Empirical Transfer Function Research Articles

Simulation of multiphase flow in fractured reservoirs using a fracture-only model with transfer functions

We present a fracture-only reservoir simulator for multiphase flow: the fracture geometry is modeled explicitly, while fluid movement between fracture and matrix is accommodated using empirical transfer functions. This is a hybrid between discrete fracture discrete matrix modeling where both the fracture and matrix are gridded and dual-porosity or dual-permeability simulation where both fracture and matrix continua are upscaled. The advantage of this approach is that the complex fracture geometry that controls the main flow paths is retained. The use of transfer functions, however, simplifies meshing and makes the simulation method considerably more efficient than discrete fracture discrete matrix models. The transfer functions accommodate capillary- and gravity-mediated flow between fracture and matrix and have been shown to be accurate for simple fracture geometries, capturing both the early- and late-time average behavior. We verify our simulator by comparing its predictions with simulation results where the fracture and matrix are explicitly modeled. We then show the utility of the approach by simulating multiphase flow in a geologically realistic fracture network. Waterflooding runs reveal the fraction of the fracture–matrix interface area that is infiltrated by water so that matrix imbibition can occur. The evolving fraction of the fracture–matrix interface area turns out to be an important characteristic of any particular fracture system to be used as a scaling parameter for capillary driven fracture–matrix transfer.

Seasonal cycle as template for climate variability on astronomical timescales

We propose a new concept for insolation‐driven temperature variability on orbital timescales. It relies on the modern relationship between insolation and temperature throughout the year. The method consists of (1) estimating empirical transfer functions between daily insolation and daily temperature and (2) applying these transfer functions on the long‐term insolation to model the late Quaternary temperature evolution. On the basis of the observed insolation‐temperature relationship, different temperature response regimes across the Earth are identified. Linear relationships dominate extratropical land areas whereas in midlatitude oceans, the seasonally varying mixed layer depth renders the temperature more sensitive to summer than to winter insolation. The temperature in monsoon regions and regions of seasonal sea ice cover also shows a seasonally varying response to insolation. These transfer functions characterize the shape of the seasonal cycle in temperature and influence the temperature evolution on orbital timescales by rectifying the insolation signal. On the basis of our seasonal template model, we estimate the temperature evolution of the last 750,000 years. The model largely reproduces the Holocene temperature trends as simulated by a coupled climate model. In the frequency domain, significant temperature variability in the eccentricity and semiprecession frequency band in the tropics is found. Midlatitudes are dominated by precession, and high latitudes are dominated by obliquity. Further, it is found that the expected frequency response highly depends on the location. Our local time‐independent approach complements the global Milankovitch hypothesis (climate variations are driven by northern summer insolation) in explaining observed climate variability and potentially offers new insights in interpreting paleoclimate records.

Impediments to Predicting Site Response: Seismic Property Estimation and Modeling Simplifications

Abstract We compare estimates of the empirical transfer function (ETF) to the plane SH -wave theoretical transfer function (TTF) within a laterally constant medium for invasive and noninvasive estimates of the seismic shear-wave slownesses at 13 Kiban-Kyoshin network stations throughout Japan. The difference between the ETF and either of the TTFs is substantially larger than the difference between the two TTFs computed from different estimates of the seismic properties. We show that the plane SH -wave TTF through a laterally homogeneous medium at vertical incidence inadequately models observed amplifications at most sites for both slowness estimates, obtained via downhole measurements and the spectral analysis of surface waves. Strategies to improve the predictions can be separated into two broad categories: improving the measurement of soil properties and improving the theory that maps the 1D soil profile onto spectral amplification. Using an example site where the 1D plane SH -wave formulation poorly predicts the ETF, we find a more satisfactory fit to the ETF by modeling the full wavefield and incorporating spatially correlated variability of the seismic properties. We conclude that our ability to model the observed site response transfer function is limited largely by the assumptions of the theoretical formulation rather than the uncertainty of the soil property estimates.

