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A fast Bayesian inversion method for 3D lithology and fluid prediction from prestack seismic data, and a corresponding feasibility analysis were developed and tested on a real data set. The objective of the inversion is to find the probabilities for different lithology-fluid classes from seismic data and geologic knowledge. The method combines stochastic rock physics relations between the elastic parameters and the different lithology-fluid classes with the results from a fast Bayesian seismic simultaneous inversion from seismic data to elastic parameters. A method for feasibility analysis predicts the expected modification of the prior probabilities to posterior probabilities for the different lithology-fluid classes. The feasibility analysis can be carried out before the seismic data are analyzed. Both the feasibility method and the seismic lithology-fluid probability inversion were applied to a prospect offshore Norway. The analysis improves the probability for gas sand from 0.1 to about 0.2–0.4 with seismic data.

Spatial coupling of the model parameters in an inversion problem provides lateral consistency and robust solutions. We have defined the inversion problem in a Bayesian framework, where the solution is represented by a posterior distribution obtained from a prior distribution and a likelihood model for the recorded data. The spatial coupling of the model parameters is imposed via the prior distribution by a spatial correlation function. In the Fourier domain, the spatially correlated model parameters can be decoupled, and the inversion problem can be solved independently for each frequency component. For a spatial model parameter represented on n grid nodes, the computing time for the inversion in the Fourier domain follows a linear function of the number of grid nodes, while the computing time for the fast Fourier transform follows an n log n function. We have developed a 3D linearized amplitude variation with offset (AVO) inversion method with spatially coupled model parameters, where the objective is to obtain posterior distributions for P‐wave velocity, S‐wave velocity, and density. The inversion algorithm has been tested on a 3D dataset from Sleipner field with 4 million grid nodes, each with three unknown model parameters. The computing time was less than 3 minutes on the inversion in the Fourier domain, while each 3D Fourier transform used about 30 s on a single 400‐MHz Mips R12000 CPU.

The spatial continuity of facies is one of the key factors controlling flow in reservoir models. Traditional pixel-based methods such as truncated Gaussian random fields and indicator simulation are based on only two-point statistics, which is insufficient to capture complex facies structures. Current methods for multi-point statistics either lack a consistent statistical model specification or are too computer intensive to be applicable. We propose a Markov mesh model based on generalized linear models for geological facies modeling. The approach defines a consistent statistical model that is facilitated by efficient estimation of model parameters and generation of realizations. Our presentation includes a formulation of the general framework, model specifications in two and three dimensions, and details on how the parameters can be estimated from a training image. We illustrate the method using multiple training images, including binary and trinary images and simulations in two and three dimensions. We also do a thorough comparison to the snesim approach. We find that the current model formulation is applicable for multiple training images and compares favorably to the snesim approach in our test examples. The method is highly memory efficient.

We have developed a Bayesian methodology for inversion of controlled source electromagnetic (CSEM) data and magnetotelluric (MT) data. The inversion method provided optimal solutions and also the associated uncertainty for any sets of electric and magnetic components and frequencies from CSEM and MT data. The method is based on a 1D forward modeling method for the electromagnetic (EM) response for a plane-layered anisotropic earth model. The inversion method was also designed to invert common midpoint (CMP)-sorted data along a 2D earth profile assuming locally horizontal models in each CMP position. The inversion procedure simulates from the posterior distribution using a Markov chain Monte Carlo (McMC) approach based on the Metropolis-Hastings algorithm. The method that we use integrates available geologic prior knowledge with the information in the electromagnetic data such that the prior model stabilizes and constrains the inversion according to the described knowledge. The synthetic examples demonstrated that inclusion of more data generally improves the inversion results. Compared to inversion of the inline electric component only, inclusion of broadside and magnetic components and an extended set of frequency components moderately decreased the uncertainty of the inversion. The results were strongly dependent on the prior knowledge imposed by the prior distribution. The prior knowledge about the background resistivity model surrounding the target was highly important for a successful and reliable inversion result.

