technical article
first break volume 31, April 2013
Automated salt body extraction from
seismic data using the level set method
Jarle Haukås,1* Oda Roaldsdotter Ravndal,1 Bjørn Harald Fotland,1 Aicha Bounaim1 and Lars
Sonneland1
Abstract
A solution for automated salt body extraction from seismic data has been developed. The solution is based on a level set
algorithm, used in combination with seismic attributes that discriminate between salt and sediments and highlight top and
base salt reflections and terminations of sediments against salt. In an automated process, steps to obtain the gross volume of
salt are combined with local adjustments to place the salt boundary at the appropriate attribute extrema. The process also
includes a local stop criterion based on a salt boundary confidence measure. The ability to separate completed salt boundary
parts from uncertain regions where the salt boundary has not been identified enables the interpreter to focus on the parts
where manual interpretation is required. User constraints, including manual interpretations, are honoured by the algorithm.
The methodology is demonstrated on a multi-client seismic data set from the Gulf of Mexico.
Introduction
In recent years, major hydrocarbon discoveries have been
made in deep-water, subsalt basins. When exploring for subsalt hydrocarbon plays, a proper model of the salt deposits is
of great importance, both for the seismic depth imaging, and
for identifying salt-related drilling hazards.
The current state of the art in salt body extraction is a
time-consuming process, mainly based on manual interpretation. In an iterative depth migration process, the time spent
on interpreting salt bodies is multiplied by the number of
required migration iterations. To speed up salt body extraction from seismic data and better assess the quality of the
extracted salt bodies, an automated process is needed.
Automated salt body extraction should aim at pulling out
all relevant salt bodies from a seismic volume. The interfaces
between salt and sediments should be properly identified,
i.e., as attribute extrema or sediment terminations. The
extraction should also allow for the possibility that there are
sediments within the salt body. The algorithm must handle
complex geometries, e.g., top and base salt should not be limited to surfaces that are single-valued in depth. In addition,
the quality of the extracted salt body should be assessed, so
that the manual quality control and editing to produce the
final result is reduced to a minimum.
Automated salt body extraction from seismic data has
been discussed by several authors. Lomask et al. (2007)
described the use of the normalized cut algorithm; Ferguson
et al. (2010) produced geobodies from thresholds of various
seismic attributes; and Berthelot et al. (2011) described an
approach based on graph-cut.
1
*
In this paper, we describe automated salt body extraction using the level set method. The level set method is
a well-known method for tracking interfaces and shapes
(Osher and Sethian, 1988). A broad overview of the level
set method and its applications was provided by Sethian
(1999). An advantage of the level set method is that it does
not require an explicit surface parameterization, and can
easily follow objects that change topology, e.g., split and
develop holes, and the reverses of these operations. The
use of the level set method for interactive visualization and
interpretation of geobodies was discussed by Kadlec et al.
(2009).
Automated salt body extraction relies on a set of seismic
attributes that can help to identify a proper salt body.
Examples include attributes related to the structure of the
seismic, reflectivity, and amplitude extrema. An overview
of seismic attributes is given in Iske and Randen (2000),
and references to the extrema technology include Sonneland
(1994) and Borgos et al. (2009). Attributes for salt body
extraction were also discussed by Ferguson et al. (2010) and
Berthelot et al. (2011). However, since attribute responses
are not always sufficient to give a complete and geologically
reasonable definition of the salt body, the algorithm should
honour user constraints, e.g., manually interpreted parts of
the salt boundary.
The automated salt body extraction methodology presented in this paper includes a local stop criterion. The stop
criterion means that further calculations are omitted in
regions where a salt boundary has been found, i.e., where the
level set evolution of the salt body has stopped. Thus com-
Schlumberger Stavanger Research, PO Box 8013, N-4068 Stavanger, Norway.
Corresponding author, E-mail: jhaukaas@slb.com
© 2013 EAGE www.firstbreak.org
35
technical article
first break volume 31, April 2013
putation is speeded up, and it is also possible to distinguish
between completed and still evolving parts of the salt body in
the extraction process. Consequently, attention can be drawn
to the parts that require further investigation.
The implemented automated salt body extraction tool
addresses performance and memory usage, and enables
extraction of salt bodies from large data sets, possibly at basin
scale. In this paper, examples are from the Gulf of Mexico. The
tool has also been tested on data from Angola and offshore
Brazil.
