Adjoint tomography with full envelope for scattering and intrinsic attenuation - resolution and trade-off

2021 ◽  
Author(s):  
Tuo Zhang ◽  
Christoph Sens-Schönfelder
Keyword(s):  
Spatial Distribution ◽  
High Frequency ◽  
Small Scale ◽  
Model Parameters ◽  
Mathematical Framework ◽  
Forward Simulation ◽  
Trade Off ◽  
Intrinsic Attenuation ◽  
Scale Heterogeneity ◽  
Rigorous Framework

<p>A rigorous framework exists for deterministic imaging the subsurface seismic velocity structure. Full-waveform inversion (FWI) that combines the forward simulation of waveforms with an adjoint (backward) simulation of the data misfit provides the gradient of the model misfit with respect to the changes in the model parameters. This gradient is used for iterative improvements of the model to minimize the data misfit. To investigate the small scale heterogeneity of the medium below the resolution limits the waveform tomography the envelopes of high-frequency seismic waves have been used to derive a statistical description of the small scale structure. Such studies employed a variety of misfit measures or empirical parameters and various assumptions about the spatial sensitivity of the measurements to derive some information about the spatial distribution of the high-frequency attenuation and scattering properties. A rigorous framework for the inversion of seismogram envelopes for the spatial imaging of heterogeneity and attenuation has been missing so far. Here we present a mathematical framework for the full envelope inversion that is based on a forward simulation of seismogram envelopes and an adjoint (backward) simulation of the envelope misfit, in full analogy to FWI. </p><p>Different from FWI that works with the wave equation, our approach is based on the Radiative Transfer Equation. In this study, the forward problem is solved by modelling the 2-D multiple nonisotropic scattering in a random elastic medium with spatially variable heterogeneity and attenuation using the Monte-Carlo method. The fluctuation strength <em>ε</em> and intrinsic quality factors <em>Q<sub>P</sub><sup>-1</sup></em> and <em>Q<sub>S</sub><sup>-1</sup></em> in the random medium are used to describe the spatial variability of attenuation and scattering. The misfit function is defined as the differences between the full observed and modelled envelopes.</p><p>We derived the sensitivity kernels corresponding to this misfit function that is minimized during the iterative adjoint inversion with the L-BFGS method. We have applied this algorithm in some numerical tests in the acoustic approximation. We show that it is possible in a rigorous way to image the spatial distribution of small scale heterogeneity and attenuation separately using seismogram envelopes. The resolution and the trade-off between scattering and intrinsic attenuation are discussed. Our analysis shows that relative importance of scattering and attenuation anomalies need to be considered when the model resolution is assessed. The inversions confirm, that the early coda is important for imaging the distribution of heterogeneity while later coda waves are more sensitive to intrinsic attenuation.</p>

scholarly journals A sequential inversion with outer iterations for the velocity and the intrinsic attenuation using an efficient wavefield inversion

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. R447-R459 ◽  
Author(s):  
Chao Song ◽  
Tariq Alkhalifah ◽  
Yuanyuan Li
Keyword(s):  
Frequency Domain ◽  
Null Space ◽  
Joint Inversion ◽  
Waveform Inversion ◽  
Significant Loss ◽  
Model Parameters ◽  
Trade Off ◽  
Intrinsic Attenuation ◽  
Highly Nonlinear ◽  
Wavefield Inversion

Full-waveform inversion (FWI) has become a popular method to retrieve high-resolution subsurface model parameters. It is a highly nonlinear optimization problem based on minimizing the misfit between the observed and predicted data. For intrinsically attenuating media, wave propagation experiences significant loss of energy. Thus, for better data fitting, it is sometimes crucial to consider attenuation in FWI. Viscoacoustic FWI aims at achieving a joint inversion of the velocity and attenuation models. However, multiparameter FWI imposes additional challenges including expanding the null space and facing parameter trade-off issues. Theoretically, an ideal way to mitigate the trade-off issue in multiparameter FWI is to apply the inverse Hessian operator to the parameter gradients. However, it is often not practical to calculate the full Hessian and its matrix inverse because this will be extremely expensive. To improve the computational efficiency and mitigate the trade-off issue, we have used an efficient wavefield inversion (EWI) method to invert for the velocity and the intrinsic attenuation. This approach is implemented in the frequency domain, and the velocity, in this case, is complex-valued in the viscoacoustic EWI. We evaluate a sequential update strategy for the velocity and the intrinsic attenuation, and we repeat the separate optimizations, which we refer to as outer iterations, until the convergence is achieved. Because viscoacoustic EWI is able to recover an accurate velocity model, the velocity update leakage to the [Formula: see text] model is largely reduced. We determine the effectiveness of this approach using synthetic data generated for the viscoacoustic Marmousi and Overthrust models. To further demonstrate the validity of our approach, we generate data in the time domain using a viscoelastic wave equation solver and obtain reasonable inversion results in the frequency domain using the viscoacoustic approximation.

