Fast finite-difference time-domain modeling for marine-subsurface electromagnetic problems

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. A19-A23 ◽  
Author(s):  
Frank A. Maaø
Keyword(s):  
Low Frequency ◽  
Computational Time ◽  
Small Displacement ◽  
Displacement Current ◽  
Domain Modeling ◽  
Low Frequencies ◽  
Electromagnetic Problems ◽  
Time Domain Modeling ◽  
Displacement Currents ◽  
Propagation Velocities

In the low-frequency limit, the displacement currents in the Maxwell equations can be neglected. However, for numerical simulations, a small displacement current should be present to achieve numerical stability. This requirement leads to a large range of propagation velocities with high velocities for the high frequencies and low velocities for the low frequencies. As a consequence, the number of time steps may become large. I show that it is possible to transform mathematically the original physical problem to one that has propagation velocities with less frequency dependence. Hence, the number of time steps necessary for a signal to travel a certain distance with the lowest velocity is significantly reduced. A typical example shows a reduction in computational time by a factor of 40. A comparison of the solutions from plane-layered modeling in the frequency and wavenumber domain and the proposed method shows good agreement between the two. The proposed method can also be used for other systems of diffusive equations.

scholarly journals Model Calibration of Stochastic Process and Computer Experiment for MVO Analysis of Multi-Low-Frequency Electromagnetic Data

Processes ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 605
Author(s):  
Muhammad Naeim Mohd Aris ◽  
Hanita Daud ◽  
Khairul Arifin Mohd Noh ◽  
Sarat Chandra Dass
Keyword(s):  
Stochastic Process ◽  
Computer Simulation ◽  
Model Calibration ◽  
Low Frequency ◽  
Computer Experiment ◽  
Hydrocarbon Exploration ◽  
Computational Time ◽  
Low Frequencies ◽  
Uncertainty Measurement ◽  
Mathematical Equations

An electromagnetic (EM) technique is employed in seabed logging (SBL) to detect offshore hydrocarbon-saturated reservoirs. In risk analysis for hydrocarbon exploration, computer simulation for subsurface modelling is a crucial task. It can be expensive and time-consuming due to its complicated mathematical equations, and only a few realizations of input-output pairs can be generated after a very lengthy computational time. Understanding the unknown functions without any uncertainty measurement could be very challenging as well. We proposed model calibration between a stochastic process and computer experiment for magnitude versus offset (MVO) analysis. Two-dimensional (2D) Gaussian process (GP) models were developed for low-frequencies of 0.0625–0.5 Hz at different hydrocarbon depths to estimate EM responses at untried observations with less time consumption. The calculated error measurements revealed that the estimates were well-matched with the computer simulation technology (CST) outputs. Then, GP was fitted in the MVO plots to provide uncertainty quantification. Based on the confidence intervals, hydrocarbons were difficult to determine especially when their depth was 3000 m from the seabed. The normalized magnitudes for other frequencies also agreed with the resulting predictive variance. Thus, the model resolution for EM data decreases as the hydrocarbon depth increases even though multi-low frequencies were exercised in the SBL application.

scholarly journals Effect of Displacement Current on the Finite-Difference Modeling of Natural Source Electromagnetic Diffusion

2020 ◽  
Vol 10 (8) ◽  
pp. 2744
Author(s):  
Yahui Xue ◽  
Jianxin Liu ◽  
Rong Liu ◽  
Zhuo Liu ◽  
Rongwen Guo ◽  
...  
Keyword(s):  
Finite Difference ◽  
Displacement Current ◽  
Low Frequencies ◽  
Static Approximation ◽  
Conduction Current ◽  
Quasi Static Approximation ◽  
Modeling Accuracy ◽  
Em Field ◽  
Displacement Currents ◽  
Earth Conductivity