Spatial non-stationarity and scale-dependency of prediction accuracy in the remote estimation of LAI over a tropical rainforest in Sulawesi, Indonesia

The technique of Geographically Weighted Regression (GWR) was used for estimation of Leaf Area Index (LAI) from remote sensing-based multi-spectral vegetation indices (VI) such as Normalized Difference Vegetation Index (NDVI), the mid-infrared corrected Normalized Difference Vegetation Index (NDVIc), Simple Ratio (SR), Soil-Adjusted Vegetation Index (SAVI) and Reduced Simple Ratio (RSR) in a region of equatorial rainforest in Central Sulavesi, Indonesia. The linear regressions between NDVI, NDVIc, SR, SAVI and RSR as explanatory variables and ground measurements of LAI at 166 plots as a dependent variable were produced using common modelling approach — Ordinary Least Squares (OLS) regression fitted to all data points, as well as GWR. Accuracy and precision statistics indicate that the GWR method made significantly better predictions of LAI in all simulations than OLS did. The relationships between LAI and the explanatory variables were found to be significantly spatially variable and scale-dependent. GWR has the potential to reveal local patterns in the spatial distribution of parameter estimates, it demonstrated sensitivity of the model's accuracy and performance to scale variation. The GWR approach enables finding the most appropriate scale for data analysis. This scale was different for each VI. The results suggest that spatial non-stationarity and scale-dependency in the relationship between LAI and remote sensing data has important implications for estimations of LAI based on empirical transfer functions.

RESPUESTA SÍSMICA EN EL LAGO DE TEXCOCO. RESULTADOS A PARTIR DE REGISTROS DE MOVIMIENTOS FUERTES

En 1995 se instaló un arreglo acelerométrico constituido por seis estaciones en superficie, que formaron dos triángulos con aperturas de 30 y 400 m y un arreglo vertical con instrumentos en cinco profundidades, que alcanzaron los 40 m. La base de datos de este arreglo consta de ocho eventos de movimientos fuertes (5.9 < M < 7.9) que analizamos para obtener la respuesta sísmica, el modelo de velocidades y el espectro de respuesta de sitio. Los resultados de este estudio muestran que la respuesta de sitio está caracterizada por la frecuencia fundamental en 0.37 Hz. El análisis de los registros en pozo permitió obtener un modelo de velocidades que está constituido por dos capas, con factores de atenuación Q distintos para cada una; la amplificación dinámica, debida a las propiedades físicas de las arcillas lacustres, domina la respuesta de sitio. Finalmente, el espectro de respuesta muestra que las seudoaceleraciones máximas en el sitio se encuentran en dos intervalos de periodo: entre 0 y 1 s y entre 2 y 3 s, con ordenadas espectrales de 0.6 g y 0.74 g, respectivamente.

Polarisation basis transformation of weather radar measurements in the power domain

Abstract. Polarisation diversity in radar remote sensing proved to be very successful in a variety of applications. Hydrometeors as raindrops or ice crystals are anisotropic radar targets giving rise to the use of polarisation diversity in weather radars. One advanced polarimetric weather radar is DLR's POLDIRAD in Oberpfaffenhofen. The huge data archive of this radar consists mainly of power measurements at diverse polarisation bases. This study investigates the possibility to apply the polarisation basis transformation directly on power measurements. As a result, empirical transfer functions for the change of the polarisation basis of radar reflectivities are derived. To check their validity they are applied to appropriate polarimetric radar data from the POLDIRAD.

