System and method for data inversion with phase unwrapping

A system and computer-implemented method for inverting data from an area of interest to determine physical properties of the area of interest is disclosed. The method includes transforming the data into a Fourier frequency domain to obtain frequency domain data wherein the frequency domain data includes an amplitude portion and a phase portion, performing phase unwrapping of the phase portion of the frequency domain data to generate an unwrapped phase portion, and inverting the unwrapped phase portion to determine the physical properties of the area of interest. The method may also extrapolate the phase. The data inverted may be, for example, seismic data or synthetic aperture radar data. The system includes a data source, a user interface, and a processor configured to execute computer modules designed to execute the method

Crosswell traveltime tomography in three dimensions

Conventional crosswell direct-arrival traveltime tomography solves for velocity in a 2-D slice of the subsurface joining two wells. Many 3-D aspects of real crosswell surveys, including well deviations and out-of-well-plane structure, are ignored in 2-D models. We present a 3-D approach to crosswell tomography that is capable of handling severe well deviations and multiple-profile datasets. Three-dimensional pixelized models would be even more seriously underdetermined than the pixelized models that have been used in 2-D tomography. We, therefore, employ a thinly layered, vertically discontinuous 3-D velocity model that greatly reduces the number of model parameters. The layers are separated by 2-D interfaces represented as 2-D Chebyshev polynomials that are determined using a priori structural information and remain fixed in the traveltime inversion. The velocity in each layer is also represented as a 2-D Chebyshev polynomial. Unlike pixelized models that provide limited vertical resolution and may be overparameterized horizontally, this 3-D model provides vertical resolution comparable to the scale of wireline logs, and reduces the degrees of freedom in the horizontal parameterization to the expected in-line and out-of-well-plane horizontal resolution available in crosswell traveltime data. Ray tracing for the nonlinear traveltime inversion is performed in three dimensions. The 3-D tomography problem is regularized using penalty constraints with a continuation strategy that allows us to extrapolate the velocity field to a 3-D region containing the 2-D crosswell profile. Although this velocity field cannot be expected to be accurate throughout the 3-D region, it is at least as accurate as 2-D tomograms near the well plane of each 2-D crosswell profile. Futhermore, multiple-profile crosswell data can be inverted simultaneously to resolve better the 3-D distribution of velocity near the profiles. Our velocity parameterization is quite different from pixelized models, so resolution properties will be different. Using wave-modeled synthetic data, we find that near horizontal raypaths have the largest mismatch between ray-traced traveltimes and traveltimes estimated from the data. In conventional tomography, horizontal raypaths are essential for high vertical resolution. With our model, however, the highest resolution and most accurate inversions are achieved by excluding raypaths that travel nearly parallel to the geologic layering. We perform this exclusion in both a static and model-based manner. We apply our 3-D method to a multiple-profile crosswell survey at the Cymric oil field in California, an area of very steep structural dips and significant well trajectory deviations. Results of this multiple-profile 3-D tomography correlate very well with the independently-processed single profile results, with the advantage of an improved tie at the common well

Removal of phosphate from water by a highly selective La(III)-chelex resin

A new polymer ligand exchanger (PLE) has been developed for the removal of phosphate in wastewater. This PLE, consisting of lanthanum(III) bound to chelex-100 resin, was prepared by passing LaCl 3 solution through a column of chelex-100. Uptake of phosphate from water by this La-chelex resin was investigated in the column mode. The La-chelex resin was able to remove phosphate efficiently from water, and the uptake of phosphate was not affected by the presence of large amounts of anions (0.1 M) such as chloride and sulfate. The La-chelex resin was also able to efficiently remove phosphate from seawater to <0.1 mg-P l -1, and regenerated for reuse by removing the sorbed phosphate by eluting with 6 M HCl. © 2007 Elsevier Ltd. All rights reserved.link_to_subscribed_fulltex