Paulo M. Carvalho

An inverse‐scattering series method for attenuating multiples in seismic reflection data

We present a multidimensional multiple‐attenuation method that does not require any subsurface information for either surface or internal multiples. To derive these algorithms, we start with a scattering theory description of seismic data. We then introduce and develop several new theoretical concepts concerning the fundamental nature of and the relationship between forward and inverse scattering. These include (1) the idea that the inversion process can be viewed as a series of steps, each with a specific task; (2) the realization that the inverse‐scattering series provides an opportunity for separating out subseries with specific and useful tasks; (3) the recognition that these task‐specific subseries can have different (and more favorable) data requirements, convergence, and stability conditions than does the original complete inverse series; and, most importantly, (4) the development of the first method for physically interpreting the contribution that individual terms (and pieces of terms) in the inv...

Inverse scattering series and seismic exploration

This paper presents an overview and a detailed description of the key logic steps and mathematical-physics framework behind the development of practical algorithms for seismic exploration derived from the inverse scattering series. There are both significant symmetries and critical subtle differences between the forward scattering series construction and the inverse scattering series processing of seismic events. These similarities and differences help explain the efficiency and effectiveness of different inversion objectives. The inverse series performs all of the tasks associated with inversion using the entire wavefield recorded on the measurement surface as input. However, certain terms in the series act as though only one specific task, and no other task, existed. When isolated, these terms constitute a task-specific subseries. We present both the rationale for seeking and methods of identifying uncoupled task-specific subseries that accomplish: (1) free-surface multiple removal; (2) internal multiple attenuation; (3) imaging primaries at depth; and (4) inverting for earth material properties. A combination of forward series analogues and physical intuition is employed to locate those subseries. We show that the sum of the four task-specific subseries does not correspond to the original inverse series since terms with coupled tasks are never considered or computed. Isolated tasks are accomplished sequentially and, after each is achieved, the problem is restarted as though that isolated task had never existed. This strategy avoids choosing portions of the series, at any stage, that correspond to a combination of tasks, i.e., no terms corresponding to coupled tasks are ever computed. This inversion in stages provides a tremendous practical advantage. The achievement of a task is a form of useful information exploited in the redefined and restarted problem; and the latter represents a critically important step in the logic and overall strategy. The individual subseries are analysed and their strengths, limitations and prerequisites exemplified with analytic, numerical and field data examples.

Wavelet estimation for surface multiple attenuation using a simulated annealing algorithm

The inverse scattering surface multiple attenuation method (Carvalho et. al., 1991 and Carvalho, 1992) requires knowledge of the source wavelet. The method itself provides a way to estimate the wavelet. The estimation process uses an optimization algorithm. A global search procedure, based on simulated annealing, is used to perform the optimization. Simulated annealing has a random component that allows it to search for the global minimum of a function containing many local minima. In this work, the surface multiple attenuation method and the wavelet estimation procedure are described and illustrated with synthetic and real data examples. Encouraging results were obtained that demonstrate the robustness of the process under real data conditions.

Inverse scattering internal multiple attenuation: Results from complex synthetic and field data examples

Seismic prospecting can be viewed as a process of extracting subsurface information from seismic measurements. Today’s interpretation and inversion technologies demand sophisticated pre-stack amplitudepreserving processing technologies that are effective in complex geologic environments. For example, the advent and increased use AVO require advanced multiple suppression technology in seismically challenging areas where conventional ‘tried and true’ methods are no longer adequate.

An inverse‐scattering sub‐series for predicting the spatial location of reflectors without the precise reference medium and wave velocity

The accurate location, resolution and identification of targets beneath complex media (e.g., salt, basalt and karsted sediments) are high priority and essentially unsolved problems today. Imaging methods that are tested and compared using synthetic data with precise model velocity as input are not addressing the real-world problem. At the very least, imaging methods need to be tested using synthetic data and a velocity model that corresponds to what would be estimated from the data using current best velocity analysis techniques. This bit of realism would help focus on the relevant issue: how do we achieve accurate imaging at depth given our current ability to estimate the velocity, especially under complex geologic circumstances? There are two responses to this challenge: (1) to significantly improve velocity estimation capability, and (2) to develop methods that can produce accurate images at depth without precise velocity. We support both approaches and this paper represents an effort in the second category.

Imaging and inversion at depth without a velocity model: theory, concepts and initial evaluation

The inverse-scattering series is a multidimensional inversion procedure that directly determines physical properties using only reflection data and a reference medium. This inversion process can be thought of as performing the following four tasks: (1) free surface multiple removal, (2) internal multiple removal, (3) location of reflectors in space, and (4) identification of medium property changes across reflectors. Since the entire process requires only reflection data and reference medium information, it is reasonable to assume that intermediate steps that are associated with achieving that objective would also be attainable with only the reference medium and reflection data. Subseries have been identified that exhibit this property for the tasks of free-surface and internal multiple attenuation (Weglein et al., 1997) and algorithms resulting from these subseries have been successfully applied to field data. Here we report our initial research efforts to address the third and fourth stages: imaging and parameter estimation. The objective is to be able to determine the precise reflector position in space and a map of earth properties, without the traditional need for the exact velocity model. Two distinct approaches are described: the first uses a series that computes the actual wavefield at depth (to be used for subsequent imaging and inversion) and the second is a series that directly computes earth physical properties. Neither approach requires or determines the actual velocity model or ever updates the reference medium. Numerical and analytical examples will be used to exemplify these concepts and to define the current state of understanding of these fundamentally new approaches to imaging and inverting seismic data. Open issues and future plans will be discussed.

Geostatistical facies simulation with geometric patterns of a petroleum reservoir

During exploration and pre-feasibility studies of a typical petroleum project many analyses are required to support decision making. Among them is reservoir lithofacies modeling, preferably using uncertainty assessment, which can be carried out with geostatistical simulation. The resulting multiple equally probable facies models can be used, for instance, in flow simulations. This allows assessing uncertainties in reservoir flow behavior during its production lifetime, which is useful for injector and producer well planning. Flow, among other factors, is controlled by elements that act as flow corridors and barriers. Clean sand channels and shale layers are examples of such reservoir elements that have specific geometries. Besides simulating the necessary facies, it is also important to simulate their shapes. Object-based and process-based simulations excel in geometry reproduction, while variogram-based simulations perform very well at data conditioning. Multiple-point geostatistics (MPS) combines both characteristics, consequently it was employed in this study to produce models of a real-world reservoir that are both data adherent and geologically realistic. This work aims at illustrating how subsurface information typically available in petroleum projects can be used with MPS to generate realistic reservoir models. A workflow using the SNESIM algorithm is demonstrated incorporating various sources of information. Results show that complex structures (e.g. channel networks) emerged from a simple model (e.g. single branch) and the reservoir facies models produced with MPS were judged suitable for geometry-sensitive applications such as flow simulations.