Neural network modeling of Herglotz—Wiechert inversion of multiparametric travel-time curves of seismic waves
Using artificial neural networks to solve a problem of plotting travel-time curves of seismic waves can create nonlinear travel-time model of P and S phases of seismic waves arrangement as a function of several arguments: source depth, magnitude, back azimuth and epicenter distance. Construction of...
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| Cite this: | Neural network modeling of Herglotz—Wiechert inversion of multiparametric travel-time curves of seismic waves / M. Lazarenko, O. Herasymenko // Геофизический журнал. — 2017. — Т. 39, № 4. — С. 3-14. — Бібліогр.: 8 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1252742025-02-09T22:20:49Z Neural network modeling of Herglotz—Wiechert inversion of multiparametric travel-time curves of seismic waves Lazarenko, M. Herasymenko, O. Using artificial neural networks to solve a problem of plotting travel-time curves of seismic waves can create nonlinear travel-time model of P and S phases of seismic waves arrangement as a function of several arguments: source depth, magnitude, back azimuth and epicenter distance. Construction of three-dimensional travel-time relationships and their use for modeling of hadographs and their inversion are considered on examples of seismic records Ukrainian seismic stations. Examples of inversion locus within the model Herglotz—Wiechert and features of application of the model in a real environment for single seismic stations, and generalization for arbitrary coordinate of the source and the point of signal registration in the Black Sea region are given. Використання мереж штучних нейронів у задачі побудови годографів сейсмічних хвиль дає змогу створювати нелінійні моделі поля часів поширення P- і S-фаз сейсмічних хвиль як функцій декількох аргументів: глибини розміщення вогнища, магнітуди, азимуту надходження хвиль і епіцентральної відстані. Побудову тривимірних годографів розглянуто на прикладах сейсмічних записів українських сейсмостанцій і їх використання для моделювання годографів та інверсії останніх. Наведено приклади інверсії годографа в рамках моделі Герглотца— Віхерта, а також особливості застосування моделі в реальному середовищі для одиничних сейсмостанцій і узагальнення для випадку довільних координат джерела і точки реєстрації сигналу в Чорноморському регіоні. 2017 Article Neural network modeling of Herglotz—Wiechert inversion of multiparametric travel-time curves of seismic waves / M. Lazarenko, O. Herasymenko // Геофизический журнал. — 2017. — Т. 39, № 4. — С. 3-14. — Бібліогр.: 8 назв. — англ. 0203-3100 DOI: doi.org/10.24028/gzh.0203-3100.v39i4.2017.107503 https://nasplib.isofts.kiev.ua/handle/123456789/125274 550.344.094.6:528.087.4:004.032.26 en Геофизический журнал application/pdf Інститут геофізики ім. С.I. Субботіна НАН України |
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Using artificial neural networks to solve a problem of plotting travel-time curves of seismic waves can create nonlinear travel-time model of P and S phases of seismic waves arrangement as a function of several arguments: source depth, magnitude, back azimuth and epicenter distance. Construction of three-dimensional travel-time relationships and their use for modeling of hadographs and their inversion are considered on examples of seismic records Ukrainian seismic stations. Examples of inversion locus within the model Herglotz—Wiechert and features of application of the model in a real environment for single seismic stations, and generalization for arbitrary coordinate of the source and the point of signal registration in the Black Sea region are given. |
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Lazarenko, M. Herasymenko, O. Neural network modeling of Herglotz—Wiechert inversion of multiparametric travel-time curves of seismic waves Геофизический журнал |
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Lazarenko, M. Herasymenko, O. |
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Lazarenko, M. |
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Neural network modeling of Herglotz—Wiechert inversion of multiparametric travel-time curves of seismic waves |
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Neural network modeling of Herglotz—Wiechert inversion of multiparametric travel-time curves of seismic waves |
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Neural network modeling of Herglotz—Wiechert inversion of multiparametric travel-time curves of seismic waves |
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Neural network modeling of Herglotz—Wiechert inversion of multiparametric travel-time curves of seismic waves |
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Neural network modeling of Herglotz—Wiechert inversion of multiparametric travel-time curves of seismic waves |
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neural network modeling of herglotz—wiechert inversion of multiparametric travel-time curves of seismic waves |
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Інститут геофізики ім. С.I. Субботіна НАН України |
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Neural network modeling of Herglotz—Wiechert inversion of multiparametric travel-time curves of seismic waves / M. Lazarenko, O. Herasymenko // Геофизический журнал. — 2017. — Т. 39, № 4. — С. 3-14. — Бібліогр.: 8 назв. — англ. |
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AT lazarenkom neuralnetworkmodelingofherglotzwiechertinversionofmultiparametrictraveltimecurvesofseismicwaves AT herasymenkoo neuralnetworkmodelingofherglotzwiechertinversionofmultiparametrictraveltimecurvesofseismicwaves |
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Neural Network modeliNg of Herglotz—wiecHert iNversioN of multipara ...