Level set method
The level set method is based on solving a differential equation that describes the motion of an object boundary subject
to forces. In this application, the object is a salt body. The salt
body is represented by a pseudo seismic cube where positive
voxels represent the inside of the salt body, while negative
voxels represent the outside of the salt body. The initial set
of salt voxels is specified by the user, and can range from a
set of points to a voxel body.
Throughout the extraction process, the salt boundary
is implicitly defined by the iso-surface(s) of value zero in
the pseudo seismic cube. Artificial forces based on seismic
attributes are applied to move the salt boundary so that it
becomes consistent with the attribute responses.
Three types of forces have been implemented: a normal
force that acts normal to the salt boundary (positive force
expands body, negative force shrinks body); a directional
force that acts in a specific direction locally; and a smoothness force that controls the smoothness of the salt boundary.
Different forces can be combined and weighted differently
in different regions. The implemented forces are illustrated
in Figure 1.
In cases where salt is characterized by lack of spatially
coherent seismic reflections, a useful attribute is the squared
Frobenius norm of the local structure tensor, as described
below. The attribute discriminates between regions where
the seismic reflections are spatially coherent, e.g., locally
stratified, and regions where there is no spatial coherency.
The basic idea is that in stratified regions, a locally consistent
set of normal vectors to the strata can be generated, whereas
in salt regions, the normal vector field has no preferred
orientation.
To calculate the normal vector field, we use a polynomial reconstruction of the seismic signal (Sonneland,
1994). This allows for calculation of analytical derivatives
in each direction (inline, crossline, vertical). The vector
of first order derivatives is referred to as the gradient of
the seismic data, and represents the direction of steepest
ascent/descent in terms of amplitude. Assuming that there
exists a sub-horizontal layer structure in the seismic data,
represented by iso-surfaces, we can use the derivatives to
construct representative normal vectors to the iso-surfaces.
Appropriate iso-surfaces are the zero values of the seismic
amplitude and the zero values of the vertical derivative of
the amplitude. The latter are referred to as extrema surfaces
(Borgos et al., 2009). For consistency, upwards pointing
vectors are chosen, and the vectors are normalized to unit
length.
To analyse the local variations in the normal vector field
at a given scale, a 3D neighbourhood around each voxel is
defined, and the normal vectors
, i = 1,2,...,N in
that neighbourhood are used to form a local structure tensor
.
Obtaining the gross volume of salt
The normal forces used in the salt body extraction process
are associated with attributes that separate salt from sediments. The forces are applied so that the salt body expands
if the attributes indicate salt, and shrinks if the attributes
suggest sediment.
a
b
The structure tensor can be analysed in terms of principal
directions (eigenvectors) and their weights (eigenvalues λ1,
λ2, λ3). In particular, we can distinguish between stratified
regions where there is one dominating direction (λ1 ≈ 1, λ2 ≈
λ3 ≈ 0) and chaotic regions where there is no preferred orien-
c
Figure 1 The implemented forces and their effect when applied to an object. (a) A normal force field that is negative in the upper part and positive in the lower
part acts to shrink the upper part of the object and expand the lower part. (b) A directional force field locally pointed towards a pre-defined boundary acts to
move the object so that it fits with the boundary. (c) A smoothness force field acts to smooth the boundary of the object.
36
www.firstbreak.org © 2013 EAGE
technical article
first break volume 31, April 2013
a
c
b
d
tation (λ1 ≈ λ2 ≈ λ3 ≈ 1/3). Other limiting cases are regions
where two almost orthogonal directions are represented
(λ1 ≈ λ2 ≈ 1/2, λ3 ≈ 0), e.g., salt diapir tops, and regions where
chaos meets stratification (λ1 ≈ 2/3, λ2 ≈ λ3 ≈ 1/6), e.g., terminations. We note that the use of unit normal vectors implies
that the eigenvalues sum to unity. The limiting cases are
shown in Figure 2.