scholarly journals Allelic correlation is a marker of tradeoffs between barriers to transmission of expression variability and signal responsiveness in genetic networks

2021 ◽  
Author(s):  
Ryan H Boe ◽  
Vinay Ayyappan ◽  
Lea Schuh ◽  
Arjun Raj
Keyword(s):  
Response Time ◽  
Mammalian Cells ◽  
Genetic Networks ◽  
Model Parameters ◽  
Mathematical Framework ◽  
Odds Ratios ◽  
Trade Off ◽  
Expression Variability ◽  
Noise Transmission ◽  
Allele Specific

Accurately functioning genetic networks should be responsive to signals but prevent transmission of stochastic bursts of expression. Existing data in mammalian cells suggests that such transcriptional "noise" is transmitted by some genes and not others, suggesting that noise transmission is tunable, perhaps at the expense of other signal processing capabilities. However, systematic claims about noise transmission in genetic networks have been limited by the inability to directly measure noise transmission. Here we build a mathematical framework capable of modeling allelic correlation and noise transmission. We find that allelic correlation and noise transmission correspond across a broad range of model parameters and network architectures. We further find that limiting noise transmission comes with the trade-off of being unresponsive to signals, and that within the parameter regimes that are responsive to signals, there is a further trade-off between response time and basal noise transmission. Using a published allele specific single cell RNA-sequencing dataset, we found that genes with high allelic odds ratios are enriched for cell-type specific functions, and that within multiple signaling pathways, factors which are upstream in the pathway have higher allelic odds ratios than downstream factors. Overall, our findings suggest that some degree of noise transmission is required to be responsive to signals, but that minimization of noise transmission can be accomplished by trading-off for a slower response time.

Small-Scale Heterogeneity in the Spatial Distribution of Carabid Beetles in the Southern Finnish Taiga

1992 ◽  
Vol 19 (2) ◽  
pp. 173 ◽  
Author(s):  
Jari Niemela ◽  
Yrjo Haila ◽  
Eero Halme ◽  
Timo Pajunen ◽  
Pekka Punttila
Keyword(s):  
Spatial Distribution ◽  
Carabid Beetles ◽  
Small Scale ◽  
Scale Heterogeneity

Impact of the Small-Scale Spatial Distribution of Dust Particles on the Chemical Evolution of the Diffuse Interstellar Medium

2020 ◽  
Vol 64 (8) ◽  
pp. 693-710
Author(s):  
V. A. Sokolova ◽  
A. I. Vasyunin ◽  
A. B. Ostrovskii ◽  
S. Yu. Parfenov
Keyword(s):  
Spatial Distribution ◽  
Interstellar Medium ◽  
Chemical Evolution ◽  
Dust Particles ◽  
Small Scale

Simulation of mechanically stirred two-phase liquid-gas flow

1986 ◽  
Vol 51 (5) ◽  
pp. 1001-1015 ◽  
Author(s):  
Ivan Fořt ◽  
Vladimír Rogalewicz ◽  
Miroslav Richter
Keyword(s):  
Spatial Distribution ◽  
Velocity Field ◽  
Gas Flow ◽  
Liquid Velocity ◽  
Model Parameters ◽  
Two Phase ◽  
Mean Velocity ◽  
Rushton Turbine ◽  
Low Viscosity ◽  
Volumetric Gas Flow Rate