For electromagnetic (EM) modeling based on the electric-field formulation at low frequencies, the quasi-static approximation (i.e., only the conduction current is considered and the displacement current is ignored) is commonly applied, and a small conductivity value for the air layer is chosen subjectively. Actually, in the air layer, due to the use of the small conductivity value, the quasi-static approximation is ubiquitously violated. However, the effect of the violation of the quasi-static approximation in the air on EM modeling is not well examined in the literature. In this paper, we investigate this issue by comparing the finite-difference modeling results from the calculation with the quasi-static approximation and those considering both the conduction and displacement currents. For the quasi-static approximation, the conductivity in the air is set to be different small values, and zero air conductivity is used for the modeling with both the conduction and displacement currents considered. Several simple models are designed to verify the numerical solution and study how the assigned conductivity for the air affects the modeling accuracy. One flat model and two models with topography are designed to examine the effect of the quasi-static approximation on the EM modeling results. For frequencies used in typical geophysical applications of EM diffusion, using the quasi-static approximation is able to produce accurate modeling results for models with typical earth conductivity. However, if the rough surface topography is considered, the use of the quasi-static approximation can reduce the EM modeling accuracy substantially at much lower frequencies (as low as several hundred Hz), which is probably due to the inaccurate description of EM waves in the air, and poses problems for applications based on direct EM field interpretation.

Time domain waveform inversion—A frequency domain view: How well we need to match waveforms?

1991 ◽  
Vol 81 (6) ◽  
pp. 2351-2370
Author(s):  
Zoltan A. Der ◽  
Robert H. Shumway ◽  
Michael R. Hirano
Keyword(s):  
Time Domain ◽  
High Frequency ◽  
Waveform Inversion ◽  
Quantitative Measure ◽  
Domain Modeling ◽  
Low Frequencies ◽  
Waveform Modeling ◽  
Time Domain Modeling ◽  
Frequency Components ◽  
The Time Domain

Abstract Waveform modeling in the time domain matches the various frequency components of seismic signals unevenly; the agreement is better at low frequencies and becomes progressively worse towards higher frequencies. The net effect of this kind of time-domain modeling is that the resolution in the spatial details of the source is less than optimal since the high-frequency components of the signal with their short wavelengths to resolve finer details do not fit the data. These problems are demonstrated by numerical simulations and by the reanalysis of some aspects of the El Golfo earthquake in using a new seismic imaging technique based on a generalization of an f-k algorithm. This procedure computes a statistic that can be used to derive confidence limits of the parameters sought in the inversion, thus providing a quantitative measure of the uncertainties in the results.

The Effect of Parameter Uncertainty on the Reliability of Pressure Accumulator Simulations

2002 ◽  
Author(s):  
Jyrki T. Kajaste ◽  
Heikki O. J. Kauranne ◽  
Asko U. Ellman ◽  
Matti T. Pietola
Keyword(s):  
Research Work ◽  
Low Frequency ◽  
Future Research ◽  
Hydraulic Fluid ◽  
Domain Modeling ◽  
Nitrogen Gas ◽  
Fundamental Parameters ◽  
Charge Pressure ◽  
Time Domain Modeling ◽  
Operation Pressure

The aim of this study is to demonstrate how the various parameters and the uncertainty associated with them affect the simulation results of a pressure accumulator. The parameters to be studied are related mainly to the pre-charging procedure of a membrane accumulator and cover the constants for the pressure and temperature of the nitrogen gas and the efficient volume of accumulator. These parameters are included in the non-linear model which is suited especially for large amplitude and low frequency transients. The background of the work is related to the fact that simulation is already an important tool in product development work. To be able to design the control of the system and predict the performance of it an estimate of the accuracy of the calculations is needed. The usability of simulation is determined by the fact how reliable the information is. To gain full benefit of simulation more attention has to be paid to the validity of the models, the accuracy of the parameter values needed in the models and the sensitivity of these parameters. The most sensitive parameters have to be recognized and paid special attention to the accuracy of the values given to them. Also the changes of these values in time due to wear or other modification in the system have to be noticed. Numerous factors have an influence on the accumulator operation. The most important of these are the ratio of the operation pressure to the pre-charge pressure, the amplitude of the flow rate disturbances, the temperature of the hydraulic fluid and the gas, the viscosity of the hydraulic fluid, the thermodynamic process of the nitrogen gas in the accumulator and the changes in the speed of sound. Also the mounting of the accumulator, the fittings used and the connecting pipes may have a significant role in the dynamics of an accumulator. The methods used in the study include measurements in time domain, modeling, simulations, and analytical work. The accumulator dynamics may alter due to remarkable changes in operating points like pressure levels. These are possible because of large amplitudes of flow rates particularly at the low frequency area where the presented study is focused on. The results include model analysis and information of the importance of the most fundamental parameters of the models and suggestions for future research work.