The squared Frobenius norm of the structure tensor,
which is defined as the sum of the squares of the eigenvalues,
is a convenient measure of the eigenvalue distribution. It can
also be calculated as the sum of the squares of the diagonal
elements of the structure tensor, so no explicit eigenvalue
decomposition is required. Furthermore, it gives the required
discrimination between stratified regions (λ1 ≈ 1, λ2 ≈ λ3 ≈ 0, so
the squared Frobenius norm is ≈ 1), chaos/salt (λ1 ≈ λ2 ≈ λ3 ≈ 1/3,
so the squared Frobenius norm is ≈ 1/3) and terminations/salt
diapir tops (λ1 ≈ λ2 ≈ 1/2, λ3 ≈ 0 or λ1 ≈ 2/3, λ2 ≈ λ3 ≈ 1/6, so the
squared Frobenius norm is ≈ 1/2)
a
b
Figure 2 Four limiting cases for analysing the local
structure tensor based on the seismic normal vector field: (a) mostly one dominant direction; (b)
two almost orthogonal directions represented; (c)
stratification meets chaos (terminations); and (d)
no dominant direction (chaos).
For convenience, the squared Frobenius norm is
rescaled so that it is +1 in regions indicating chaos/salt,
–1 where the attribute suggests strata, and 0 where the
squared Frobenius norm indicates a transition region or
terminations of the strata against salt. The use of a normal
force based on the squared Frobenius norm is illustrated
in Figure 3.
In regions with poor spatial coherency, e.g., resulting
from inferior signal to noise conditions, or if the salt is
stratified, salt may not be discriminated from sediments
using the squared Frobenius norm. In that case, seismic
amplitude may be used as a normal force, taking advantage
of the fact that sediments typically have different seismic
reflectivity than salt. In general, any attribute that discriminates salt from sediments can be used as a normal force.
The attributes described above are useful for extracting
the gross volume of salt. They also allow for the identification of stratified pockets inside salt. Furthermore, in regions
c
Figure 3 Level set salt body extraction based on the normal vector field attribute: (a) seismic intersection and corresponding intersection of extracted boundary
in green; (b) intersection of rescaled Frobenius norm attribute (red indicates lack of spatially coherent seismic reflections, blue indicates locally stratified region)
and corresponding intersection of extracted boundary in green; and (c) 3D view of extracted salt body.
© 2013 EAGE www.firstbreak.org
37
technical article
first break volume 31, April 2013
a
a
b
b
c
c
Figure 4 Use of directional force based on gradient of seismic data: (a) seismic
intersection and initial boundary (black line); (b) vertical component of the
gradient of the seismic data (blue indicates force pointing downwards, red
indicates force pointing upwards); and (c) boundary after applying force
(green line).
where there is no clear reflector representing the salt boundary, the attributes provide an unbiased salt interpretation.
Local adjustments to the salt body
In regions where the salt boundary is represented by an
amplitude peak or trough, the extracted salt body can be
further improved. Given that the starting point is sufficiently
close to the appropriate peak or trough, the gradient of the
seismic data, as described above, is used as a directional force
to pull the salt boundary to the correct amplitude extrema.
38
Figure 5 Effect of applying a smoothness constraint. (a) Normal force attribute
(blue colours indicate positive normal force, red colours indicate negative normal force, white represents zero values). The black line is the boundary starting point. (b) Green line illustrates boundary that results from applying the
normal force with a smoothness constraint. The result represents a smooth
envelope of the positive (blue) attribute values. (c) Green line illustrates a
boundary that results from applying normal force with no smoothness constraints. This result includes narrow, non-smooth features.
The force is directed towards the closest peak (or trough),
and can be scaled so that it only moves the boundary in
regions of strong amplitudes, i.e., where the salt boundary
corresponds to a clear reflector (Figure 4).
Smoothness constraints
Depending on the quality of the seismic data, the attribute
response may be noisy, possibly leading to extraction of a
www.firstbreak.org © 2013 EAGE
technical article
first break volume 31, April 2013
a
b
c
d
Figure 6 Illustration of the stop criterion showing the salt boundary in 3D overlain on seismic intersections as the salt body is extracted. (a) Initial salt boundary
(pink). (b) Intermediate display. (c) Salt boundary after a prescribed number of iteration steps. Pink indicates still evolving parts of the object boundary, while
green indicates where evolution has stopped, suggesting a plausible salt boundary. (d) Completed salt boundary displayed separately.
highly irregular salt body including small narrow features that
should not be labelled as salt. However, by applying a smoothness constraint, problems with noisy regions can be avoided.