The study describes simulation of the motion of bubbles in gas, dispersed by a mechanical impeller in a turbulent low-viscosity liquid flow. The model employs the Monte Carlo method and it is based both on the knowledge of the mean velocity field of mixed liquid (mean motion) and of the spatial distribution of turbulence intensity ( fluctuating motion) in the investigated system - a cylindrical tank with radial baffles at the wall and with a standard (Rushton) turbine impeller in the vessel axis. Motion of the liquid is then superimposed with that of the bubbles in a still environment (ascending motion). The computation of the simulation includes determination of the spatial distribution of the gas holds-up (volumetric concentrations) in the agitated charge as well as of the total gas hold-up system depending on the impeller size and its frequency of revolutions, on the volumetric gas flow rate and the physical properties of gas and liquid. As model parameters, both liquid velocity field and normal gas bubbles distribution characteristics are considered, assuming that the bubbles in the system do not coalesce.

scholarly journals Accommodating Taste and Scale Heterogeneity for Front-Seat Passenger’ Choice of Seat Belt Usage

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 460 ◽  
Author(s):  
Mahdi Rezapour ◽  
Khaled Ksaibati
Keyword(s):  
Mixed Model ◽  
Seat Belt ◽  
Model Fit ◽  
Model Parameters ◽  
Extended Model ◽  
Random Parameters ◽  
Front Seat ◽  
Scale Heterogeneity ◽  
Error Terms ◽  
The Cost

There is growing interest in implementation of the mixed model to account for heterogeneity across population observations. However, it has been argued that the assumption of independent and identically distributed (i.i.d) error terms might not be realistic, and for some observations the scale of the error is greater than others. Consequently, that might result in the error terms’ scale to be varied across those observations. As the standard mixed model could not account for the aforementioned attribute of the observations, extended model, allowing for scale heterogeneity, has been proposed to relax the equal error terms across observations. Thus, in this study we extended the mixed model to the model with heterogeneity in scale, or generalized multinomial logit model (GMNL), to see if accounting for the scale heterogeneity, by adding more flexibility to the distribution, would result in an improvement in the model fit. The study used the choice data related to wearing seat belt across front-seat passengers in Wyoming, with all attributes being individual-specific. The results highlighted that although the effect of the scale parameter was significant, the scale effect was trivial, and accounting for the effect at the cost of added parameters would result in a loss of model fit compared with the standard mixed model. Besides considering the standard mixed and the GMNL, the models with correlated random parameters were considered. The results highlighted that despite having significant correlation across the majority of the random parameters, the goodness of fits favors more parsimonious models with no correlation. The results of this study are specific to the dataset used in this study, and due to the possible fact that the heterogeneity in observations related to the front-seat passengers seat belt use might not be extreme, and do not require extra layer to account for the scale heterogeneity, or accounting for the scale heterogeneity at the cost of added parameters might not be required. Extensive discussion has been made in the content of this paper about the model parameters’ estimations and the mathematical formulation of the methods.

scholarly journals A Model-Based Tool for Assessing the Impact of Land Use Change Scenarios on Flood Risk in Small-Scale River Systems—Part 1: Pre-Processing of Scenario Based Flood Characteristics for the Current State of Land Use

Hydrology ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 102
Author(s):  
Frauke Kachholz ◽  
Jens Tränckner
Keyword(s):  
Land Use ◽  
River Flow ◽  
Land Use Changes ◽  
Small Rivers ◽  
Small Scale ◽  
Model Parameters ◽  
Ungauged Catchments ◽  
Model Based ◽  
Current State ◽  
The Impact

Land use changes influence the water balance and often increase surface runoff. The resulting impacts on river flow, water level, and flood should be identified beforehand in the phase of spatial planning. In two consecutive papers, we develop a model-based decision support system for quantifying the hydrological and stream hydraulic impacts of land use changes. Part 1 presents the semi-automatic set-up of physically based hydrological and hydraulic models on the basis of geodata analysis for the current state. Appropriate hydrological model parameters for ungauged catchments are derived by a transfer from a calibrated model. In the regarded lowland river basins, parameters of surface and groundwater inflow turned out to be particularly important. While the calibration delivers very good to good model results for flow (Evol =2.4%, R = 0.84, NSE = 0.84), the model performance is good to satisfactory (Evol = −9.6%, R = 0.88, NSE = 0.59) in a different river system parametrized with the transfer procedure. After transferring the concept to a larger area with various small rivers, the current state is analyzed by running simulations based on statistical rainfall scenarios. Results include watercourse section-specific capacities and excess volumes in case of flooding. The developed approach can relatively quickly generate physically reliable and spatially high-resolution results. Part 2 builds on the data generated in part 1 and presents the subsequent approach to assess hydrologic/hydrodynamic impacts of potential land use changes.

