We present a seismic inversion method driven by a petroelastic model, providing fine-scale geological models, in depth, fully compatible with pre-stack seismic measurements.

Granular effective medium (GEM) models rely on the physics of a random packing of spheres. Although the relative simplicity of these models contrasts with the complex texture of most grain-based sedimentary rocks, their analytical form makes them easier to apply than numerical models designed to simulate more complex rock structures. Also, unlike empirical models, they do not rely on data acquired under specific physical conditions and can therefore be used to extrapolate beyond available observations. In addition to these practical considerations, the appeal of GEM models lies in their parameterization, which is suited for a quantitative description of the rock texture. As a result, they have significantly helped promote the use of rock physics in the context of seismic exploration for hydrocarbon resources by providing geoscientists with tools to infer rock composition and microstructure from sonic velocities. Over the years, several classic GEM models have emerged to address modeling needs for different rock types such as unconsolidated, cemented, and clay-rich sandstones. We describe how these rock-physics models, pivotal links between geology and seismic data, can be combined into extended models through the introduction of a few additional parameters (matrix stiffness index, cement cohesion coefficient, contact-cement fraction, and laminated clays fraction), each associated with a compositional or textural property of the rock. A variety of real data sets are used to illustrate how these parameters expand the realm of seismic rock-physics diagnostics by increasing the versatility of the extended models and facilitating the simulation of plausible geologic variations away from the wells.

We introduce a stratigraphic inversion method that simultaneously integrates pre-stack seismic data with petrophysical and geological data. We use simulated annealing to invert directly for reservoir properties such as porosity, lithology and fluid content in a 3D geocellular model. Well and seismic data are integrated in their respective domains along with physical constraints at different vertical scales to produce an optimal solution. Application of user-defined Petro-Elastic Models (PEM) is a key element of the proposed methodology. In addition to connecting the inverted properties to the seismic response, the PEMs are used to maintain consistency between the time, depth and derived velocities throughout the inversion process. The proposed methodology overcomes the limitations faced by many existing techniques with regards to vertical resolution, time-to-depth conversion and the link between seismic response and reservoir properties. The result of our petrophysical seismic inversion is a fine-scale shared earth model in depth that is consistent with both log and seismic data and can be used for reservoir performance prediction. After demonstrating the robustness of the method on synthetic data, we present a result from a real dataset. The proposed methodology has been successfully applied to porosity inversion on one of the largest undeveloped oil fields in the North Sea. A fine-scale reservoir model has been obtained which reveals previously undetected geological structures and leads to a better understanding of the reservoir zone. Introduction Challenges of seismic reservoir characterization. Detailed 3D reservoir models are increasingly relied upon for prediction of reservoir performance, in particular through flow simulation. These models are commonly required to contain petrophysical information about lithology, rock properties (such as porosity, permeability, grain density, dry frame modulus, shear modulus, etc) and fluid properties (such as saturations, densities and compressibilities) on a very fine vertical scale, with a typical resolution of one meter. It is widely acknowledged that a better integration of all available measurements is the key to improving the reliability of the reservoir model, and therefore the reliability of the decisions based upon it. The reservoir model must be coherent as far as possible with the seismic volumes, wireline logs, core plug analyses and well production data, which are the response of the same subsurface to different experiments. In this paper we will focus more specifically on the integration of static information. Seismic data in particular are an invaluable source of information as they provide an extensive coverage with dense and regular lateral sampling, especially when compared to the sparse well locations. However, the integration of seismic data into the reservoir characterization process poses a number of challenges. Although the subsurface physically exists in depth, seismic traces portray it in two-way travel time, which is related to the depth domain via the wave propagation velocity. Similarly, seismic amplitudes are a highly indirect measurement of reservoir property variations. Seismic reacts to changes in the elastic properties of the subsurface, which are themselves related to petrophysical characteristics but also affected in a complex way by many factors. Finally, the vertical resolution that is recoverable from seismic data is low compared to the target geologic resolution: whereas wireline logging tools in wells can resolve details to within a few centimeters to a few meters, ten meters is a typical order of magnitude for seismic.

Deep neural networks (DNNs) have the potential to streamline the integration of seismic data for reservoir characterization by providing estimates of rock properties that are directly interpretable by geologists and reservoir engineers instead of elastic attributes like most standard seismic inversion methods. However, they have yet to be applied widely in the energy industry because training DNNs requires a large amount of labeled data that is rarely available. Training set augmentation, routinely used in other scientific fields such as image recognition, can address this issue and open the door to DNNs for geophysical applications. Although this approach has been explored in the past, creating realistic synthetic well and seismic data representative of the variable geology of a reservoir remains challenging. Recently introduced theory-guided techniques can help achieve this goal. A key step in these hybrid techniques is the use of theoretical rock-physics models to derive elastic pseudologs from variations of existing petrophysical logs. Rock-physics theories are already commonly relied on to generalize and extrapolate the relationship between rock and elastic properties. Therefore, they are a useful tool to generate a large catalog of alternative pseudologs representing realistic geologic variations away from the existing well locations. While not directly driven by rock physics, neural networks trained on such synthetic catalogs extract the intrinsic rock-physics relationships and are therefore capable of directly estimating rock properties from seismic amplitudes. Neural networks trained on purely synthetic data are applied to a set of 2D poststack seismic lines to characterize a geothermal reservoir located in the Dogger Formation northeast of Paris, France. The goal of the study is to determine the extent of porous and permeable layers encountered at existing geothermal wells and ultimately guide the location and design of future geothermal wells in the area.