P566
3D-imaging of 2D-time Reverse Modeling
B. Steiner* (Spectraseis) & E.H. Saenger (ETH Zürich/Spectraseis)
SUMMARY
Time reverse modeling has become an efficient tool to detect the origin of low-frequency (<10 Hz) seimic
tremor signals. Examples of such signals are observed before volcanic eruptions or above hydrocarbon
reservoirs. Technical expertise has mainly been developed for 2D application. However, effects from using
three-component signals for 2D reverse modeling are still widely unknown. An example is reverse
propagation of signals on a plane vertically below a seismometer array. In this case, reverse calculation is
performed with the vertical and the horizontal component parallel to the array. The horizontal component
perpendicular to the array is dropped. This causes partial loss of particle motion and directivity of the
recorded waves. The concept of merging multiple 2D images to one 3D image is presented to meet
problems arising from this loss. A synthetic study with a tremor source demonstrates how this source is
imaged in different vertical planes. Planes within the distance of two wavelengths from the source render
artificial focusing at the horizontally projected source location. However, these artificial focusing points
are weak relative to the focusing at the corret location. A source seems to be locatable with 2D reverse
modeling and successive analysis in a 3D image.
72nd EAGE Conference & Exhibition incorporating SPE EUROPEC 2010
Barcelona, Spain, 14 - 17 June 2010
Introduction
Tremor signals such as swarms of seismic events make up a considerable part of the seismic signals in
the Earth. They are indications of mechanical processes, e.g. the motion of fluids like magma shortly
before a possible eruption (Chouet, 1996), or related to processes in hydrocarbon reservoirs (e.g. van
Mastrigt and Al-Dulaijan, 2008; Saenger et al., 2009). Identification of some of these processes and
locating their source therefore is of interest, either economically or as prevention from natural hazard
(Shelly et al., 2007). Localization of tremor signals is especially challenging as they are, in many
cases, invisible in the seismograms (e.g. Shelly et al., 2007).
Promising approaches to locate seismic tremor sources are time reversal techniques. Basic description
and an overview are given by Fink (1999). A numerical version of reversal techniques is time reverse
modeling (TRM). The seismic signals are reversed in time and numerically back-propagated through
the media. During reverse modeling, the reversed signals are continuously inserted as input signals at
the location of the seismometers. Signals originating from the same seismic source in the subsurface
will return to their origin at the same time and become visible due to positive interference. Examples
of locating the origin of seismic signals with time reversal techniques can be found in Gajewski and
Tessmer (2005), Mehta and Snieder (2006) and Larmat et al. (2008). This process is applicable for
single pulses, if the source time is approximately known. It becomes more difficult if there is no
knowledge about the source time. Every single time step during reverse modeling then has to be
imaged and analyzed. This is also the case for multiple pulses forming a quasi continuous tremor-like
event. Time reverse modeling can be expanded by imaging conditions to detect permanent tremor
sources as presented by Artman et al. (2009) and Steiner et al. (2009).
Major steps have been taken in research and application of two-dimensional (2D) TRM on tremor-like
signals. Calculation in 2D is much faster than 3D computation. Questions and problems from 3D
applications therefore are often modeled in the 2D space. However, effects from using information
from 3-component seismic signals for 2D reverse simulations are still widely unknown. For reverse
simulation of signals on a vertical plane below the seismometer array, the horizontal component
perpendicular to the plane is dropped. Particle motion of the surface waves and directivity, among
other wave characteristics, are partially lost by this process. These losses may significantly affect the
validity of the resulting images. At this point, we introduce the workflow of performing multiple 2D
reverse simulations and successive 3D display of the images in one figure as a concept to meet these
problems. We perform a synthetic experiment to test this concept. A 3D forward simulation calculates
signals produced by tremor-like sources and propagates them through a heterogeneous media. Three
lines of synchronous seismometers at the surface record the incoming signals. The vertical component
and the horizontal component parallel to the lines are then used as input signals for 2D reverse
propagation on the planes vertically below the stations. The horizontal component perpendicular to
the lines is discarded. This approach conserves the particle motion recorded for each component
individually. Reverse calculation is performed for each line independently. One seismometer array is
directly above the tremor-like sources. The other two arrays have a lateral distance of one or two
wavelengths respectively.
Synthetic example with 3-component signals
A real 3D P-wave velocity model from Voitsdorf (Austria), shown in Figure 1a, serves as background
model for numerical wave propagation. The Voitsdorf model provides a suitable large-scale
heterogeneous velocity model for this synthetic case study. Several synthetic and field measurements
have been carried out in this area to test the hypothesis whether hydrocarbon reservoirs act as seismic
sources of tremor-like signals (e.g. Steiner et al., 2008; Lambert et al., 2009). The velocity model has
a size of 1000 x 2000 x 500 grid points (Easting x Northing x Depth). The spatial resolution of the
rectangular grid is 10 m in each direction. The forward simulation was computed for 15000 time steps
with a numerical time step of 1.5 ms. A horizontally planar and circular source is placed at the
position of one of the known hydrocarbon reservoirs. Its center lies at [5800 m, 8300 m, 1900 m]
(Easting, Northing, Depth) and its horizontal radius is 400 m. In the velocity model, this seismic
72nd EAGE Conference & Exhibition incorporating SPE EUROPEC 2010
Barcelona, Spain, 14 - 17 June 2010
source lies directly above the basement at the intersection of the solid black line and the dashed white
line in Figure 1a. The source signal is modeled as a vertical stress discontinuity with a Ricker wavelet
and central frequency of 2 Hz. Computations are performed with a parallelized finite-difference code
which simulates full elastic wave propagation with a displacement-stress formulation (Saenger et al.,
2000).