scholarly journals Small-scale spatial distribution of COVID-19-related excess mortality

MethodsX ◽  
2021 ◽  
Vol 8 ◽  
pp. 101257
Author(s):  
Dino Gibertoni ◽  
Francesco Sanmarchi ◽  
Kadjo Yves Cedric Adja ◽  
Davide Golinelli ◽  
Chiara Reno ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Excess Mortality ◽  
Small Scale

scholarly journals Multi-Domain Communication Systems and Networks: A Tensor-Based Approach

Network ◽  
2021 ◽  
Vol 1 (2) ◽  
pp. 50-74
Author(s):  
Divyanshu Pandey ◽  
Adithya Venugopal ◽  
Harry Leib
Keyword(s):  
Communication Systems ◽  
Physical Layer ◽  
Mathematical Framework ◽  
Trade Off ◽  
Information Theoretic ◽  
Time Frequency ◽  
Tensor Formulation ◽  
Processing Techniques ◽  
Multiple Domains ◽  
Signal Processing Techniques

Most modern communication systems, such as those intended for deployment in IoT applications or 5G and beyond networks, utilize multiple domains for transmission and reception at the physical layer. Depending on the application, these domains can include space, time, frequency, users, code sequences, and transmission media, to name a few. As such, the design criteria of future communication systems must be cognizant of the opportunities and the challenges that exist in exploiting the multi-domain nature of the signals and systems involved for information transmission. Focussing on the Physical Layer, this paper presents a novel mathematical framework using tensors, to represent, design, and analyze multi-domain systems. Various domains can be integrated into the transceiver design scheme using tensors. Tools from multi-linear algebra can be used to develop simultaneous signal processing techniques across all the domains. In particular, we present tensor partial response signaling (TPRS) which allows the introduction of controlled interference within elements of a domain and also across domains. We develop the TPRS system using the tensor contracted convolution to generate a multi-domain signal with desired spectral and cross-spectral properties across domains. In addition, by studying the information theoretic properties of the multi-domain tensor channel, we present the trade-off between different domains that can be harnessed using this framework. Numerical examples for capacity and mean square error are presented to highlight the domain trade-off revealed by the tensor formulation. Furthermore, an application of the tensor framework to MIMO Generalized Frequency Division Multiplexing (GFDM) is also presented.

Modern and Holocene microbial mats and associated microbially induced sedimentary structures (MISS) on the southeastern coast of Tunisia (Mediterranean Sea)

2020 ◽  
pp. 1-21
Author(s):  
Rached Lakhdar ◽  
Mohamed Soussi ◽  
Rachida Talbi
Keyword(s):  
Spatial Distribution ◽  
High Frequency ◽  
Depositional Environment ◽  
Microbial Mats ◽  
Coastal Environment ◽  
Tidal Dynamics ◽  
Very High Frequency ◽  
Intertidal Zones ◽  
Sedimentary Structures ◽  
Very High

Abstract On the southeastern Tunisian coastline, very diverse living microbial mats colonize the lower supratidal and intertidal zones, and locally may extend into the upper infratidal zone. The interaction between the benthic cyanobacteria and their siliciclastic substratum leads to the development of several types of microbially induced sedimentary structures (MISS). The mapping of the microbial mats has allowed the identification of the types of MISS that characterize the different segments of the coastal environment. The modern microbial mats have been compared with those recorded at the top of the Holocene deposits, which are composed of biodegraded microbial black mats alternating with white laminae made of clastic and evaporitic sediments, indicative of very high frequency cycles of flood and drought. A hypothetic profile showing their occurrences along the different areas bordering the coastline is proposed as a guide for the reconstruction of the ancient depositional environment. The roles of tidal dynamics, storms, and climate in controlling their genesis and spatial distribution, are discussed and highlighted. The modern MISS of southeastern Tunisia are compared with their equivalents that are well documented through the different geological eras.

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