Геофизический журнал № 4, Т. 39, 2017 3
Herglotz—Wiechert inversion of the tra
vel-time curves of seismic waves, recorded
by the network of seismic stations, gene
rated by 4dimentional model. The number
of recorded events with reliably defined ar-
rivals of the phases of seismic waves are 392
for the seismic station (s/s) «Skvira», 501 for
s/s «Odessa», and 371 for s/s «Poltava». Each
seismic event, recorded at stations «Odessa»,
«Skvira» and «Poltava», was characterized by
the following vector of parameters
( ), ,1 ,2 ,4, , , ,n i n n n nx x x x t= , (1)
where x1=h (focal depth), x2=M (magnitude),
x3=r (distance), x4=b_az (back azimuth), tn is a
target value, which is equal to the arrival time
to the observation point of a certain phase of
the wave, generated by the n-th earthquake
[Лазаренко, Герасименко, 2010].
The set of vectors for each seismic station
was used as a training layered, fully connec-
ted, strait-line, managed network of artificial
neurons model travel-time curve at three
seismic stations with the parameters listed in
SET1.
A set of such vectors for each seismic sta-
tion was used as a learning set for a direct
flow, multilayered, fully connected, con-
trolled network of artificial neurons [Хайкин,
2008], using for learning a method the back-
ward transmission of errors in neural networks
[Chauvin, Rumelhart, 1995], while a sigmoid
function in the form of a hyperbolic tangent
was used as an activation function (Fig. 1).
In view of the mentioned above, the con-
nectionist model of a seismic wave propaga-
tion time was designed as a combination of
Fig. 1. Schematic diagram of a three-layer network of
artificial neurons.
УДК 550.344.094.6:528.087.4:004.032.26 DOI: http://dx.doi.org/10.24028/gzh.0203-3100.v39i4.2017.107503
Neural network modeling of Herglotz—Wiechert inversion
of multiparametric travel-time curves of seismic waves
© M. Lazarenko , O. Herasymenko, 2017
Institute of Geophysics, National Academy of Sciences of Ukraine, Kiev, Ukraine
Received 2 February 2017
Використання мереж штучних нейронів у задачі побудови годографів сейсмічних хвиль
дає змогу створювати нелінійні моделі поля часів поширення P- і S-фаз сейсмічних хвиль як
функцій декількох аргументів: глибини розміщення вогнища, магнітуди, азимуту надходження
хвиль і епіцентральної відстані. Побудову тривимірних годографів розглянуто на прикладах
сейсмічних записів українських сейсмостанцій і їх використання для моделювання годогра-
фів та інверсії останніх. Наведено приклади інверсії годографа в рамках моделі Герглотца—
Віхерта, а також особливості застосування моделі в реальному середовищі для одиничних
сейсмостанцій і узагальнення для випадку довільних координат джерела і точки реєстрації
сигналу в Чорноморському регіоні.
