Using Stochastic Seismic Inversion as Input for 3D Geomechanical Models
Authors: Trudeng Tone , Garcia-Teijeiro Xavier , Rodriguez-Herrera Adrian , Khazanehdari Jalal 
Published: March 2015

Abstract
The dual issues of band-limited vertical resolution and nonuniqueness of deterministic inversion results has led to the development of methodologies known as geostatistical, or stochastic, inversion. In these approaches, seismic data are typically inverted directly into a high-resolution geological model. Compared to deterministic inversion, stochastic methods deliver multiple realizations that are consistent with the available well and seismic data.
The seismic inversion process is inherently nonunique, meaning that there is an unbounded number of elastic property models that fit the seismic data equally well above some threshold misfit. We explore the notion of the equally large number of possible stress states that could be interpreted from same seismic observations.
We make use of stochastic inversion results to incorporate the impact of subseismic uncertainty in seismic-driven geomechanical models. By taking ultiple realizations from a prestack stochastic inversion--acoustic impedance, Vp/Vs, and density--we generate and feed a series of distributions of elastic constants into a finite element stress simulator. The multiple stress solutions allow us to account for uncertainties in the inversion results that can be ultimately captured in a suite of numerical models to predict a set of possible geomechanical states of a field. Therefore, beyond a unique geomechanical forecast for a field, we can now solve for the range of variability in geomechanically safe operational parameters within the field's development plan.

Introduction
Determinisic seismic inversion has become a standard practice in the industry. Conventional deterministic seismic inversion results provide important information about the spatial distribution of reservoir properties between wells (see Bosch et al. 2010; Bailey et al. 2010). Together with well data, deterministic seismic inversion can be used to construct 3D geomechanical models (see Herwanger and Koutabeloulis, 2011; Rodriguez-Herrera et al. 2013; Adachi et al. 2012; Sengupta et al. 2011). For instance, it provides a means to populate the geomechanical models with mechnical properties, which ultimately affects the response of the subsurface to the presence of loading/unloading mechanisms and guides the distribution of stress in the model.
Typically, however, deterministic seismic inversion results have limited vertical resolution compared to the scale of the well logs. In addition, the seismic inversion process is inherently nonunique, meaning that there are an infinite number of elastic property models that fit the seismic data. The output of a deterministic inversion is limited to to the input seismic resolution, capturing only a bulk elastic response and with all layering details smeared over the seismic wavelength. At such a level of detail, there can be multiple combinations of layer stacks that generate the same seismic response above some threshold misfit.
As an alternative, stochastic seismic inversion generates a set of realizations that agree with the bulk seismic response and well data and that can account for uncertainties or non-uniqueness associated with the seismic inversion process. The multiple realizations can be ultimately captured in a suite of geomechanical models fed by the AVO inversion outputs, which in turn can provide insight to the range of possible responses of the reservoir under the prescribed geological conditions. The following sections will explore this idea.