The smoothness constraint is based on a penalty term
associated with the mean curvature of the evolving boundary.
In addition to avoiding ‘leakage’ through a salt boundary
that has an incomplete attribute response, the smoothness
constraint provides a plausible interpolation in regions where
the normal and directional forces are weak/inconclusive. The
smoothness constraint may be different in different regions, as
specified by the user. If required, the smoothness force can be
used in a separate post-processing step to obtain a smoother
salt boundary.
Figure 5 illustrates the effect of applying a smoothness
constraint together with a normal force field that discriminates
between salt and sediments. The normal force is the squared
Frobenius norm of the local structure tensor in a 5 × 5 × 5
neighbourhood around each voxel, rescaled so that +1 corresponds to no spatially coherent seismic events, whereas –1
corresponds to local stratification (one consistent dominating
normal vector represented in the data). As illustrated, the
smoothness constraint helps to avoid leakages and provides
a smooth transition in zones where a clear boundary is not
evident from the squared Frobenius norm attribute.
© 2013 EAGE www.firstbreak.org
Stop criterion
When the level set evolution stabilizes in a region due
to equilibrium of the applied forces, it suggests that a
plausible boundary has been identified. However, unless
otherwise specified, calculations would continue in this
region. Depending on the stability of the force equilibrium
and the smoothness constraints, the extracted body could
eventually start moving away from the plausible boundary.
To solve this problem, a stop criterion has been introduced.
The criterion says that if a voxel has been in the boundary
set for more than a prescribed number of iteration steps, the
voxel and the corresponding boundary can be regarded as
completed. Consequently, the risk of missing plausible salt
boundaries is reduced. At the same time, the overall run
time is reduced, since calculations in the completed regions
can be omitted.
By using the stop criterion, the extracted boundary
can be split into regions where the evolution of the salt
body is completed, and regions where the evolution has
not yet hit a proper salt boundary. This is an important
input for quality control and editing of the level set result,
as it highlights the regions where further investigation is
needed. Such a separation is also useful in an iterative depth
migration process, where top salt often must be established
39
technical article
a
first break volume 31, April 2013
b
Figure 7 User-constrained salt body extraction. (a) Interpreted top salt input to salt body extraction tool as an explicit user constraint. (b) Salt body (green volume) extracted by specifying a seed point below the user-constrained region, and applying a uniform positive normal force together with the local directional
force field imposed by the user constraint.
a
b
Figure 8 Polygon-based initialization of a level set salt body. (a) Quick interpretation in terms of polygons. (b) Corresponding voxel body used as the starting
point for the level set algorithm.
before base salt can be identified. In that case, the level set
algorithm can be stopped when top salt is completed, even
if no proper base salt interface has been identified. After a
new migration step that improves the base salt definition, the
level set algorithm can be restarted from the previous result.
The stop criterion concept is illustrated in Figure 6.
User interaction
If a previous salt boundary interpretation exists, or the interpreter wants to override the level set salt body extraction, an
interpreted boundary can be input as an explicit user constraint. In the algorithm, a local directional force field is used
to honour that constraint, and all other forces are ignored in
the neighbourhood of the constraint. The directional force
field points towards the location of the constraint. Figure 7
illustrates how a user constraint is honoured. Other examples of user constraints include gravimetric constraints, i.e.,
40
limiting the vertical extent of the extracted salt body to honour the measured gravimetric response.
In addition, a volumetric starting point for the level set evolution can be provided by the user through polygons interpreted
at a series of seismic intersections (Figure 8). A quick polygon
based interpretation that puts the boundary sufficiently close to
the correct amplitude extrema is an excellent starting point for
using the gradient of the seismic as a directional force.
Salt body extraction workflow
The salt body extraction workflow is summarized in Figure 9.