Ключові слова: нейронна мережа, поширення сейсмічних хвиль, навчання, інверсія Гер-
глотца—Віхерта, розбіжності, годографи, градієнт швидкості.
m. lazareNko , o. HerasymeNko
4 Геофизический журнал № 4, Т. 39, 2017
nonlinear outputs (in notation of Fig. 1) of
nodes h of the hidden layer
1
h
k k kj j k
j
y f b
=
= +
∑w z w , (2)
where
1
n
j j hi i h
i
z f b
=
= +
∑w x w (3)
and ( )if • is the function of firing a neuron.
Thus a set is formed to learn the network
of artificial neurons. After learning the latter
forms the recording model for the seismic
wave phases relating to the specific seismic
station and the area the learning set relates to.
In the real-time mode, this model enables to
forecast the s/s arrival time of a seismic wave,
generated at a random point of the simulated
area, with the source parameters within the
range of the existence intervals of the vector
components of the learning set.
The domain within the northern latitude, φ,
and the eastern longitude, λ, ranges from 50
to 36° and 25 to 42°, respectively, was cho sen
for the modelling of the travel-time curves of
P- and S-seismic waves. In the selected region,
«fields», controlled seismic stations «Skvira»
and «Poltava», have dimensions of 1250—
1500 km, and «Odessa» — 1250÷1200 km
(Fig. 2).
The learning of the travel-time curve NN
Fig. 2. Map of the region of research.
Ta b l e . Parameters used in the NN learning=4: 20: 7: 2: 1
Seismic
Event
Station
Total
Events
Coefficient of
learning speed Learned×10–1 <5 % Specific
error, s
Standard
deviation, s
от 2,5×10–1 P S P S P S P S
Skvira 392/359 до ~4,0×10–5 6,8 4,3 13 10 3,7 2,6 2,6 1,7
Odessa 501/483 до ~2,5×10–5 6,6 4,9 27 15 3,2 2,8 1,6 2,1
Poltava 371/357 до ~6,0×10–4 7,7 6,1 10 8 3,2 2,6 3,2 2,6
Neural Network modeliNg of Herglotz—wiecHert iNversioN of multipara ...
Геофизический журнал № 4, Т. 39, 2017 5
model for these seismic stations was studied
with the parameters, shown in Table. The
learning was carried out in the stochastic
mode with a hyperbolic tangent as the activa-
tion function for all the hidden words, exclud-
ing the output one, for which a unit (linear)
function was used. The learning samples in-
clude the events, falling within the epicentral
distance range of 2000 km for each seismic
station. The number of these events in the
table after a slash is shown. The normaliza-
tion of input data was carried out for the mean
range, as well as for the range equal to 0, and
the range equal to 2.
The learning was carried out in the interac-
tive mode, opening the access to the global
parameters of learning after the execution of
some (controlled) number of the iterations or
epochs, referred to as «silent» epochs. The
learning level of the model was estimated by
the number of the members of the learning
sample, for which the mis-tie between the
output of the network and the size of its tar-
get value exceeded 5 % of the latter, which
matches the value of the characteristic func-
tion ϕ =1.
1,
( )
0, not
p p
kif y t
y
− ≤eϕ =
. (4)
Here p
ky is the network output, exited by
р-th member of the training sample, t
p is a tar-
get value, e=5б0×10–3t
p. The process control
of the training was based on rating the beha-
viour of the loss function, a specific error of
miss-ties in the subset of the members of the
training sample, not meeting the term ϕ(y)=1.
The residual value in the subset of «un-
permitted» members of the training sample is
usually distributed uniformly. Any deviations
from such uniformity are usually caused by
accidental errors, introduced at the stages of
collection, primary processing and different
types of manipulating the seismic data.
The neural network model of the 4-dimen-
sional field of the arrival times of the seismic
wave phases to the observation point enables
the generation of travel-time curves for a ran-
dom azimuth within the plane of the area un-
der study. It is known that in the case of the
medium, having a horizontal zero gradient
of the propagation velocity of elastic waves
and a non-decreasing gradient with depth,
the inverse problem for a time curve has a
Herglotz—Wiechert (H-W) unique solution
and is written in the Abel form:
( ) ( )2
0
1 ln 1
x
z x k k dx= + −
π ∫ , (5)
where
( )
x
x
tk x
t
∂
∂= , x — is the distance to the
point of a ray exit to the earth surface, t — is
the time at an exit point and
( ) ( )
x
dxv z x dt = (6)
is the phase velocity at the point of the maxi-
mum immersion of a ray in the medium.
