Reciprocity and Representations for Wave Fields in 3D Inhomogeneous Parity-Time Symmetric Materials

Inspired by recent developments in wave propagation and scattering experiments with parity-time (PT) symmetric materials, we discuss reciprocity and representation theorems for 3D inhomogeneous PT-symmetric materials and indicate some applications. We start with a unified matrix-vector wave equation which accounts for acoustic, quantum...

Marchenko Green’s Function Retrieval in Layered Elastic Media from Two-Sided Reflection and Transmission Data

By solving a Marchenko equation, Green’s functions at an arbitrary (inner) depth level inside an unknown elastic layered medium can be retrieved from single-sided reflection data, which are collected at the top of the medium. To date, it has only been possible to obtain an exact solution if the medium obeyed stringent monotonicity conditions and...

The propagator and transfer matrix for a 3D inhomogeneous dissipative acoustic medium, expressed in Marchenko focusing functions

Standard Marchenko redatuming and imaging schemes neglect evanescent waves and are based on the assumption that decomposition into downgoing and upgoing waves is possible in the subsurface. Recently we have shown that propagator matrices, which circumvent these assumptions, can be expressed in terms of Marchenko focusing functions. In this paper...

Towards understanding the impact of the evanescent elastodynamic mode coupling in Marchenko equation-based demultiple methods

Marchenko equation-based methods promise data-driven, true-amplitude internal multiple elimination. The method is exact in 1-D acoustic media, however it needs to be expanded to account for the presence of 2- and 3-D elastodynamic wave-field phenomena, such as compressional (P) to shear (S) mode conversions, total reflections or evanescent waves...

On Green’s functions, propagator matrices, focusing functions and their mutual relations

Green’s functions and propagator matrices are both solutions of the wave equation, but whereas Green’s functions obey a causality condition in time (G = 0 for t < 0), propagator matrices obey a boundary condition in space. Marchenko-type focusing functions focus a wave field in space at zero time. We discuss the mutual relations between Green...

Target-Enclosed Least-Squares Seismic Imaging

Least-squares reverse-time migration (LSRTM) is a method that seismologists utilize to compute a high-resolution subsurface image. Nevertheless, LSRTM is a computationally demanding problem. One way to reduce the computational costs of the LSRTM is to choose a small region of interest (ROI) and compute the image of that region. However, finding...

Minimum-phase property and reconstruction of elastodynamic dereverberation matrix operators

Minimum-phase properties are well-understood for scalar functions where they can be used as physical constraint for phase reconstruction. Existing scalar applications of the latter in geophysics include, for example the reconstruction of transmission from acoustic reflection data, or multiple elimination via the augmented acoustic Marchenko...

Erratum: Wave-field representations with Green's functions, propagator matrices, and Marchenko-type focusing functions (J. Acoust. Soc. Am. (2022) 151 (587-608) DOI: 10.1121/10.0009236)

For the elastodynamic wave equation discussed in Appendix A.4 in Ref. 1, the expressions for matrices ∼L 6 1 and ∼L 6 2 in Eqs. (A32) and (A33) must be multiplied by 61. In other words, the signs of ∼L _ ₁and ∼L _ ₂have to be changed, whereas the signs of ∼L 1 and ∼L 2 remain unchanged. With these corrections, matrix ∼L ...

A framework for subsurface monitoring by integrating reservoir simulation with time-lapse seismic surveys

Reservoir simulations for subsurface processes play an important role in successful deployment of geoscience applications such as geothermal energy extraction and geo-storage of fluids. These simulations provide time-lapse dynamics of the coupled poromechanical processes within the reservoir and its over-, under-, and side-burden environments...

Propagator and transfer matrices, Marchenko focusing functions and their mutual relations

Many seismic imaging methods use wavefield extrapolation operators to redatum sources and receivers from the surface into the subsurface. We discuss wavefield extrapolation operators that account for internal multiple reflections, in particular propagator matrices, transfer matrices and Marchenko focusing functions. A propagator matrix is a...

Extracting small time-lapse traveltime changes in a reservoir using primaries and internal multiples after Marchenko-based target zone isolation

Geophysical monitoring of subsurface reservoirs relies on detecting small changes in the seismic response between a baseline and monitor study. However, internal multiples, related to the over- and underburden, can obstruct the view of the target response, hence complicating the time-lapse analysis. To retrieve a response that is free from...

The impact of crustal scattering on body-wave reflection interferometry by cross-correlation and multidimensional deconvolution

Previous studies indicate that scattering may pose a trade-off for the performance of seismic interferometry (SI) applications for retrieving body-wave reflections of a target reflector. While it has been demonstrated that a higher scattering strength of the overburden improves the Green's function estimated by cross-correlation SI, other...

Time-lapse applications of the Marchenko method on the Troll field

The data-driven Marchenko method is able to redatum wavefields to arbitrary locations in the subsurface, and can, therefore, be used to isolate zones of specific interest. This creates a new reflection response of the target zone without interference from over- or underburden reflectors. Consequently, the method is well suited to obtain a...

Wavefield focusing using a generalised, potentially asymmetric homogeneous Green's function

Marchenko-type integrals typically relate so-called focusing functions and Green's functions via the reflection response measured on the open surface of a volume of interest. Originating from one dimensional inverse scattering theory, the extension to two and three dimensions set in motion various new developments regarding imaging in complex...

Design, implementation and application of the Marchenko plane-wave algorithm

The Marchenko algorithm can suppress the disturbing effects of internal multiples that are present in seismic reflection data. To achieve this, a set of coupled equations with four unknowns is solved. These coupled equations are separated into a set of two equations with two unknowns using a time window. The two unknown focusing functions can...

Target-oriented least-squares reverse-time migration with Marchenko redatuming and double-focusing: Field data application

Recently, the focus of reflection seismologists has shifted to applications where a high-resolution image of the subsurface is required. Least-Squares Reverse-Time Migration (LSRTM) is a common tool used to compute such images. Still, its high computational costs have led seismologists to use target-oriented LSRTM for imaging only a small target...