Tarek Habashy - Academia.edu (original) (raw)

Papers by Tarek Habashy

67th EAGE Conference & Exhibition, 2005

Numerical simulation of wave propagation in heterogeneous medium provides a fundamental tool in m... more Numerical simulation of wave propagation in heterogeneous medium provides a fundamental tool in many inverse scattering problems. Although real data are acquired in three-dimensional (3D) world, we can still apply some approximation to simplify the model and to accelerate the computation. For example, when the data are acquired along a straight line, they are mainly sensitive to the formation in the vertical plane of the acquisition line. Therefore, we can use a two-dimensional (2D) model as an approximation while maintaining the 3D acquisition layout. This defines the settings of the two-and-a-half dimensional (2.5D) modeling schemes. Here we study a two-and-a-half dimensional (2.5D) finite-difference algorithm to model elastic wave propagation in heterogeneous media. In 2.5D problems, it is assumed that the elastic properties of models are invariant along a certain direction. Therefore, we can convert the three-dimensional (3D) problem into a set of two-dimensional (2D) problems in the spectral domain. The 3D solutions are then obtained by applying a numerical integration in the spectral domain. Usually the quadrature points used in this spectral-domain integration are sampled from the real axis in the spectral domain. However, because of the oscillating nature of the integrand, the convergence of this quadrature can be very slow especially at high frequencies. In this work, we apply the near-optimal quadrature scheme to the spectral integration. This is equivalent to transform the contour of integration from the real axis into a path in the complex plane and near-optimal quadrature is computed along the path numerically. Numerical studies show more than ten times of reduction in the number of quadrature points compared with sampling along the real axis in the spectral domain. This scheme alleviates the bottleneck of computing speed in the 2.5D elastic wave modeling. Furthermore, it can improve the computational efficiency of 2.5D elastic full waveform inversion algorithms. This technique can also be applied to solve 2.5D electromagnetic problems.

71st EAGE Conference and Exhibition incorporating SPE EUROPEC 2009, 2009

This paper includes a twofold result for the Nonlinear Conjugate Gradient (NCG) method, in large ... more This paper includes a twofold result for the Nonlinear Conjugate Gradient (NCG) method, in large scale unconstrained optimization. First we consider a theoretical analysis, where preconditioning is embedded in a strong convergence framework of an NCG method from the literature. Mild conditions to be satisfied by the preconditioners are defined, in order to preserve NCG convergence. As a second task, we also detail the use of novel matrix-free preconditioners for NCG. Our proposals are based on quasi-Newton updates, and either satisfy the secant equation or a secant-like condition at some of the previous iterates. We show that, in some sense, the preconditioners we propose also approximate the inverse of the Hessian matrix. In particular, the structures of our preconditioners depend on lowrank updates used, along with different choices of specific parameters. The low-rank updates are obtained as by-product of NCG iterations. The results of an extended numerical experience using large scale CUTEst problems is reported, showing that our preconditioners can considerably improve the performance of NCG methods.

Geophysics, Sep 1, 2016

We have developed a deterministic multiphysics joint inversion approach integrating seismic, elec... more We have developed a deterministic multiphysics joint inversion approach integrating seismic, electromagnetic (EM), and production data to map relevant reservoir properties, such as permeability and porosity, and the time evolution of the flooding front movement, i.e., saturation changes with time. These measurements are complementary in terms of their sensitivity to individual reservoir properties and their coverage of reservoir volumes. As a consequence, integration reduces ambiguities in the interpretation. In the workflow, a reservoir model is first built based on prior information. The production data are simulated by evolving the model in time based on the known well-control strategy. Simultaneously, the temporal and spatial distribution of fluid properties, such as saturation, salt concentration, density, and pressure are also obtained from the forward modeling. These properties, together with in situ rock properties, are transformed to formation resistivity and elastic properties using prescribed petrophysical relationships, such as Archie’s law and effective medium rock-physics models. From the transformation results, synthetic EM and full-waveform seismic data can be subsequently simulated. A Gauss-Newton optimization scheme is used to iteratively update the reservoir permeability and porosity fields until the mismatch between the synthetic data and the observed data becomes less than a predefined threshold. This inverse problem is usually highly underdetermined; hence, it is necessary to bring in prior information to further constrain the inversion. Different regularization approaches are investigated to facilitate incorporation of prior information into the joint inversion algorithm.