Predrill assessment of the probability that a potential drilling spot holds hydrocarbons (HC) is of vital importance to any oil company. Of equally great value is the assessment of hydrocarbon volumes and distributions. We have developed a methodology that uses seismic data to find the probability that a vertical earth profile contains hydrocarbons and the probability distribution of hydrocarbon volumes. The method combines linearized amplitude variation with offset (AVO) inversion and stochastic rock models and predicts the joint probability distribution of the combined lithology and fluid for the entire profile. We use a Bayesian approach and find the solution of the inverse problem by Markov chain Monte Carlo simulation. The stochastic simulation benefits from a new and tailored simulation algorithm. The computational cost of finding the full joint probability distribution is relatively high and implies that the method is best suited to the investigation of a few potential drilling spots. We applied the method to a case with well control and to two locations in a prospect: one in the center and one at the outskirts. At the well location, we identify the two reservoir zones and obtain volumes that fit the log data. At the prospect, we obtain significant increases in HC probability and volume in the center, whereas there are decreases at the outskirts. Despite the large noise components in the data, the risked volumes in the center changed by a factor of three. We have designed an algorithm for computing the joint distribution of lithology, fluid, and elastic parameters for a full vertical profile. As opposed to what can be done with pointwise approaches, this allows us to calculate success probability and HC volumes.

We invert prestack seismic amplitude data to nd rock properties of a vertical prole of the earth. In particular we focus on lithology, porosity and uid. Our model includes vertical dependencies of the rock properties. This allows us to compute quantities valid for the full prole such as the probability that the vertical prole contains hydrocarbons and volume distributions of hydrocarbons. In a standard point wise approach, these quantities can not be assessed. We formulate the problem in a Bayesian framework, and model the vertical dependency using spatial statistics. Litho-uid prediction from seismic 2The relation between rock properties and elastic parameters is established through a stochastic rock model, and a convolutional model links the reectivity to the seismic. A Markov chain Monte Carlo (MCMC) algorithm is used to generate multiple realizations that honours both the seismic data and the prior beliefs and respects the additional constraints imposed by the vertical dependencies. Convergence plots are used to provide quality check of the algorithm and to compare it with a similar method. The implementation has been tested on three dierent data sets oshore Norway, among these one prole has well control. For all test cases the MCMC algorithm provides reliable estimates with uncertainty quantication within three hours. The inversion result is consistent with the observed well data.In the case example we show that the seismic amplitudes make a signicant impact on the inversion result even if the data have a moderate well tie, and that this is due to the vertical dependency imposed on the lithology uid classes in our model.The vertical correlation in elastic parameters mainly inuences the upside potential of the volume distribution.The approach is best suited to evaluate a few selected vertical proles since the MCMC algorithm is computer demanding.

Working in a Bayesian framework, we have derived a procedure for inverting rock properties based on geophysical data. The purpose was to arrive at a widely applicable and general procedure in which few and weak assumptions are required for application to various inverse problems within the geophysical industry. Our Bayesian statistical approach combines sampling-based techniques and Gaussian approximations to assess local approximations to quantities related to the posterior distribution of rock properties. These approximated quantities define the Bayesian inversion. A conceptual advantage of our approach is that there are few restrictions on the initial model, allowing realistic statistical models to be approximated directly. The methodology is easily parallelized and offers a range of procedures, which gives a trade-off between inversion speed and accuracy. We have tested the approach in a monitoring setting using seismic amplitudes by evaluating a synthetic case and real data from the Sleipner [Formula: see text] injection project. For the synthetic case, the inversion results correspond well with the rock properties used to generate the data and the posterior distribution derived using an MCMC approach. We also found improved accuracy compared with a frequently used Gaussian inversion approach. In the real data case, we clearly identified high-saturation layers present in previous qualitative interpretations.