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Uncertainty in the transmitter position, theory error and insufficient model parameterization amongst various other factors can lead to significant correlated error in observed controlled source electromagnetic data. These errors come to light by an examination of the residuals after performing inversion. Since correlated error violates the assumption of independent data noise it can manifest in spurious structure in inverted models. We demonstrate this using both synthetic data and real data from Scarborough gas field, North West Australia. In this work we propose a method which uses a hierarchical Bayesian framework and reversible jump Markov chain Monte Carlo to account for correlated error. We find that this removes suspect structure from the inverted models and within reasonable prior bounds, provides information on the resolution of resistivity at depth.
We propose to apply a transdimensional inversion algorithm, reversible-jump Markov chain Monte Carlo (rjMCMC), to seismic waveform inversion to characterize reservoir impedance and estimate uncertainty using post-stack data. This method can help to automatically determine a proper parameterization, specifically an optimal number of layers for a given data set and earth structure. The rjMCMC can also enhance uncertainty estimation since its transdimensional sampler can prevent a biased sampling of model space, including the number of unknowns. An ensemble of solutions with different parameterizations can statistically reduce the bias for parameter estimation and uncertainty quantification. Our results show that the inversion uncertainty, which includes uncertainty in both properties and their locations, is related to the contrast in properties across an interface. That is, there is a trade-off between property uncertainty and location uncertainty. A larger discontinuity will cause more uncertainty in model property values at the location of the interface, but less uncertainty in its location. Therefore, we propose to use the inversion uncertainty as a novel attribute to facilitate delineation of subsurface reflectors and quantify the magnitude of discontinuities.
Presentation Date: Wednesday, October 19, 2016
Start Time: 8:50:00 AM
Presentation Type: ORAL
Jian, Wang (Institute of Acoustics, Chinese Academy of Sciences) | Lei, Zhang (Institute of Acoustics, Chinese Academy of Sciences) | Hao, Chen (Institute of Acoustics, Chinese Academy of Sciences) | Xiu-ming, Wang (Institute of Acoustics, Chinese Academy of Sciences)
Real-time geosteering technology plays a key role in horizontal well development, which keeps the wellbore trajectories within target zones to maximize reservoir contact. Deep-directional-resistivity logging while drilling (LWD) tools have longer detection range and directionality to provide sufficient information for the operators, but meanwhile bring challenges to inversion of logging data, especially when the number of model layers is not fixed in priori. In this paper, we have developed an automatic inversion method to include the number of layers as a variable based on the trans-dimensional Markov chain Monte Carlo (MCMC) algorithm. The method assumes a 1D model based on planar layered formations penetrated by arbitrary well trajectories. In addition, a synthetic example demonstrates the inversion method can efficiently estimate the number of layers, positions, resistivities and also provide the probabilities of parameters without introducing bias.
Presentation Date: Wednesday, October 17, 2018
Start Time: 1:50:00 PM
Location: Poster Station 10
Presentation Type: Poster
Biswas, Reetam (University of Texas at Austin, and BP) | Arnulf, Adrien F. (University of Texas at Austin) | Sen, Mrinal K. (University of Texas at Austin) | Datta, Debanjan (University of Texas at Austin, and Shell International Exploration and Production) | Zhao, Zeyu (University of Texas at Austin) | Mishra, Pankaj K. (University of Texas at Austin) | Jaysaval, Piyoosh (University of Texas at Austin, and Pacific Northwest National Laboratory)
Full Waveform Inversion (FWI) has become a powerful tool to generate high-resolution subsurface velocity models. FWI attempts to solve a non-linear and non-unique inverse problem, and is traditionally based on a local optimization technique. As a result, it can easily get stuck in a local minimum. To mitigate this deleterious effect, FWI requires a good starting model, which should be close enough to the optimal model to properly converge to the global minimum. Here, we investigate a two-step approach for solving this problem. In the first step, we generate a starting model for FWI, that includes the low-wavenumber information, from first-arrival traveltime tomography of downward extrapolated streamer data. We solve the tomography problem using a trans-dimensional approach, based on a Bayesian framework. The number of model parameters is treated as a variable, similar to the P-wave velocity information. We use an adaptive cloud of nuclei points and Voronoi cells to represent our 2D velocity model. We use Reversible Jump Markov Chain Monte Carlo (RJMCMC) to sample models from a variable dimensional model space and obtain an optimum starting model for local elastic FWI. We also estimate uncertainty in our tomography derived model. We solve for the Eikonal equation using a shortest path method for ray tracing in tomography and we solve the elastic wave equation using a time-domain finite-difference method in FWI. To compute the gradient we used the adjoint method. We demonstrate our algorithm on a real 2-D seismic streamer dataset from Axial Seamount, which is the most volcanically active site of the northeastern Pacific. We ran 17 Markov chains with different starting number of nuclei and convergence for all chains was attained in about 1000 iterations. Marginal posterior density plots of velocity models demonstrate uncertainty in the obtained starting velocity models. We then ran a local FWI using the combined result from all chains. Presentation Date: Tuesday, October 13, 2020 Session Start Time: 1:50 PM Presentation Time: 2:40 PM Location: 362A Presentation Type: Oral
Within this decade, the logging-while-drilling (LWD) resistivity tools have been enhanced with over one hundred feet deep-reading capability. The geosteering inversion, which interprets the logging measurements to the geophysical parameters, become much more challenging since the earth structure involved turns more complicated. The traditional methods cannot handle the highly nonlinear inverse problems and meanwhile give justifiable uncertainty information. While the current application of the real-time geosteering inversions adopts a fixed-model profile, which introduces another ambiguity into the model interpretation, this paper develops a general trans-dimensional Bayesian methodology for geosteering inverse problems, which is a purely data-driven approach to search out the multi-dimensional parameter spaces. The simulations tell that the algorithm can efficiently answer these two questions: What is the possible earth model, and what the uncertainty of this model is.
Presentation Date: Tuesday, October 16, 2018
Start Time: 8:30:00 AM
Location: 212A (Anaheim Convention Center)
Presentation Type: Oral