A Bayesian approach to inverse modelling of stratigraphy, part 1: method

Abstract

International audienceThe inference of ancient environmental conditions from their preserved response in the sedimentary record still remains an outstanding issue in stratigraphy. Since the 1970s, conceptual stratigraphic models (e.g. sequence stratigraphy) based on the underlying assumption that accommodation space is the critical control on stratigraphic architecture have been widely used. Although these methods considered more recently other possible parameters such as sediment supply and transport efficiency, they still lack in taking into account the full range of possible parameters, processes, and their complex interactions that control stratigraphic architecture. In this contribution, we present a new quantitative method for the inference of key environmental parameters (specifically sediment supply and relative sea level) that control stratigraphy. The approach combines a fully non-linear inversion scheme with a 'process­response' forward model of stratigraphy. We formulate the inverse problem using a Bayesian framework in order to sample the full range of possible solutions and explicitly build in prior geological knowledge. Our methodology combines Reversible Jump Markov chain Monte Carlo and Simulated Tempering algorithms which are able to deal with variable-dimensional inverse problems and multi-modal posterior probability distributions, respectively. The inverse scheme has been linked to a forward stratigraphic model, BARSIM (developed by Joep Storms, University of Delft), which simulates shallow-marine wave/storm-dominated systems over geological timescales. This link requires the construction of a likelihood function to quantify the agreement between simulated and observed data of different types (e.g. sediment age and thickness, grain size distributions). The technique has been tested and validated with synthetic data, in which all the parameters are specified to produce a 'perfect' simulation, although we add noise to these synthetic data for subsequent testing of the inverse modelling approach. These tests addressed convergence and computational-overhead issues, and highlight the robustness of the inverse scheme, which is able to assess the full range of uncertainties on the inferred environmental parameters and facies distributions

Transdimensional change-point modeling as a tool to investigate uncertainty in applied geophysical inference: An example using borehole geophysical logs

“…To solve this problem, we use a reversible jump MCMC sampling approach (Green, 1995(Green, , 2003. There are recent applications of this technique and related approaches in earth sciences (Malinverno, 2002;Malinverno and Leaney, 2005;Jasra et al, 2006;Bodin and Sambridge, 2009;Charvin et al, 2009;Hopcroft et al, 2009;Agostinetti and Malinverno, 2010;Gallagher, 2012). In the description following, we briefly summarize the algorithm described by Gallagher et al (2011), which includes mathematical details in the supplementary material.…”

Similarity measure of sedimentary successions and its application in inverse stratigraphic modeling

“…The succession simulated by forward modeling very commonly contains time resolution, say, 5000 year (modeling time step), whereas the observed succession contains dated time resolution usually in million years, or at higher resolution hundreds of thousand years. The method published so far to calculate the mismatch of simulated and observed successions is to only compare the thickness of the smallest dated stratigraphic units such as a strata cycle (Cross and Lessenger 1999;Charvin et al 2009), or the unit thickness maps (Falivene et al 2014). Of course, in these methods, the higher resolution of time calibration the observed succession has, the more accurate the comparison of the simulated and observed successions is.…”

“…One of the main reasons why this technique has been delayed to dominate in petroleum reservoir modeling is its inability to implement data conditioning. Since late 1990s, similar techniques but under different names were proposed to overcome the inability and initiated a new research front in computational stratigraphy and sedimentology, such as inverse stratigraphic modeling (ISM) (Griffiths et al 1996;Lessenger and Cross 1996;Cross and Lessenger 1999;Duan et al 2001a;Imhof and Sharma 2006;Charvin et al 2009;Griffiths 2009;Charvin et al 2011), adaptive modeling (Duan et al 1998), modeling optimization (Bornholdt and Westphal 1998;Wijns et al 2003Wijns et al , 2004, or model calibration (Falivene et al 2014). However, the progress of these techniques, all of which will be called ISM afterward for simplicity, has been limited, and one of the major hurdles is still the data conditioning.…”

Uncertainty management in stratigraphic well correlation and stratigraphic architectures: A training-based method

“…They generate 3D models 8 of a quality that generally cannot be achieved by traditional geostatistical and geometric interpolation methods, though implementing the physics of deposition and erosion (Tetzlaff and Harbaugh, 1989;Burgess, 2012). Cross and Lessenger (1999) and Charvin et al (2009) have proposed to use inverse methods to match available subsurface data with process-based models. Although these results are promising, they are very computationally intensive and may not match dense data sets as provided for instance by seismic data or dense drilling campaigns.…”

“…Unfortunately, despite some successful attempts (Cross and Lessenger, 1999;Charvin et al, 2009;Falivene et al, 2014;Sacchi et al, 2015), conditioning forward stratigraphic models to seismic and well data remains a difficult computational challenge.…”