For any length of the hodograph, simu-
lated along the path, drawn from a seismic
station through a random node of the region,
the estimates of the maximum depth of the
ray penetration and phase velocity at this
depth may be obtained. Actually, these esti-
mates are obtained for a certain infinitely thin
plate, along the upper edge of which the path
Fig. 3. The behaviour of the loss function depending on the number of iterations in training the NS models of the
arrival times of the P and S phases of seismic waves to seismic stations «Skvira», «Odessa», «Poltava».
m. lazareNko , o. HerasymeNko
6 Геофизический журнал № 4, Т. 39, 2017
under consideration lies [Lay, Wallace, 1995].
Since, by the definition, the seismic velo-
city is independent of the horizontal coordi-
nate, all the estimates of the velocities and the
depths may be attributed to a random position
along the path, say, a net node, and written
in the form of two sequences: depths and the
velocities matching these depths. It is evident
that such two vectors may be obtained for
each net node, and the distribution of phase
velocities may be built by interpolation within
the bounds of the net region from a certain
range of depths.
As it was previously noted, the solutions
(5) and (6) allow to find the values of the
maximum depths of the ray penetration and
the velocities matching them at the nodes of
the net covering the region (Fig. 4) and to
estimate the velocity at any point within the
depth range studied.
The survey sheets of the three seismic sta-
tions are net regions with a spacing of nodes
longitudinally (х) and latitudinally (у), equal
to 50 km.
The seismic stations are placed at the up-
per edge of the survey sheets (see Fig. 4),
Fig. 4. The ray penetration depth and the phase velocity at the depth.
Fig. 5. Contour diagrams of the velocity gradients of the Р and S seismic waves at the depth of 50 km, obtained
as result of inverting the time curves, generated by the connectionist model of the arrival times of the phases,
recorded at s/s «Skvira».
Neural Network modeliNg of Herglotz—wiecHert iNversioN of multipara ...
Геофизический журнал № 4, Т. 39, 2017 7
and for each of them the H-W inversion of
the travel time of the Р and S seismic waves
was carried out for the simulated travel-time
curves.
It is more convenient to represent the
three-dimensional images of the velocity
vectors of seismic waves in the form of their
gradients, as it is shown in Fig. 5 for three
seismic stations at the depth of 50 km.
The estimatees of the velocities at nodal
points of the net, carried out under the «fan-
ning» scheme, do not consider the variations
in the velocity along the path but rather simu-
late only the dependence of the wave arrival
on the direction due to the velocity variation
between the paths. It is evident that the path
spacing, controlled by the density of the net,
determines the discreteness of this quasi
three-dimensional image.
The dependence of the maximum depths
of the ray penetration on the length of a tra-
vel-time curve may be used to estimate a deep
structure of the geological medium beneath
the studied area.
It is clear that the plotting of the time curves
for separate seismic stations, using a gene-
ralising (4-dimentional) approach, although
extends the assortment of the studied chara-
cteristics of the propagation medium of seis-
mic waves in comparison with the traditional
approach, using a 1-dimensional time curve,
but narrows its application, enabling the re-
ception of only gradient estimates (Fig. 5) of
the phase velocities of seismic waves at the
depths, which are limited by the stationarity
of the behaviour depending on the maximum
depth of the ray penetration from the epicen-
tric distance.
Under the similar scheme of representing
the gradient of the velocity, based on simula-
ting of the seismic wave arrival times to all the
nodes of the net, we get the estimates of the
gradient in the form of the projection on the
direction (see Fig. 5).