Determination of an Empirical Transfer Function of a Solid Oxide Fuel Cell Gas Turbine Hybrid System Via Frequency Response Analysis

This paper presents the study of the effect variations in the heat effluence from a solid oxide fuel cell (SOFC) has on a gas turbine hybrid configuration. The SOFC is simulated through hardware at the U.S. Department of Energy, National Energy Technology Laboratory (NETL). The gas turbine, compressor, recuperative heat exchanger, and other balance of plant components are represented by actual hardware in the Hybrid Performance Test Facility at NETL. Fuel cell heat exhaust is represented by a combustor that is activated by a fuel cell model that computes energy release for various sensed system states System structure is derived by means of frequency response data generated by the sinusoidal oscillation of the combustor fuel valve over a range of frequencies covering three orders of magnitude. System delay and order are obtained from Bode plots of the magnitude and phase relationships between input and output parameters. Transfer functions for mass flow, temperature, pressure, and other states of interest are derived as a function of fuel valve flow, representative of fuel cell thermal effluent. The Bode plots can validate existing analytical transfer functions, provide steady state error detection, give a stability margin criterion for the fuel valve input, estimate system bandwidth, identify any nonminimum phase system behavior, pinpoint unstable frequencies, and serve as an element of a piecewise transfer function in the development of an overall transfer function matrix covering all system inputs and outputs of interest. Further loop shaping techniques and state space representation can be applied to this matrix in a multivariate control algorithm.

Accuracy assessment of fraction of vegetation cover and leaf area index estimates from pragmatic methods in a cropland area

The fraction of vegetation cover (FVC) and the leaf area index (LAI) are important parameters for many agronomic, ecological and meteorological applications. Several in‐situ and remote sensing techniques for estimating FVC and LAI have been developed in recent years. In this paper, the uncertainty of in‐situ FVC and LAI measurements was evaluated by comparing estimates from LAI‐2000 and digital hemispherical photography (DHP). The accuracy achieved with a spectral mixture analysis algorithm and two vegetation indices‐based methods was assessed using atmospherically corrected Landsat Thematic Mapper (TM) data over the Barrax cropland area where the European Space Agency (ESA) SENtinel‐2 and FLuorescence EXperiment (SEN2FLEX) field campaign was carried out in July 2005. The results indicate that LAI‐2000 and DHP performances are comparable, with uncertainties of 5% for FVC and 15% for effective LAI. The selected remote sensing methods are shown to be consistent, with a notable overall accuracy (root mean square error, RMSE) of 0.07 (10% in relative terms) for FVC and 0.8 (30%) for LAI. Similar bounds were found on upscaling in‐situ measurements with empirical transfer functions (TFs). These results suggest that the pragmatic methods considered applied at high resolution with minimum calibration data could be useful for mapping FVC and LAI in the study area, reducing in‐situ labour‐intensive characterization necessities for validation studies.

Transfer function coefficients for time varying coupled heat transfers in vertically heated hollow concrete bricks

This paper describes a two step numerical procedure to determinate empirical transfer function coefficients (TFCs) for vertically heated hollow concrete bricks. For such systems TFCs cannot be generated using the analytical techniques available in the literature such as the z-transfer function method or the space state representation method because of the nonlinear local character of the heat transfer by natural convection and radiation in the air cells of the hollow concrete bricks. The first step of the procedure consists in predicting coupled heat transfer by conduction, convection, and radiation in realistic time varying conditions using a detailed numerical simulation. In the second step, the results of the simulation (the time-varying heat fluxes at the hollow brick surfaces) are used to obtain empirical transfer function coefficients using an identification technique. Transfer function coefficients are generated for three different types of hollow concrete bricks mostly used in practice. It is shown that the empirical transfer function coefficients permit fast and accurate prediction of heat transfer for thermal excitations that differ markedly from those used to generate these coefficients without solving the complex system of equations governing the coupled heat transfer mechanisms.