Geophysics, Sep 1, 2003

We analyze and compare the computational requirements and dispersion relationships, for the Lebed... more We analyze and compare the computational requirements and dispersion relationships, for the Lebedev (LBG) and rotated staggered grids (RSG) for anisotropic,elastic finite-difference calculations. Comparing the computational costs of these two methods for equivalent dispersion errors, we conclude that the Lebedev grid is preferred. The RSG requires at least 20% more memory per volume unit for storing the field variables, and twice as many floating point operations per time-volume unit. The LBG has the added advantage that for models with common material symmetries, it can be decomposed into uncoupled subgrids, and only one of these grids must be stored. This has important implications for applications such as elastic reverse-time migration and full-waveform inversion.

IEEE Transactions on Antennas and Propagation, 2016

In this communication, we apply the variable projection method to calibrate measured data for ele... more In this communication, we apply the variable projection method to calibrate measured data for electromagnetic (EM) data inversion. In the calibration process, we need to determine the amplitude and phase of the sources so that the simulated data can match the measured data. These data are difficult to measure due to the casing effect from metallic well pipes. Previous work usually defines the source amplitude and phase as unknowns. They are either computed before or inverted simultaneously during the inversion process. Using the variable projection method, we transform these unknowns into a least-square representation of measured and simulate data. This way we avoid these unknowns in the inversion process. Therefore, this method shows a better computational efficiency. Moreover, it improves the robustness of the inversion especially for gradient methods such as the nonlinear conjugate gradient method. We have incorporated this scheme into the two-and-half-dimensional EM data inversion algorithm and it works effectively in reconstructing the conductivity distribution.

We present an approach for estimating in-situ relative permeability and capillary pressure throug... more We present an approach for estimating in-situ relative permeability and capillary pressure through the joint inversion of array resistivity logging and formation test data. Considering a scenario of drilling a vertical well into an oil-bearing formation with water-based mud, the mud-filtrate invasion process can be regarded as a controlled experiment under reservoir conditions. Array resistivity logging can sense the formation resistivity perturbed by the two-phase flow invasion. Formation testing with fluid sampling can also provide information on the radially varying saturation and the associated changes in mobility, as well as information on the effect of capillary pressure. A facies-based workflow is developed to invert for the relative permeability and capillary pressure from the abovementioned two data sets. The inversion strategy is adjustable based on a sensitivity analysis as well as on the data available and the operational sequence of collecting the data. A hybrid inversion framework combining deterministic and stochastic optimization approaches is developed for the inversion of the data.

AGU Spring Meeting Abstracts, May 1, 2005

We consider the problem of computing the electromagnetic field in 3D anisotropic media for electr... more We consider the problem of computing the electromagnetic field in 3D anisotropic media for electromagnetic logging applications. The proposed finite-difference scheme for Maxwell equations has the following new features: coercivity, i.e., the complete discrete analogy of all continuous equations in every grid cell; a special conductivity averaging that does not require the grid to be small compared to layering or

We present a model-based inversion scheme to reconstruct 3D targets from microwave measured data.... more We present a model-based inversion scheme to reconstruct 3D targets from microwave measured data. In this scheme, the inversion domain is partitioned into sub-domains based on a priori information. Every subdomain is described by its geometrical shape and material properties. These parameters are reconstructed during the inversion process so that the simulated response matches the measured data. In this scheme, we apply radial basis functions to represent a surface. This is very suitable for inversion because we avoid the difficulties in tracking the connecting information among points on surfaces. As a complementary algorithm to the typical pixel-based inversion algorithms, the model-based inversion algorithm employs much less unknowns by only inverting the parameters that determine the shape and material properties of the targets. The model-based inversion algorithm can also help to reduce the non-uniqueness in the inversion process. Numerical examples show that it can reconstruct 3D targets with good accuracy and efficiency.

All Days, Mar 26, 2013

We present a model compression scheme for improving the efficiency of the regularized Gauss-Newto... more We present a model compression scheme for improving the efficiency of the regularized Gauss-Newton inversion algorithm for marine controlled-source electromagnetic applications. In this scheme the unknown model parameters (the resistivity distribution) are represented in terms of a basis such as Fourier, cosine, or wavelet. By applying a proper truncation criterion, the model may then be approximated by a reduced number of basis functions, which is usually much less than the number of the model parameters. Furthermore, since the controlled-source electromagnetic measurements have low-resolution, we will show that for inversion it is sufficient to only keep the low-spatial frequency part of the image. This model compression scheme accelerates the computational time as well as reduces the memory usage of the Gauss-Newton method. For demonstration purposes, we show both synthetic and field data inversions. The results show that we are able to significantly reduce the algorithm computational complexity without compromising the quality of the inverted models.

