Building_Complex_Seismic_Velocity_Models_for_Deep_Learning_Inversion.pdf

Received January 6, 2021, accepted January 8, 2021, date of publication January 12, 2021, date of current version May 3, 2021.
Digital Object Identifier 10.1109/ACCESS.2021.3051159
Building Complex Seismic Velocity Models
for Deep Learning Inversion
YUXIAO REN 1, LICHAO NIE 2, SENLIN YANG 1, PENG JIANG 1, (Member, IEEE),
AND YANGKANG CHEN 3
1School of Qilu Transportation, Shandong University, Jinan 250061, China
2Geotechnical and Structural Engineering Research Center, Shandong University, Jinan 250061, China
3School of Earth Sciences, Zhejiang University, Hangzhou 310027, China
Corresponding authors: Lichao Nie (lichaonie@163.com) and Peng Jiang (sdujump@gmail.com)
This work was supported by the Fundamental Research Funds of Shandong University. The work of Yangkang Chen was supported by the
Starting Funds from Zhejiang University.
ABSTRACT Training a deep learning inversion network usually requires hundreds of thousands of complex
velocity models, which is labor-intensive and expensive to acquire. In this work, we develop a new framework
to automatically generate various velocity models with common geological structures, such as folding layers,
faults and salt bodies. There are three main modules in the proposed framework. The first module generates
a folded model with a given number of layers; the other two modules can add faults and salt bodies onto the
folded model to form a fault or salt model, respectively. To best simulate the shape of subsurface geological
structures while ensuring a good application effect in deep learning inversion, we generate the structural
model based on composition of several basic functions with recommended parameter ranges. Then the
generated structural model will be assigned with velocity values based on assumptions of underground
seismic velocity distribution. To investigate the application effect of the generated 3D models, we conduct
a deep learning inversion test. Since currently there is no 3D deep learning inversion algorithms available,
the latest 2D inversion network called SeisInvNet is used to test the feasibility of the randomly generated
velocity models. Through the experiments, we can see that the 2D inversion results are consistent with the
true models from the aspects of velocity values and geological structure shapes, which demonstrates the
rationality of the designed 3D models. In the end, we further discuss the feasibility of applying the proposed
3D model dataset to train a 3D inversion network. This work paves the way for the development of 3D deep
learning inversion methods.
INDEX TERMS Automatic construction algorithm, deep learning inversion, seismic velocity models, three
dimensional.
I. INTRODUCTION
Underground seismic velocity distribution is of great signif-
icance for the interpretation of subsurface structures, which
plays an essential role in the investigation of the Earth’s
crustal activities as well as the near-surface geology [1], [2].
Especially in terms of resource exploitation and underground
space development, the underground geological condition
inferred from seismic velocity estimations is a vital factor
to consider in engineering activities like site selection, con-
struction planning, etc. [3], [4]. Thus, obtaining an accurate
seismic velocity model has become a hot topic that attracts
the attention of geophysicists for decades [5]–[7].
The associate editor coordinating the review of this manuscript and
approving it for publication was Giovanni Angiulli .
One classic way to estimate underground velocity distribu-
tion is via full waveform inversion (FWI), which originated
in the early 1980s. By iteratively minimising the data misfit
between the simulated and the observed data, the correspond-
ing velocity model can be retrieved by various optimization
methods [8]–[12]. During the development of FWI theory,
complex and realistic velocity models are often required for
the synthetic study of seismic wavefield. Usually, this type
of velocity model is generated by experts with extensive
knowledge about the geological condition of a certain area
on the Earth. For example, one of the most famous and
standard acoustic velocity models in exploration geophysics,
namely the Marmousi model, was created by the French
Institute of Petroleum (IFP for short in French) in 1988 and its
geometry is designed based on seismic profiles in the Cuanza
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Y. Ren et al.: Building Complex Seismic Velocity Models for Deep Learning Inversion
Basin, Angola [13]. Later in 2006, according to the empirical
relation between the velocity of P-wave, S-wave and density
in different lithologic formations, an elastic version of the
Marmousi model was further proposed in [14]. Other popular
velocity models, such as the Sigsbee models [15] and the BP
model [16] from the Gulf of Mexico, are also handcrafted
models with some special geologic bodies as the model sam-
ples. Considering the large amount of experience, resources
and efforts required in building such kind of velocity model,
it is understandable that there are only a handful of realistic
velocity models that researchers could have access to. With
the in-depth research for seismic property in more complex
and realistic condition like anisotropic media, the demand
for more standard velocity models in a large scale indicates
a potential research interest for the academic and industrial
community.