Three synthetic seismometer arrays directing toward north, array A, B and C in Figure 1a, are placed
on the top of the velocity model. They are parallel to each other with a distance of 1 km and consist of
200 seismometers each. The spacing of 1 km between the arrays roughly corresponds to one
wavelength in this modeling study. The vertical and the Northing particle displacement measured for
array A, B and C are shown in Figures 1b and 1c. These are the two particle displacement components
which are used as source signals for 2D TRM. The Easting particle displacement is dropped as it is
horizontally perpendicular to the arrays. The seismograms presented in Figures 1b and 1c visualize
the difficulty to identify events from the seismograms directly due to the tremor-like behavior of the
seismic source.
Figure 1 (a) P-wave velocity model of Voitsdorf (Austria). A seismic source is located at the
intersection of the dashed white line and the solid black line directly above the basement. (b and c)
Synthetic seismograms from numerical forward modeling: (b) Vertical particle displacement and (c)
Northing particle displacement versus time at the surface for the 3 different seismometer arrays A, B
and C. The Northing of the seismic source is indicated by the black dot.
The 2D planes vertically below the arrays are called plane A, B and C according to the arrays. These
2D planes are extracted as background models for 2D TRM. Reverse propagation is performed for
each plane individually. According to the layout in Figure 1a, the source lies within plane A. Plane B
72nd EAGE Conference & Exhibition incorporating SPE EUROPEC 2010
Barcelona, Spain, 14 - 17 June 2010
and C therefore have a horizontal distance of 1 km and 2 km from the center of the source
respectively.
Source detection with 2D-TRM and 3D-display
The images resulting from 2D TRM are presented in full 3D display in Figure 2. They are analyzed
for two imaging conditions:
 Maximum absolute particle displacement (MAP): max t[ 0,T ] u  x, t 
(1)
  x, t  x, t 
(2)
 Maximum energy density (MED): max t[ 0,T ]
ij
i
ij
j
Figure 2a presents MAP described by equation (1) and Figure 2b presents MED described by equation
(2). Note that an individual color range for each slice is applied. The circle surrounds the source
location. The dashed white lines in all slices indicate depth and Northing of the source location.
Both images render focusing spots at the source location in plane A. A remarkably weaker focusing
spot also appears for plane B in both images. However, an isolated focusing spot is present for MAP
and absent for MED on plane C. Furthermore, both images render traces of high values between the
surface and the source location. These traces are artifacts due to discrete seismometer spacing and the
velocity model. The artifacts, already discussed in detail by Steiner (2009), are considerably narrow
for plane A and become weaker for planes B and C.
Figure 2 2D TRM images in 3D display with data shown in Figure 1: (a) Maximum absolute particle
displacement and (b) maximum energy density. The circle surrounds true source location in plane A.
The dashed white lines indicate depth and Northing of the source. Strong focusing patterns are visible
for plane A. They are weaker for plane B and disappear for plane C.
A source generally remains locatable with 2D TRM as visible in plane A. However, plane B shows an
artificial focusing which spatially meets the location of the focusing spot in plane A. A source being
active outside of this plane creates a focusing spot which could be interpreted as a true source within
this plane. However, comparison of the planes illustrates that the focusing spot in plane B is a side
effect as it is much weaker as the focusing spot in plane A. Risk of misinterpretation is significantly
reduced by comparison of multiple 2D slices in full 3D display.
72nd EAGE Conference & Exhibition incorporating SPE EUROPEC 2010
Barcelona, Spain, 14 - 17 June 2010
Discussion & Conclusion
The concept of performing multiple 2D reverse simulations and successive comparison of the images
in 3D display is presented. Reduction of 3D information of a wave field to 2D signals for 2D reverse
propagation causes partial loss of directivity and particle motion of the measured wave field. We
investigated discarding the component perpendicular to the plane and using only the other two
components as input signals for reverse propagation. This approach conserves the particle motion
regardless of their affiliation to specific wave modes. Out-of-plane P-waves and in-plane SH-waves
with particle motion perpendicular to the plane are discarded. Furthermore, out-of-plane SH-waves
with particle motion perpendicular to the plane are incorrectly treated as in-plane SH-waves with
particle motion parallel to the plane. Nevertheless, a seismic source in the subsurface remains
locatable in the TRM images. A strong focusing spot is visible for the plane which contains the
seismic source. However, this focusing point is still present at the same location for neighbored planes
which do not contain the source. Its strength significantly weakens with increasing lateral distance
between the plane and the source location. It disappears at a distance roughly corresponding to two
wavelengths of the recorded signals. A simultaneous display of all 2D planes in one 3D image
visualizes this context in a useful way. Multiple 2D TRM images compared with each other after
merged to a 3D image seem to allow reliable localization of a seismic source. Continuative studies
aim to qualitatively and quantitatively evaluate the validity of 2D TRM and possible necessity of 3D
imaging techniques.
Acknowledgements
We thank Rohöl-Aufsuchungsgesellschaft (RAG) and Proseis AG for providing the velocity model.
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72nd EAGE Conference & Exhibition incorporating SPE EUROPEC 2010
Barcelona, Spain, 14 - 17 June 2010