161 research outputs found
An acoustic imaging method for layered non-reciprocal media
Given the increasing interest for non-reciprocal materials, we propose a
novel acoustic imaging method for layered non-reciprocal media. The method we
propose is a modification of the Marchenko imaging method, which handles
multiple scattering between the layer interfaces in a data-driven way. We start
by reviewing the basic equations for wave propagation in a non-reciprocal
medium. Next, we discuss Green's functions, focusing functions, and their
mutual relations, for a non-reciprocal horizontally layered medium. These
relations form the basis for deriving the modified Marchenko method, which
retrieves the wave field inside the non-reciprocal medium from reflection
measurements at the boundary of the medium. With a numerical example we show
that the proposed method is capable of imaging the layer interfaces at their
correct positions, without artefacts caused by multiple scattering.Comment: 21 pages, 8 figure
Reciprocity and representation theorems for flux- and field-normalised decomposed wave fields
We consider wave propagation problems in which there is a preferred direction
of propagation. To account for propagation in preferred directions, the wave
equation is decomposed into a set of coupled equations for waves that propagate
in opposite directions along the preferred axis. This decomposition is not
unique. We discuss flux-normalised and field-normalised decomposition in a
systematic way, analyse the symmetry properties of the decomposition operators
and use these symmetry properties to derive reciprocity theorems for the
decomposed wave fields, for both types of normalisation. Based on the
field-normalised reciprocity theorems, we derive representation theorems for
decomposed wave fields. In particular we derive double- and single-sided
Kirchhoff-Helmholtz integrals for forward and backward propagation of
decomposed wave fields. The single-sided Kirchhoff-Helmholtz integrals for
backward propagation of field-normalised decomposed wave fields find
applications in reflection imaging, accounting for multiple scattering.Comment: 31 pages, 5 figure
Monitoring induced distributed double-couple sources using Marchenko-based virtual receivers
We aim to monitor and characterize signals in the subsurface by combining
these passive signals with recorded reflection data at the surface of the
Earth. To achieve this, we propose a method to create virtual receivers from
reflection data using the Marchenko method. By applying homogeneous Green's
function retrieval, these virtual receivers are then used to monitor the
responses from subsurface sources. We consider monopole point sources with a
symmetric source signal, where the full wavefield without artefacts in the
subsurface can be obtained. Responses from more complex source mechanisms, such
as double-couple sources, can also be used and provide results with comparable
quality as the monopole responses. If the source signal is not symmetric in
time, our technique that is based on homogeneous Green's function retrieval
provides an incomplete signal, with additional artefacts. The duration of these
artefacts is limited and they are only present when the source of the signal is
located above the virtual receiver. For sources along a fault rupture, this
limitation is also present and more severe due to the source activating over a
longer period of time. Part of the correct signal is still retrieved, as well
as the source location of the signal. These artefacts do not occur in another
method which creates virtual sources as well as receivers from reflection data
at the surface. This second method can be used to forecast responses to
possible future induced seismicity sources (monopoles, double-couple sources
and fault ruptures). This method is applied to field data, where similar
results to synthetic data are achieved, which shows the potential for the
application on real data signals
Virtual plane-wave imaging via Marchenko redatuming
Marchenko redatuming is a novel scheme used to retrieve up- and down-going
Green's functions in an unknown medium. Marchenko equations are based on
reciprocity theorems and are derived on the assumption of the existence of so
called focusing functions, i.e. functions which exhibit time-space focusing
properties once injected in the subsurface. In contrast to interferometry but
similarly to standard migration methods, Marchenko redatuming only requires an
estimate of the direct wave from the virtual source (or to the virtual
receiver), illumination from only one side of the medium, and no physical
sources (or receivers) inside the medium. In this contribution we consider a
different time-focusing condition within the frame of Marchenko redatuming and
show how this can lead to the retrieval of virtual plane-wave responses, thus
allowing multiple-free imaging using only a 1 dimensional sampling of the
targeted model. The potential of the new method is demonstrated on a 2D
synthetic model.Comment: 12 pages, 5 figure
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