Modeling and validation of hitch loading effects on tractor yaw dynamics

This paper develops a yaw dynamic model for a farm tractor with a hitched implement, which can be used to understand the effect of tractor handling characteristics for design applications and for new automated steering control systems. Dynamic equations which use a tire-like model to capture the characteristics of the implement are found to adequately describe the tractor implement yaw dynamics. This model is termed the “3-wheeled” Bicycle Model since it uses an additional wheel (from the traditional bicycle model used to capture lateral dynamics of passenger vehicles) to account for the implement forces. The model only includes effects of lateral forces as it neglects differential longitudinal or draft forces between inner and outer sides of the vehicle. Experiments are taken to verify the hitch model using a three-dimensional force dynamometer. This data shows the implement forces are indeed proportional to lateral velocity and that differential draft forces can be neglected as derived in the “3-wheeled” Bicycle Model. Steady state and dynamic steering data are used for implements at varying depths and speeds to quantify the variation in the hitch loading. The dynamic data is used to form empirical transfer function estimates (ETFEs) of the implements and depths in order to determine the coefficients used in the “3-wheeled” Bicycle Model. Changes in a single parameter, called the hitch cornering stiffness, can capture the various implement configurations. Finally, a model that includes front wheel drive forces is derived. Experiments are taken which provide a preliminary look into the effect of four-wheel drive traction forces, and show a difference with two-wheel versus four-wheel drive, on the yaw dynamics of a tractor with the hitched implement.

Empirical transfer functions: Application to determination of outermost core velocity structure using SmKS phases

SmKS waves provide good resolution of outer‐core velocity structure, but are affected by heterogeneity in the D″ region. We have developed an Empirical Transfer Function (ETF) technique that transforms a reference pulse (here, SmKS) into a target waveform (SKKS) by: (1) time‐windowing the respective pulses, (2) applying Wiener deconvolution, and (3) convolving the output with a Gaussian waveform. Common source and path effects are implicitly removed by this process. We combine ETFs from 446 broadband seismograms to produce a global stack, from which S3KS‐SKKS differential time can be measured accurately. As a result of stacking, the scatter in our measurements (0.43 s) is much less than the 1.29 s scatter in previous compilations. Although our data do not uniquely constrain outermost core velocities, we show that the fit of most standard models can be improved by perturbing the outermost core velocity. Our best‐fitting model is formed using IASP91 with PREM‐like velocity at the top of the core.

Choice of Weighting for Averaged Nonparametric Transfer Function Estimates

The statistical properties of nonparametric transfer function estimates formed via the weighted sum of empirical transfer function estimates are considered. In the case that the system input is considered deterministic, it is shown that the weighting corresponding to the classical averaged periodogram estimate is optimal. A similar asymptotic result is derived for the case where the input is considered stochastic.

On the efficiency of barometric arrays to improve the reduction of atmospheric effects on gravity data

Air pressure reduction in local gravity measurements is usually done by means of an empirical transfer function (barometric admittance) between pressure and gravity both measured at the same site. In the local zone (<50 km) pressure can change rapidly, but is spatially coherent, so pressure observations at the gravity site are sufficient except when a front is passing through the local zone. When large horizontal gradients affect the gravity station, the local zone becomes a critical area for which it may be useful to have more detailed pressure data. One way to model the local atmosphere is to use an array of sensors located around the gravity station. We model the barometric local effect on gravity data using superconducting gravity (SG) data, collected in Strasbourg and barometric records in five sites around the SG station at distances ranging between 10 and 60 km. Six months of gravity and air pressure records are analysed both in the time and frequency domains. The admittance factors for each station are computed by means of different numerical analyses and their time and frequency behaviour investigated. The results demonstrate that in normal weather conditions a single barometer can be enough to account for the pressure effect originating in the local zone and the pressure data from an array are redundant. The use of the barometric array pressure data is found to improve the reduction of the air pressure effects in only one time span among those selected. The improvement is significant at low frequency, while an artificial increase in the residual gravity derives from the array reduction in the high-frequency band (>3.0 cycles/day). The atmospheric reduction from the barometric array is also compared to global loading computations from ECMWF-4Dvar surface pressure data, having a sampling rate of 3 h and a spatial resolution of 0.5°. We also tested a hybrid method based on a spline interpolation of joint ECMWF-4Dvar surface pressure data and local observations collected on the barometric array. The findings are discussed in light of the main features (dimension, geometry and instrumental accuracy) of the barometric array.

