Summary statistics from training images as prior information in probabilistic inversion

A strategy is presented to incorporate prior information from conceptual geological models in probabilistic inversion of geophysical data. The conceptual geological models are represented by multiple-point statistics training images (TIs) featuring the expected lithological units and structural patterns. Information from an ensemble of TI realizations is used in two different ways. First, dominant modes are identified by analysis of the frequency content in the realizations, which drastically reduces the model parameter space in the frequency-amplitude domain. Second, the distributions of global, summary metrics (e.g. model roughness) are used to formulate a prior probability density function. The inverse problem is formulated in a Bayesian framework and the posterior pdf is sampled using Markov chain Monte Carlo simulation. The usefulness and applicability of this method is demonstrated on two case studies in which synthetic crosshole ground-penetrating radar traveltime data are inverted to recover 2-D porosity fields. The use of prior information from TIs significantly enhances the reliability of the posterior models by removing inversion artefacts and improving individual parameter estimates. The proposed methodology reduces the ambiguity inherent in the inversion of high-dimensional parameter spaces, accommodates a wide range of summary statistics and geophysical forward problems

Probabilistic electrical resistivity tomography of a CO2 sequestration analog

Electrical resistivity tomography (ERT) is a well-established method for geophysical characterization and has shown potential for monitoring geologic CO2 sequestration, due to its sensitivity to electrical resistivity contrasts generated by liquid/gas saturation variability. In contrast to deterministic inversion approaches, probabilistic inversion provides the full posterior probability density function of the saturation field and accounts for the uncertainties inherent in the petrophysical parameters relating the resistivity to saturation. In this study, the data are from benchtop ERT experiments conducted during gas injection into a quasi-2D brine-saturated sand chamber with a packing that mimics a simple anticlinal geological reservoir. The saturation fields are estimated by Markov chain Monte Carlo inversion of the measured data and compared to independent saturation measurements from light transmission through the chamber. Different model parameterizations are evaluated in terms of the recovered saturation and petrophysical parameter values. The saturation field is parameterized (1) in Cartesian coordinates, (2) by means of its discrete cosine transform coefficients, and (3) by fixed saturation values in structural elements whose shape and location is assumed known or represented by an arbitrary Gaussian Bell structure. Results show that the estimated saturation fields are in overall agreement with saturations measured by light transmission, but differ strongly in terms of parameter estimates, parameter uncertainties and computational intensity. Discretization in the frequency domain (as in the discrete cosine transform parameterization) provides more accurate models at a lower computational cost compared to spatially discretized (Cartesian) models. A priori knowledge about the expected geologic structures allows for non-discretized model descriptions with markedly reduced degrees of freedom. Constraining the solutions to the known injected gas volume improved estimates of saturation and parameter values of the petrophysical relationship. (C) 2014 Elsevier B.V. All rights reserved

Initial patient characteristics can predict pattern and risk of relapse in localized rhabdomyosarcoma

PURPOSE: Evaluation of primary tumor-, treatment-, and patient-related factors predicting relapse pattern, risk, and survival after relapse with the aim to design a risk-adapted, tumor-directed surveillance program for patients with localized rhabdomyosarcoma (RMS). PATIENTS AND METHODS: One thousand one hundred sixty-four patients with nonmetastatic RMS achieved complete remission at the end of multimodal therapy in the consecutive trials of the Cooperative Weichteilsarkom Studiengruppe (CWS)-81, CWS-86, CWS-91, and CWS-96 between 1980 and 2002 (median follow-up, 5 years). Three hundred thirty-seven of these individuals developed either locoregional, metastatic, or combined relapses. Predictive factors for relapse, its pattern, and postrelapse survival were analyzed. RESULTS: Age, histology, tumor size, tumor site, postsurgical stage, and omission of radiotherapy were identified as factors associated with an increased relapse risk in multivariate analyses. Relapse rates did not differ among the CWS trials. Median time to relapse was 1.43 years from first diagnosis (range, 0.13 to 13.5 years). There were 217 locoregional, 72 metastatic, and 48 combined recurrences. Only two patients developed metastases more than 4 years after diagnosis, and both had combined recurrences. Five-year postrelapse survival was 24%. Patient subsets with consistent relapse pattern, risk, and postrelapse survival rates were identified on the basis of histologic subtype and tumor size. CONCLUSION: Initial patient and tumor characteristics predict pattern and risk of relapse and also correlate with postrelapse survival probabilities. In localized RMS, tumor-directed follow-up should focus on the primary site. Screening for metastatic relapse may not be necessary more than 4 years after diagnosis. The identification of subgroups with distinctive pattern and risk of relapse may be used to develop risk-adapted, tumor-directed guidance for detection of recurrent disease in localized RMS