An essential objective of collecting measurements in the oil and gas industry is to detect, locat... more An essential objective of collecting measurements in the oil and gas industry is to detect, locate and quantify the amount of oil and gas in the Earth subsurface. Electromagnetic measurements either at DC, induction, propagation, and dielectric frequencies play a central role because electromagnetic properties of hydrocarbon and water are very different. These electromagnetic measurements can be collected either from a single borehole (e.g., laterolog, induction logging, electromagnetic geosteering, and dielectric logging), multi-boreholes (e.g., cross-well electromagnetic, surface-to-borehole electromagnetic), or at surface (e.g., magnetotelluric, controlled-source electromagnetic). The process to convert electromagnetic measurements into electromagnetic property (e.g., resistivity/conductivity and permittivity) map of the subsurface is an ill-posed problem. Furthermore, due to the substantial differences in electromagnetic properties of Earth subsurface especially hydrocarbon and water, the inverse problem can only be properly solved using a full nonlinear inversion algorithm. In addition the number of data points can be very limited, hence making the ill-posed problem more severe.

Geophysics, Jul 1, 2016

We have developed a 2.5D finite-difference algorithm to model the elastic wave propagation in het... more We have developed a 2.5D finite-difference algorithm to model the elastic wave propagation in heterogeneous media. In 2.5D problems, it is assumed that the elastic properties of models are invariant along a certain direction. Therefore, we can convert the 3D problem into a set of 2D problems in the spectral domain. The 3D solutions are then obtained by applying a numerical integration in the spectral domain. Usually, the quadrature points used in the numerical integration scheme are sampled from the real axis in the spectral domain. The convergence of this quadrature can be very slow especially at high frequencies. We have applied the optimal quadrature scheme for the spectral integration. This is equivalent to transforming the contour of integration from the real axis into a path in the complex plane. Our numerical studies have indicated more than 10 times of reduction in the number of quadrature points compared with sampling along the real axis in the spectral domain. This scheme alleviates the bottleneck of computing speed in the 2.5D elastic wave modeling. Furthermore, it can improve the computational efficiency of 2.5D elastic full-waveform inversion algorithms.

Petrophysics, Aug 1, 2013

ABSTRACT A workflow is developed for the interpretation of logging-while-drilling density images ... more ABSTRACT A workflow is developed for the interpretation of logging-while-drilling density images in high-angle and horizontal wells. The key component of the workflow is 3D parametric inversion using a robust Gauss-Newton optimization engine and a new fast-forward model based on second-order 3D sensitivity functions. The parametric model used for interpretation includes a 1D multilayer dipping formation, mud properties, 3D borehole geometry, and 3D well trajectory. Lateral (2D) variations in formation and borehole parameters are captured by defining the models in discrete trajectory segments using an adaptive segmentation based on the local relative dip. Measurement sensitivities are used to design a flexible and robust inversion-based workflow for determining optimum parameter values from all the available measurements. A sliding window is used to enforce consistency of models between adjacent segments. The result of the inversion is the accurate layer thicknesses, shoulder-bed-corrected layer densities, formation dip, and azimuth in each segment. The inversion also produces a borehole-corrected formation density image and a robust caliper that takes into account the layered formation as background. The workflow is especially tuned for scenarios with wellbore trajectory nearly parallel to layer boundaries, where ambiguity in interpretation is increased because of the difficulty in determining dip, lateral changes in layer properties, and influence of standoff and nearby noncrossed boundaries. The workflow is validated on synthetic thin-layer models with variable dip for both high-angle and near parallel scenarios. Several field datasets are successfully processed using the workflow. Inversion-derived formation-density profile and borehole caliper are shown to be more accurate than results from conventional processing.

We introduce an approach for simultaneously retrieving multiple reservoir parameters such as perm... more We introduce an approach for simultaneously retrieving multiple reservoir parameters such as permeability and porosity through joint inversion of seismic, electromagnetic, and production data. Sensitivities of those measurements with respect to different reservoir parameters are complementary, rationalizing the theoretical basis for this multi-physics joint inversion approach. In the scenario under study, production data have good sensitivity to both permeability and porosity, but only in the vicinity of wells; seismic data are more sensitive to porosity, while electromagnetic data are primarily sensitive to saturation which is a function of permeability and porosity in the context of a dynamic reservoir model. Both seismic and electromagnetic data provide large coverage within the reservoir. Therefore, it is possible to simultaneously recover permeability and porosity from the joint inversion of these measurements. However, to achieve high-quality results, prior information, such as the relationship between permeability and porosity distributions, needs to be taken into account. Different regularization approaches are investigated to facilitate incorporation of prior information into the joint inversion algorithm.