Identifying and removing noise from the Monterey ocean bottom broadband seismic station (MOBB) data

When compared to quiet land stations, the very broadband Monterey ocean bottom seismic station (MOBB) shows increased long‐period background as well as signal‐generated noise. Both sources of noise are unavoidable in shallow ocean bottom installations, and postprocessing is required to remove them from seismic observations. The long‐period background noise observed for periods longer than 20 s is mainly due to infragravity waves and ocean currents. The shorter‐period signal‐generated noise, on the other hand, is due to reverberations of the seismic waves in the shallow sedimentary layers as well as in the water layer. We first present the steps that were taken prior to and during the instrument deployment to minimize instrument generated noise as well as to avoid noise due to water flow around the instrument. We then present results from two postprocessing methods that can be used to remove the long‐period background noise, which both utilize the ocean bottom pressure signal locally recorded on a differential pressure gauge (DPG). One consists of subtracting the locally recorded ocean bottom pressure from the vertical seismic acceleration signal. In this case the frequency‐independent scale factor is linearly estimated from the data. The other one makes use of the transfer function between the vertical seismic and pressure signal to predict the vertical component deformation signal. The predicted signal is then removed from the vertical seismic data in either frequency or time domain. We also present two methods that can be used to remove the signal‐generated noise. One employs the empirical transfer function constructed from MOBB data and nearby land station data that do not show the signal‐generated noise. The other one uses a synthetic transfer function computed by modeling the response of shallow layers at the MOBB location. Using either of the two transfer functions, most of the signal‐generated noise can be removed from the MOBB data by deconvolution.

Simulation of seasonal precipitation and raindays over Greece: a statistical downscaling technique based on artificial neural networks (ANNs)

AbstractA statistical downscaling technique based on artificial neural network (ANN) was employed for the estimation of local changes on seasonal (winter, spring) precipitation and raindays for selected stations over Greece. Empirical transfer functions were derived between large‐scale predictors from the NCEP/NCAR reanalysis and local rainfall parameters. Two sets of predictors were used: (1) the circulation‐based 500 hPa and (2) its combination along with surface specific humidity and raw precipitation data (nonconventional predictor). The simulated time series were evaluated against observational data and the downscaling model was found efficient in generating winter and spring precipitation and raindays. The temporal evolution of the estimated variables was well captured, for both seasons. Generally, the use of the nonconventional predictors are attributed to the improvement of the simulated results. Subsequently, the present day and future changes on precipitation conditions were examined using large‐scale data from the atmospheric general circulation model HadAM3P to the statistical model. The downscaled climate change signal for both precipitation and raindays, partly for winter and especially for spring, is similar to the signal from the HadAM3P direct output: a decrease of the parameters is predicted over the study area. However, the amplitude of the changes was different. Copyright © 2006 Royal Meteorological Society

Definition of subsoil structure and preliminary ground response in Aigion city (Greece) using microtremor and earthquakes

An extensive campaign—including detailed geologic and geotechnical surveys both existing and news as well as noise measurements—was conducted along a cross-section in order to define both geometry and soil properties (mainly the shear wave velocity) of the main formations in Aigion city. Aigion city is located in the Gulf of Corinth, Greece, a highly seismic region of the Aegean Sea. The main objective of the accurate 2D soil model is its use in site response modeling and in the interpretation of observations from a vertical down-hole accelerograph array. This model revealed a complex geologic structure with a multi-faulted shear zone related to the Aigion fault. The defined subsurface structure offered the possibility for its correlation with estimated site effects, in terms of spectral ratios. Two different data sets, earthquakes recorded at down-hole accelerograph network and noise measurements at 17 sites, were used. To translate the empirical transfer functions with the geologic structure, the 1D estimates were also computed. All these results are consistent, indicating a satisfactory correlation between the soil model and preliminary site response.