The interpolation of nodal estimates en-
ables to develop 3D images. To illustrate, in
Fig. 5 the contour diagrams of the velocity
gradients of the P and S seismic waves are
shown for a depth of 50 km. Variation of the
direction of the velocity gradient recorded at
different stations reflects the peculiarity of
the movements of another nature prevailing
in the formation process of the tectonic struc-
tures of a various origin. It was taken into ac-
count in choosing the location of the seismic
stations within the territory of Ukraine. The
configuration of the seismic net was devel-
oped not only to study the seismic activity
between and inside the platforms, but also
to study the intensity of distribution of the
impact from the Vrancea earthquakes in the
south-west and central Ukraine.
It is evident that the connectionist models
for the seismic stations, located, for example,
on the boundaries of a certain net region, will
generate the time curves of the H-W inver-
sion, which allow to estimate the projection
of the velocity gradient in «their» direction,
i. e., the tangents to the circle of the s/s-node
radius. Whereas it is easy to recover the vec-
tor by its components.
Herglotz—Wiechert inversion of the
travel-time curves generated by the 9-di-
mensional model. In plotting the local time
curves for a seismic station, the coordinates of
the latter are not the information parameters.
For all example vectors of the behaviour of
the time function of the phase arrival, they
are single, and the position of the epicentre
is unambiguously determined by the vector
components: epicentric distance and azimuth.
Whereas the development of a generalized
model for a certain region assumes the com-
pilation of the training sample within a wide
range of the epicentric distance, containing
the examples of the events, exited not only in
a lot of sources, but also recorded in a lot of
seismic stations.
Such an approach is directed towards en-
suring the coverage by the propagation paths
of the signals from the area involved with the
uniformity as large as possible, and assum-
ing the presence of seismic anisotropy. In
this case, the position of the epicentre is not
unambiguously determined by an epicentric
distance and azimuth any longer, and should
be set in the explicit form. Therefore, the di-
mension of the vector (1) increases to N=9,
where х is an elevation of the seismic station
above sea level.
m. lazareNko , o. HerasymeNko
8 Геофизический журнал № 4, Т. 39, 2017
Fig. 6. 3D image of the velocity gradients of Р and S seismic waves, obtained as a result of inverting the time curves,
Neural Network modeliNg of Herglotz—wiecHert iNversioN of multipara ...
Геофизический журнал № 4, Т. 39, 2017 9
generated by the connectionist model of the arrival times of the phases, recorded by the network of seismic stations.
m. lazareNko , o. HerasymeNko
10 Геофизический журнал № 4, Т. 39, 2017
The records of 4542 events in the area
under study with drawing a high-quality in-
formation from international seismic centres
ISC, NEIC, ORF were used for the results
under consideration. Such sample, used as a
learning one, enables the development of the
connectionist model, representing the arrival
times of seismic phases from a random shot
point to a random point of recording the area
under study.
Knowing the geographic coordinates of a
node, the azimuth of the path and the
length of the time curve, the coordinates
of points of its beginning and end may
be determined by the algorithm of the
inverse geodesic problem. [Sjöberg,
Shirazian, 2012; Поклад, 1988]. The el-
evation of the point above sea level was
estimated by the value of a certain ras-
ter element, applied on the net region,
and being the nearest to the node. The
values of elevation were introduced by
the GOOGLE-EARTH system, and their
density was set not less than 4 per cell of
the net region. The 9-dimensional neural
model enables the simulation of the time
curve along the paths, passing through
the given node with different azimuths.
This scheme for the case of one node is
shown in Fig. 8.
The 9-dimensional model generalizes
the results of the 4-dimensional one, elimina-
ting a «single-point referencing» to the con-
crete seismic station and enables the cover-
age of the space around the node, considered
as a midpoint for the family, with the wished
density of the path location.
Fig. 9 gives an example of varying the ve-
locities of the Р and S phases of seismic waves
in the Black Sea area at the depth of 70 km
as a mathematical expectation of the results
of inverting (5, 6) the family of direct and in-
Fig. 7. Scheme of the region of data collection. Black triangles
indicate the data used by international seismological centers.