3D Laplace-domain waveform inversion using a low-frequency time-domain modeling algorithm

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. R1-R13 ◽  
Author(s):  
Wansoo Ha ◽  
Seung-Goo Kang ◽  
Changsoo Shin
Keyword(s):  
Time Domain ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Domain Modeling ◽  
Laplace Domain ◽  
Long Wavelength ◽  
Velocity Models ◽  
Time Domain Modeling ◽  
The Time Domain ◽  
Domain Inversion

We have developed a Laplace-domain full-waveform inversion technique based on a time-domain finite-difference modeling algorithm for efficient 3D inversions. Theoretically, the Laplace-domain Green’s function multiplied by a constant can be obtained regardless of the frequency content in the time-domain source wavelet. Therefore, we can use low-frequency sources and large grids for efficient modeling in the time domain. We Laplace-transform time-domain seismograms to the Laplace domain and calculate the residuals in the Laplace domain. Then, we back-propagate the Laplace-domain residuals in the time domain using a predefined time-domain source wavelet with the amplitude of the residuals. The back-propagated wavefields are transformed to the Laplace domain again to update the velocity model. The inversion results are long-wavelength velocity models on large grids similar to those obtained by the original approach based on Laplace-domain modeling. Inversion examples with 2D Gulf of Mexico field data revealed that the method yielded long-wavelength velocity models comparable with the results of the original Laplace-domain inversion methods. A 3D SEG/EAGE salt model example revealed that the 3D Laplace-domain inversion based on time-domain modeling method can be more efficient than the inversion based on Laplace-domain modeling using an iterative linear system solver.

scholarly journals Earless toads sense low frequencies but miss the high notes

2017 ◽  
Vol 284 (1864) ◽  
pp. 20171670 ◽  
Author(s):  
Molly C. Womack ◽  
Jakob Christensen-Dalsgaard ◽  
Luis A. Coloma ◽  
Juan C. Chaparro ◽  
Kim L. Hoke
Keyword(s):  
High Frequency ◽  
Species Differences ◽  
Low Frequency ◽  
Auditory Brainstem ◽  
Low Frequencies ◽  
Hearing Sensitivity ◽  
Sensory Pathways ◽  
Airborne Sound ◽  
Vibrational Sensitivity ◽  
Species Specific

Sensory losses or reductions are frequently attributed to relaxed selection. However, anuran species have lost tympanic middle ears many times, despite anurans' use of acoustic communication and the benefit of middle ears for hearing airborne sound. Here we determine whether pre-existing alternative sensory pathways enable anurans lacking tympanic middle ears (termed earless anurans) to hear airborne sound as well as eared species or to better sense vibrations in the environment. We used auditory brainstem recordings to compare hearing and vibrational sensitivity among 10 species (six eared, four earless) within the Neotropical true toad family (Bufonidae). We found that species lacking middle ears are less sensitive to high-frequency sounds, however, low-frequency hearing and vibrational sensitivity are equivalent between eared and earless species. Furthermore, extratympanic hearing sensitivity varies among earless species, highlighting potential species differences in extratympanic hearing mechanisms. We argue that ancestral bufonids may have sufficient extratympanic hearing and vibrational sensitivity such that earless lineages tolerated the loss of high frequency hearing sensitivity by adopting species-specific behavioural strategies to detect conspecifics, predators and prey.

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