Starting from the seismic data, a normal force field based on
attributes that separate salt from sediments is generated. Salt
boundary attributes, e.g., the gradient of the seismic data,
are used as directional forces. Additional constraints include
interpreted salt boundaries and gravimetric constraints. The
starting point for the salt extraction algorithm is specified in
www.firstbreak.org © 2013 EAGE
technical article
first break volume 31, April 2013
Figure 9 Salt body extraction workflow.
a
b
terms of a set of seed points or a voxel body. The voxel body
can be a result of a previous extraction, or a quick interpretation in terms of polygons as illustrated in Figure 8. The
level set algorithm is run for a specified number of iteration
steps, possibly stopping locally due to the stop criterion. The
extracted result is a voxel body, converted into a triangular
mesh if required. The result is quality controlled and postprocessed (e.g., smoothed), and can be used in velocity modelling, and drilling hazard analysis. If another migration step
is required, the process can be repeated on the re-migrated
data.
Field tests
The methodology has been tested on multi-client seismic
data. As part of a feasibility study on data from the Gulf
of Mexico (E-Wave pilot area), an already interpreted salt
body was adjusted to the appropriate peak/trough using the
process illustrated in Figure 4. The subsequent re-migration
of the data set improved the boundary between salt and
sediments significantly. In addition, a gross salt extraction
© 2013 EAGE www.firstbreak.org
c
Figure 10 Comparison of the level set result to the original salt model.
(a) Regions where the level set result and the original model coincide. (b)
Additional regions of salt suggested by the level set result. (c) Illumination risk
map – strong red values indicate a high number of additional salt voxels, and
represent high risk of poor subsalt illumination.
41
technical article
using the normal vector field attribute as normal force was
performed, as illustrated in Figure 3. Based on the differences
between the level set extraction and the original salt body, a
subsalt illumination risk map was produced, representing the
regions where the attribute suggested that salt was missing in
the original model (Figure 10). This map coincided well with
poorly illuminated subsalt regions.
first break volume 31, April 2013
References
Berthelot, A., Solberg, A.H.S., Morisbak, E. and Gelius, L-J. [2011] Salt
diapirs without well defined boundaries – a feasibility study of semiautomated detection. Geophysical Prospecting, 59, 682–696.
Borgos, H.G., Kvia, P., Skov, T., Sonneland, L. and Randen, T. [2009]
Extrema Classification. United States Patent 7,248,539.
Ferguson, C.J., Avu, A., Schofield, N. and Paton, G.S. [2010] Seismic
analysis workflow for reservoir characterization in the vicinity of salt.
Conclusions
An automated tool for salt body extraction using a level set
algorithm has been developed. The methodology includes
the use of normal forces based on attributes that separate
between salt and sediments, directional forces based on the
gradient of the seismic data or other salt boundary attributes,
and smoothness constraints for interpolation/smoothing. A
stop criterion helps to discriminate between completed parts
of the boundary and parts that need further investigation.
The methodology has been tested on data from the Gulf
of Mexico, Angola, and offshore Brazil. The automated salt
body extraction methodology has potential to greatly reduce
time spent on salt interpretation, and improve the quality of
the associated depth-migrated seismic data.
First Break, 28(10), 107–113.
Iske, A. and Randen, T. (Eds.) [2000] Mathematical Methods and Modelling
in Hydrocarbon Exploration and Production. Springer, Berlin.
Kadlec, B.J., Dorn, G.A. and Tufo, H.M. [2009] Interactive visualization
and interpretation of geologic surfaces in 3-D seismic data. 79th SEG
Annual Meeting, Expanded Abstracts, 1147–1151.
Lomask, J., Clapp, R.G. and Biondi, B. [2007]. Application of image
segmentation to tracking 3D salt boundaries. Geophysics, 72, 47–56.
Osher, S. and Sethian, J.A. [1988] Fronts propagating with curvaturedependent speed: algorithms based on Hamilton-Jacobi formulations.
Journal of Computational Physics, 79, 12–49.
Sethian, J.A. [1999] Level Set Methods and Fast Marching Methods, 2nd
edn. Cambridge University Press, Cambridge.
Sonneland, L. [1994] A Method of Processing Seismic Data Signals
(VRS/Orthogonal Polynomial Spectral Decomposition). PCT Patent
Acknowledgements
We thank Schlumberger GeoSolutions, Houston for providing data for testing and for valuable feedback on the usability of the automated salt body extraction tool.
42
Application No. WO/9837437.
Received 5 February 2013; accepted 14 February 2013.
doi: 10.3997/1365-2397.2013009
www.firstbreak.org © 2013 EAGE