Fig. 8. Layout of the paths around the net node as a midpoint of the family of the time curves.
Neural Network modeliNg of Herglotz—wiecHert iNversioN of multipara ...
Геофизический журнал № 4, Т. 39, 2017 11
verted time curves along 4
paths, passing with the spac-
ing of 45° through each node
of the net region.
Estimates of the maxi
mum depths of the ray pene
tration of the Р and S waves,
recorded by the network of
seismic stations. The up-
to-date notions of the deep
structure of the Earth contain
the information about a high
probability of the presence
of the areas of velocity inver-
sion in the crust and the up-
per mantle [Литосфера…,
1994; Гобаренко, Яновская,
2011], wherefore the confor-
mity of the results of using
the one-dimensional model
of inverting a time curve (5, 6)
lower these depths with the
actual structure of the me-
Fig. 9. Velocity gradient of the Р and S phases of seismic waves within the area around the Black Sea at the depth
of 70 km.
Fig. 10. The scheme of the directions of main seismically active cells of the
radiation sources, recorded by seismic stations «Odessa», «Skvira», «Pol-
tava», whereof the training sample is formed of the connectionist model of the
propagation times of seismic waves. The digits designate the back azimuths of
the radiation «centres» of five sectors of generating earthquakes for each s/s.
m. lazareNko , o. HerasymeNko
12 Геофизический журнал № 4, Т. 39, 2017
Fig. 11. The dependence of the maximum penetration depth rays P and S phase seismic waves from the epicentre
distance depending on the direction of the source of excitation signal registered on seismic stations network.
dium may raise a doubt. The non-conformity
of the H-W model with the actual medium is
contained in the requirement for the positiv-
ity of the velocity gradient with depth, that
is in the ban of the «layers» with a reduced
velocity — the H-W medium provides for the
increase in the maximum depth of the ray
penetration with the increase in the length
of a time curve. The deviation from this law
of nature may serve as a sign of breaking the
condition dv/dz>0.
Pursuant to Fig. 10 is given the dependence
of the depth of the ray penetration below on
the direction of the arrival of a seismic signal
Neural Network modeliNg of Herglotz—wiecHert iNversioN of multipara ...
Геофизический журнал № 4, Т. 39, 2017 13
from the Caucasus, Turkish, Mediterranean
(Greece, Italy) sources of earthquakes and the
Vrancea area, obtained in inverting the time
curves, generated by the connectionist model
for each of three seismic stations.
The figures show that the distortions in the
curve of the growth in the depths of the ray
maximum penetration are observed for all seis-
mic stations and both phases, but the nature of
these distortions is individual for each point of
reception and, although in a less degree, but
also for the azimuth of the arrival of a seismic
wave. Such behaviour of rating the maximum
depth requires a certain caution in using the
model of the H-W behaviour in this application
in the given area. In spite of the limitation of
the H-W model, its use attracts attention by
its analytical maturity and direct output of
results without any use of intermediate struc-
tures undergoing an iterative improvement.
Demonstrating the obtained results of us-
ing the inversion of the H-W connectionist
models of the time curves, the authors have
not set sights on interpreting various behav-
iour scenarios of the simulated function with
regard to the geologic structure of the con-
crete region under study. The point at issue is
about the possibility and necessity to develop
the operating algorithms of the modern con-
tinually operating system for displaying the
wave process within the geological medium
in the form of a digital recording system and
the image (imprint) of this process in the form
of the matrix of interneuron connections in
the completed iterative process of training a
neural network.
In particular, engineering the connecti-
onist model of the travel of seismic Р and S
waves and rating the accuracy of displaying
and functioning the model in the real-time
mode offer the opportunities of not only
an on-line building and a further inversion
of multidimensional time curves of seismic
waves, as well within randomly set geogra-
phic coordinates of the epicentre of the earth-
quake focus and seismic stations, but also the
forecast of its behaviour at «dead» distances
by the limited number of records.