Estimating the transfer function of the cantilever in atomic force microscopy: A system identification approach

Dynamic atomic force microscopy (AFM) offers many opportunities for the characterization and manipulation of matter on the nanometer scale with a high temporal resolution. The analysis of time-dependent forces is basic for a deeper understanding of phenomena such as friction, plastic deformation, and surface wetting. However, the dynamic characteristics of the force sensor used for such investigations are determined by various factors such as material and geometry of the cantilever, detection alignment, and the transfer characteristics of the detector. Thus, for a quantitative investigation of surface properties by dynamic AFM an appropriate system identification procedure is required, characterizing the force sensor beyond the usual parameters spring constant, quality factor, and detection sensitivity. Measurement of the transfer function provides such a characterization that fully accounts for the dynamic properties of the force sensor. Here, we demonstrate the estimation of the transfer function in a bandwidth of 1MHz from experimental data. To this end, we analyze the signal of the vibrations induced by snap-to-contact and snap-off-contact events. For the free cantilever, we determine both a parameter-free estimate [empirical transfer function estimate (ETFE)] and a parametric estimate of the transfer function. For the surface-coupled cantilever the ETFE is obtained. These identification procedures provide an intrinsic calibration as they dispense largely with a priori knowledge about the force sensor.

Simulation of counter-current imbibition in water-wet fractured reservoirs

Counter-current imbibition, where water spontaneously enters a water-wet rock while oil escapes by flowing in the opposite direction is a key recovery mechanism in fractured reservoirs. Fine grid, one- and two-dimensional simulations of counter-current imbibition are performed and the results are compared with experimental measurements in the literature. The experimental data are reproduced using two sets of relative permeabilities and capillary pressures. One set is derived from a counter-current experiment and one set is computed using pore-scale modelling. Two-dimensional simulations of water flow through a single high permeability fracture in contact with a lower permeability matrix are run. The results are compared with experimental measurements of fracture flow and matrix imbibition in the literature and with one-dimensional simulations that account for imbibition from fracture to matrix using an empirical transfer function. It is shown that with this transfer function the behavior of the two-dimensional displacement can be predicted using a one-dimensional model.

Acoustic time histories from vibrating surfaces of a diesel engine

An experiment on a diesel engine provides for validation of a method that retrieves source strength spectra, source strength time histories and sound pressure time histories of the engine’s complex partial sources. The method is based on empirical transfer function measurements and inverse matrix calculations briefly described in the article. Different simplifying source models were selected by comparison of calculated and measured auto spectra. The results show: (1) indication of time efficient measurements of source strength spectra, (2) the importance of correct source models in the case of separated source strength time histories, and (3) spectra of separated sound pressure time histories. Listening tests reported that it is possible to detect well differentiated sounds of the partial sources as a result of the method.

Streamline simulation of counter-current imbibition in naturally fractured reservoirs

Describing fluid transport in naturally fractured reservoirs entails additional challenge because of the complicated physics arising from matrix–fracture interactions. In this paper, the streamline-based simulation is generalized to describe fluid transport in naturally fractured reservoirs through a dual-media approach. The fractures and matrix are treated as separate continua that are connected through a transfer function, as in conventional finite difference simulators for modeling fractured systems. The transfer functions that describe fluid exchange between the fracture and matrix system can be implemented easily within the framework of the current single-porosity streamline models. In particular, the streamline time of flight concept is utilized to develop a general dual-porosity, dual-permeability system of equations for water injection in naturally fractured reservoirs. The saturations equations are solved using an operator splitting approach that involves ‘convection’ along streamline followed ‘matrix–fracture’ exchange calculations on the grid. The proposed formulation reduces to the commonly used dual-porosity model when the flow in the matrix is considered negligible. For modeling matrix–fracture interactions, two different transfer functions are examined: an empirical transfer function (ETF) and a conventional transfer function (CTF). The ETF allows for analytical solution of the saturation equation for dual porosity systems and is used to validate numerical implementation. Results obtained using the CTF are compared with a commercial finite-difference simulator (ECLIPSE) for waterflooding in five-spot and nine-spot patterns. The streamline approach shows close agreement in terms of recovery histories and saturation profiles with a marked reduction in numerical dispersion and grid orientation effects. Finally, an examination of the scaling behavior of the computation time indicates that the streamline approach is likely to result in significant savings for large-scale field applications.