Data Resolution Matrix Research Articles

Electromagnetic resolution—a CSEM study based on the Wisting oil field

SUMMARY We consider marine controlled source electromagnetic (CSEM) data and demonstrate that a typical CSEM survey is associated with significant data redundancy. Thus, it should be possible to obtain a high-quality inversion result by using only a subset of the original data. Moreover, in survey design, effort should be made to optimize the placement of the receivers. This study therefore investigates the challenges of data decimation and survey design in the case of repeated surveys by use of the data resolution matrix and model resolution matrix. A framework of analysis has been developed to efficiently use these quantities. The feasibility of the proposed approach is demonstrated using both synthetic data computed from an interpreted model of the Wisting oil field in the Barents Sea, as well as actual field data from the same oil field.

Data-resolution based optimal choice of minimum required measurements for image-guided diffuse optical tomography

Image-guided diffuse optical tomography has the advantage of reducing the total number of optical parameters being reconstructed to the number of distinct tissue types identified by the traditional imaging modality, converting the optical image-reconstruction problem from underdetermined in nature to overdetermined. In such cases, the minimum required measurements might be far less compared to those of the traditional diffuse optical imaging. An approach to choose these optimally based on a data-resolution matrix is proposed, and it is shown that such a choice does not compromise the reconstruction performance.

Data‐resolution based optimization of the data‐collection strategy for near infrared diffuse optical tomography

To optimize the data-collection strategy for diffuse optical tomography and to obtain a set of independent measurements among the total measurements using the model based data-resolution matrix characteristics. The data-resolution matrix is computed based on the sensitivity matrix and the regularization scheme used in the reconstruction procedure by matching the predicted data with the actual one. The diagonal values of data-resolution matrix show the importance of a particular measurement and the magnitude of off-diagonal entries shows the dependence among measurements. Based on the closeness of diagonal value magnitude to off-diagonal entries, the independent measurements choice is made. The reconstruction results obtained using all measurements were compared to the ones obtained using only independent measurements in both numerical and experimental phantom cases. The traditional singular value analysis was also performed to compare the results obtained using the proposed method. The results indicate that choosing only independent measurements based on data-resolution matrix characteristics for the image reconstruction does not compromise the reconstructed image quality significantly, in turn reduces the data-collection time associated with the procedure. When the same number of measurements (equivalent to independent ones) are chosen at random, the reconstruction results were having poor quality with major boundary artifacts. The number of independent measurements obtained using data-resolution matrix analysis is much higher compared to that obtained using the singular value analysis. The data-resolution matrix analysis is able to provide the high level of optimization needed for effective data-collection in diffuse optical imaging. The analysis itself is independent of noise characteristics in the data, resulting in an universal framework to characterize and optimize a given data-collection strategy.

Evaluation of Joint Inversion Algorithm with Logarithmic Treatment for Resistivity Log

The joint inversion of dual laterolog and dual-induction log was evaluated from the linear inversion theory. The generalized inversion method was used for the inverse calculation. A couple of parameters in the inversion algorithm were treated using logarithmic method. The abnormal states resulting from the logarithmic treatment on equations were analyzed. The effects of both the data-resolution matrix and model-resolution matrix on convergence of inversion process were discussed. It indicated that the logarithm treatment can not only weaken the abnormal state obviously, but also can reduce the spread of the data-resolution matrix. The improved inversion algorithm is efficient to enhance the stability and to improve the behaviors of convergence during the inversion process.

Data-resolution Matrix and Model-resolution Matrix for Rayleigh-wave Inversion Using a Damped Least-squares Method