The geological interpretation of the ob-
tained results, as well as the setting of the
seismic potential of the active tectonic struc-
tures of the observation territory on the basis
of neural networks, will get weightier with the
development of the algorithm and software of
the integral analysis of seismic and geologi-
cal data.
Гобаренко В. С., Яновская Т. Б. Скоростная структура
верхних этажей мантии басейна Черного моря.
Геофиз. журн. 2011. Т. 33. № 3. С. 62—74.
Лазаренко М. А., Герасименко О. А. Нейросетевое
моделирование годографов сейсмических волн.
Геофиз. журн. 2010. Т. 32. № 5. С. 126—141.
Литосфера Центральной и Восточной Европы: Мо-
лодые платформы и Альпийский складчатый
пояс. Под ред. А. В. Чекунова. Киев: Наук. дум-
ка, 1994. 331 с.
Поклад Г. Г. Геодезия: Учеб. для вузов Москва: Не-
дра, 1988. 304 с.
List of literature
Хайкин С. Нейронные сети: полный курс. Москва:
Вильямс, 2008. 1103 с.
chauvin y., rumelhart d. e., 1995. Back Propagation:
Theory, Architectures, and Applications. Lawrence
Erlbaum Associates, 564 р.
lay t., wallace t. c., 1995. Modern Global Seismology.
San Diego: Academic. Press, 521 p.
sjöberg l., shirazian m., 2012. Solving the Direct and ln-
verse Geodetic Problems on the Ellipsoit by Numeri-
cal Integration. J. surv. eng. 138(1), 9––16. https://doi.
org/10.1061/(ASCE)SU.1943-5428.0000061#sthash.
qIIieVw6.dpuf.
m. lazareNko , o. HerasymeNko
14 Геофизический журнал № 4, Т. 39, 2017
gobarenko v. s., yanovskaya t. B., 2011. Velocity
structure of the upper levels of the Black Sea
mantle. geofizicheskiy zhurnal 33(3), 62—74
(in Russian).
lazarenko m. a., gerasimenko o. a., 2010. Neural
network modeling of the travel time curves of
seismic waves. geofizicheskiy zhurnal 32(5),
62—74 (in Russian).
Lithosphere of Central and Eastern Europe: Young
platforms and the Alpine folded belt, 1994. Ed.
A. V. Chekunov. Kiev: Naukova Dumka, 331 p.
(in Russian).
poklad g. g., 1988. Geodesy: Proc. For high
schools .Moscow: Nedra, 304 p. (in Russian).
References
khaykin s., 2008. Neural networks: a full course.
Moscow: Williams, 1103 p. (in Russian).
chauvin y., rumelhart d. e., 1995. Back Propaga-
tion: Theory, Architectures, and Applications.
Lawrence Erlbaum Associates, 564 р.
lay t., wallace t. c., 1995. Modern Global Seis-
mology. San Diego: Academic. Press, 521 p.
sjöberg l., shirazian m., 2012. Solving the Direct
and lnverse Geodetic Problems on the Ellipsoit
by Numerical Integration. J. surv. eng. 138(1),
9––16. https://doi.org/10.1061/(ASCE)SU.1943-
5428.0000061#sthash.qIIieVw6.dpuf.
Neural network modeling of Herglotz—Wiechert inversion
of multiparametric traveltime curves of seismic waves
© M. Lazarenko , O. Herasymenko, 2017
Using artificial neural networks to solve a problem of plotting travel-time curves of
seismic waves can create nonlinear travel-time model of P and S phases of seismic waves
arrangement as a function of several arguments: source depth, magnitude, back azimuth
and epicenter distance. Construction of three-dimensional travel-time relationships and
their use for modeling of hadographs and their inversion are considered on examples of
seismic records Ukrainian seismic stations. Examples of inversion locus within the model
Herglotz—Wiechert and features of application of the model in a real environment for
single seismic stations, and generalization for arbitrary coordinate of the source and the
point of signal registration in the Black Sea region are given.
Key words: neural network, seismic waves propagation, training, the Herglots—Wiechert
inversion, discrepancies, travel-time curves, velocity gradient.
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