## Full-Waveform Inversion for High-Resolution Reservoir Characterization

### Course Description

The purpose of this course is to teach participants the fundamentals of extracting quantitative property information from seismic data. In the end this leads to an inversion process, which is called linear if the data are supposed to consist in primaries only and is non-linear if all multiple scattering and multiple mode conversion over a target interval (typically 500 m around the reservoir) is taken into account. Non-linear inversion leads to a higher resolution than obtained from conventional linear inversion techniques. All steps required in these processes are based on wave equations and it is important, therefore, to have a good understanding of acoustic and elastic wave equations. In linear (AVO) inversion, first the reflection coefficients are derived from the data and subsequently the rock properties are derived from the reflection coefficients. In non-linear inversion, the properties are directly derived from the data. Non-linear inversion is an iterative process of which the first iteration (the Born approximation) represents the linear inversion result. The method is based on an integral representation of the wave equation. An important aspect of reservoir oriented full-waveform inversion (FWI-res) is that the surface recorded data are localized (focused) to the target area. This can be achieved by redatuming or by local demigration of migrated data. Both the linear AVO data model in terms of reflection coefficients and the non-linear data model in terms of property contrasts against backgrounds are presented. Inversion, linear, or non-linear, requires regularization. Several regularization options are presented. Finally, linear and non-linear inversions at the reservoir scale are demonstrated by highly realistic synthetic reservoir models and real data case studies. The real data case studies include the extraction of low-frequency models (backgrounds) from well data and the extraction of angle dependent wavelets from the seismic-to-well match.

### Course Objectives

Upon completion of the course, participants will be able to: • Understand what quantitative property information is contained in seismic data and how to extract it. • Make better judgements as to what inversion method to apply to what problem. • Adopt a more quantitative approach to seismic-to-well matching and low frequency background model extraction • Further the role of reservoir geophysics in multidisciplinary projects.

### Course Outline

• Introduction • Short recap on complex integral transforms (Fourier, Laplace, F/K and linear Radon) • The acoustic wave equation in inhomogeneous media • Integral representations of the acoustic wave equation; Kirchhoff- Rayleigh and the Scattering Integral (Lippmann-Schwinger) • The AVO data model; Zoeppritz reflection coefficients • Linear inversion of AVO data including regularisation; synthetic and real data examples • The non-linear data model for inversion; data equation and object equation; iterative, multiplicatively regularised inversion • Applications based on an elastic full wavefield non-linear data model; realistic synthetic reservoir study, real data case studies including low- frequency model extraction and seismic-to-well matching. Synthetic time-lapse example.

### Participants’ Profile

This course is designed for geophysicists active in reservoirs and/or quantitative interpretation and processing geophysicists who would like to become involved in quantitative interpretation.

### Prerequisites

Participants should have a basic training in geophysics and mathematics, particularly complex numbers and integrals.