multi Objective ◽  
Schedule Management ◽  
Theoretical Significance ◽  
Single Objective

Resource equilibrium optimization is a typical problem in Schedule Management. Based on studying multi-resource equilibrium theory thoroughly, this paper firstly gives different weights to various resources by using fuzzy comprehensive evaluation to transform multi-objective problem to single objective problem. Then, it establishes a model for multi-resource equilibrium optimization by choosing the variance of various resources’ demands as objective function. Finally, this paper describes its basic principle and steps, which has important theoretical significance.

Pareto Artificial Life Algorithm for Multi-Objective Optimization

2011 ◽  
Vol 4 (2) ◽  
pp. 43-60
Author(s):  
Jin-Dae Song ◽  
Bo-Suk Yang
Keyword(s):  
Objective Function ◽  
Artificial Life ◽  
Pareto Set ◽  
Function Optimization ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Function ◽  
Artificial Life Algorithm ◽  
Single Objective

Most engineering optimization uses multiple objective functions rather than single objective function. To realize an artificial life algorithm based multi-objective optimization, this paper proposes a Pareto artificial life algorithm that is capable of searching Pareto set for multi-objective function solutions. The Pareto set of optimum solutions is found by applying two objective functions for the optimum design of the defined journal bearing. By comparing with the optimum solutions of a single objective function, it is confirmed that the single function optimization result is one of the specific cases of Pareto set of optimum solutions.

Pareto Artificial Life Algorithm for Multi-Objective Optimization

2013 ◽  
pp. 100-115
Author(s):  
Jin-Dae Song ◽  
Bo-Suk Yang
Keyword(s):  
Objective Function ◽  
Artificial Life ◽  
Pareto Set ◽  
Function Optimization ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Function ◽  
Artificial Life Algorithm ◽  
Single Objective

Most engineering optimization uses multiple objective functions rather than single objective function. To realize an artificial life algorithm based multi-objective optimization, this paper proposes a Pareto artificial life algorithm that is capable of searching Pareto set for multi-objective function solutions. The Pareto set of optimum solutions is found by applying two objective functions for the optimum design of the defined journal bearing. By comparing with the optimum solutions of a single objective function, it is confirmed that the single function optimization result is one of the specific cases of Pareto set of optimum solutions.

scholarly journals From tomography to full-waveform inversion with a single objective function

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. R55-R61 ◽  
Author(s):  
Tariq Alkhalifah ◽  
Yunseok Choi
Keyword(s):  
Objective Function ◽  
Initial Velocity ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Half Cycle ◽  
Velocity Models ◽  
Full Waveform ◽  
Single Objective

In full-waveform inversion (FWI), a gradient-based update of the velocity model requires an initial velocity that produces synthetic data that are within a half-cycle, everywhere, from the field data. Such initial velocity models are usually extracted from migration velocity analysis or traveltime tomography, among other means, and are not guaranteed to adhere to the FWI requirements for an initial velocity model. As such, we evaluated an objective function based on the misfit in the instantaneous traveltime between the observed and modeled data. This phase-based attribute of the wavefield, along with its phase unwrapping characteristics, provided a frequency-dependent traveltime function that was easy to use and quantify, especially compared to conventional phase representation. With a strong Laplace damping of the modeled, potentially low-frequency, data along the time axis, this attribute admitted a first-arrival traveltime that could be compared with picked ones from the observed data, such as in wave equation tomography (WET). As we relax the damping on the synthetic and observed data, the objective function measures the misfit in the phase, however unwrapped. It, thus, provided a single objective function for a natural transition from WET to FWI. A Marmousi example demonstrated the effectiveness of the approach.

scholarly journals Searching for an optimized single-objective function matching multiple objectives with automatic calibration of hydrological models

2016 ◽  
Author(s):  
Fuqiang Tian ◽  
Yu Sun ◽  
Hongchang Hu ◽  
Hongyi Li
Keyword(s):  
Objective Function ◽  
Power Function ◽  
Automatic Calibration ◽  
Efficiency Coefficient ◽  
Hydrological Models ◽  
Objective Functions ◽  
Multi Objective ◽  
Hydrological Variable ◽  
Flow Part ◽  
Single Objective

Abstract. In the calibration of hydrological models, evaluation criteria are explicitly and quantitatively defined as single- or multi-objective functions when utilizing automatic calibration approaches. In most previous studies, there is a general opinion that no single-objective function can represent all of the important characteristics of even one specific kind of hydrological variable (e.g., streamflow). Thus hydrologists must turn to multi-objective calibration. In this study, we demonstrated that an optimized single-objective function can compromise multi-response modes (i.e., multi-objective functions) of the hydrograph, which is defined as summation of a power function of the absolute error between observed and simulated streamflow with the exponent of power function optimized for specific watersheds. The new objective function was applied to 196 model parameter estimation experiment (MOPEX) watersheds across the eastern United States using the semi-distributed Xinanjiang hydrological model. The optimized exponent value for each watershed was obtained by targeting four popular objective functions focusing on peak flows, low flows, water balance, and flashiness, respectively. The results showed that the optimized single-objective function can achieve a better hydrograph simulation compared to the traditional single-objective function Nash-Sutcliffe efficiency coefficient for most watersheds, and balance high flow part and low flow part of the hydrograph without substantial differences compared to multi-objective calibration. The proposed optimal single-objective function can be practically adopted in the hydrological modeling if the optimal exponent value could be determined a priori according to hydrological/climatic/landscape characteristics in a specific watershed. This is, however, left for future study.

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