Inversion of multimode surface-wave data is of increasing interest in the near-surface geophysics community. For a given near-surface geophysical problem, it is essential to understand how well the data, calculated according to a layered-earth model, might match the observed data. A data-resolution matrix is a function of the data kernel (determined by a geophysical model and a priori information applied to the problem), not the data. A data-resolution matrix of high-frequency (≥2 Hz) Rayleigh-wave phase velocities, therefore, offers a quantitative tool for designing field surveys and predicting the match between calculated and observed data. We employed a data-resolution matrix to select data that would be well predicted and we find that there are advantages of incorporating higher modes in inversion. The resulting discussion using the data-resolution matrix provides insight into the process of inverting Rayleigh-wave phase velocities with higher-mode data to estimate S-wave velocity structure. Discussion also suggested that each near-surface geophysical target can only be resolved using Rayleigh-wave phase velocities within specific frequency ranges, and higher-mode data are normally more accurately predicted than fundamental-mode data because of restrictions on the data kernel for the inversion system. We used synthetic and real-world examples to demonstrate that selected data with the data-resolution matrix can provide better inversion results and to explain with the data-resolution matrix why incorporating higher-mode data in inversion can provide better results. We also calculated model-resolution matrices in these examples to show the potential of increasing model resolution with selected surface-wave data.

Optimal Observations for Variational Data Assimilation

Abstract An important part of ocean state estimation is the design of an observing system that allows for the efficient study of climate related questions in the ocean. A solution to the design problem is presented here in terms of optimal observations that emerge as singular vectors of the modified data resolution matrix. The actual computation is feasible only for scalar quantities and in the limit of large observational errors. Identical twin experiments performed in the framework of a 1° North Atlantic primitive equation model demonstrate that such optimal observations, when applied to determining the heat transport across the Greenland–Scotland ridge, perform significantly better than traditional section data. On seasonal to interannual time scales, optimal observations are located primarily along the continental shelf and information about heat transport, wind stress, and stratification is being communicated through boundary waves and advective processes. On time scales of about 1 month, sea surface height observations appear to be more efficient in reconstructing the cross-ridge heat transport than hydrographic observations. Optimal observations also provide a tool for understanding changes of ocean state associated with anomalies of integral quantities such as meridional heat transport.

Channel selection methods for Infrared Atmospheric Sounding Interferometer radiances

AbstractAdvanced infrared sounders will provide thousands of radiance data at every observation location. The number of individual pieces of information is not usable in an operational numerical weather‐prediction context, and we have investigated the possibilities of choosing an ‘optimal’ subset of data. These issues have been addressed in the context of optimal linear estimation theory, using simulated Infrared Atmospheric Sounding Interferometer data. Several methods have been tried to select a set of the most useful channels for each individual atmospheric profile. These are two methods based on the data resolution matrix, one method based on the Jacobian matrix, and one iterative method selecting sequentially the channels with largest information content. The Jacobian method and the iterative method were found to be the most suitable for the problem. The iterative method was demonstrated to always produce the best results, but at a larger cost than the Jacobian method. To test the robustness of the iterative method, a variant has been tried. It consists in building a mean channel selection aimed at optimizing the results over the whole database, and then applying to each profile this ‘constant’ selection. Results show that this ‘constant’ iterative method is very promising, with results of intermediate quality between the ones obtained for the optimal iterative method and the Jacobian method. The practical advantage of this method for operational purposes is that the same set of channels can be used for various atmospheric profiles. Copyright © 2002 Royal Meteorological Society.

Solving Underdetermined Tracer Inverse Problems by Spatial Smoothing and Cross Validation

Tracer conservation equations may be inverted to determine the flow field and macroscopic diffusion coefficients from known tracer distributions. An underdetermined system leads to an infinite number of possible solutions. The solution that is selected is the one that is as smooth as possible while still reproducing the tracer observations. The procedure suggested here is to define a penalty function that balances solution smoothnness, based on spatial derivatives of the solution, against residuals in the conservation equations. The ratio of detail in the solution to equation error is controlled by one or more smoothing parameters, which will not usually be known prior to the inversion. A parameter estimation technique known as generalized cross-validation is used to determine the degree of smoothing based on optimizing the prediction of withheld information. The method is tested for the case of steady flow containing a range of spatial scales in a two-dimensional channel with a spatially varying diffusion coefficient. It is shown that the correct flow field and diffusivity may be reproduced relatively accurately from a knowledge of the distribution of two tracers for a variety of flow configurations. The impact on the solution of errors in the equations and errors in the tracer data is studied. It is found that relatively large (correlated) errors in the equations due to numerical truncation error have the same effect as relatively small random errors in the data. A useful qualitative diagnostic measure of the value of an inverse solution is introduced. It is a measure of the loss of independent information due to smoothing the solution and is related to the data resolution matrix of classical discrete inverse theory.