Recently, with the rapid development of deep learning
techniques and the advancement of computer hardware, deep
neural networks (DNNs) have demonstrated superior perfor-
mance over traditional methods in many fields. Therefore,
state-of-the-art deep learning techniques have been applied in
a variety of seismic problems, including interpretation of seis-
mic data (e.g. [17], [18]), automatic picking of first arrivals
(e.g. [19]–[21]) and noise attenuation (e.g. [22]–[24]). The
application of DNN can not only introduce novel perspectives
in various seismic problems, but also potentially lead to a
more efficient solution, which could liberate human labor in
the corresponding seismic data processing procedures.
Seismic velocity inversion aims to obtain the velocity dis-
tribution in the subsurface by using the observed seismic
data. The successful application examples in various com-
puter vision tasks (e.g. [25]–[28]) indicates a great poten-
tial of DNN in dealing with the ill-posedness of seismic
inversion problems. Thus, many attempts have been made
in this line of work. For instance, Araya-Polo et al. [29]
made a preliminary attempt in 2018 to obtain the velocity
model by training a DNN as a tomography operator. They
simplified the task by pre-processing the seismic data into
a velocity feature cube and post-processing the DNN output
via statistical approaches to present a reasonable velocity
model. Wu et al. [30] treated the seismic observation data
as images and adopted an end-to-end convolutional neu-
ral network (CNN), namely InversionNet, to simulate the
mapping from the raw seismic data to the velocity model.
This encoder-decoder architecture was also applied in elastic
velocity model inversion by Zheng et al. [31] and relatively
good inversion results on laterally consistent models can be
achieved. Later, Zhang et al. [32] proposed a neural net-
work based on generative adversarial network (GAN), which
demonstrated a better inversion effect than the CNN architec-
ture. Recently, by analyzing the time-series nature of seismic
data, Li et al. [33] proposed a novel DNN called SeisInvNet
based on the combination of the traditional multi-layer per-
ceptron neural network (MLP) and CNN, which could exhibit
superior inversion results than the CNN-based approach on a
dataset of layered velocity models. In general, there have been
a variety of DNNs demonstrating a good application effect in
the task of seismic velocity inversion.
However, all the aforementioned deep learning inversion
networks fall into the category of supervised learning, whose
performance and generalization ability largely depends on
the training dataset (e.g., seismic observation data and the
corresponding velocity models as labels). Due to limitation
of computer hardware, current researches on seismic deep
learning inversion are mainly based on simplified velocity
models of small size, such as the FlatVel and CurvedVel
dataset used for training InversionNet [30] and the SeisInv
dataset mentioned in the SeisInvNet paper [33]. Moreover,
to the best of our knowledge, currently there are few publicly
available velocity model sets suitable for the research of
deep learning inversion. Thus, building a sufficient number of
seismic velocity models with complex geological structures
has become a major obstacle in this line of study [34].
As mentioned above, the traditional way of generating a
complex velocity model usually relies on the expertise of
geological interpretation of seismic exploration data in a
certain subsurface area of the Earth [35], [36]. The human
effort and cost associated with the model construction process
may make a large number of fully labeled dataset infeasible.
On the other hand, considering the general requirement of
deep learning inversion at the current stage, building a set of
seismic velocity models that fits general geologic knowledge
would be sufficient for the network training [37]–[39]. For
example, to obtain sufficient data for fault identification via
multi-task learning, Wu et al. build the folding layers based on
Gaussian function and the faulting structures using the elliptic
coordinate system. On this basis, in the deep learning task of
seismic structural curvature volume extraction, Ao et al. [40]
generate complex geological models by introducing local
topographic changes to the constructed structural model.
Most recently, Liu et al. [41] construct geological models
with dense-layers, fault and salt body to achieve deep learn-
ing inversion of realistic structural models. However, it is
achieved in 2D, and not suitable for 3D cases. Thus in this
work, we propose an algorithm for automatically generating
an arbitrary number of complex seismic velocity models with
typical geological structures like folding layers, faults, salt
bodies, etc. More complex velocity models can be further
constructed by adding other special geological bodies on
them.
This article is constructed as follows. Section II introduces
a framework for automatically generating a 3D seismic veloc-
ity model with common geological structures. After present-
ing several samples of 3D velocity models in section III,
follows a validation test using the SeisInvNet. In fact, since
we currently do not possess a deep learning inversion net-
work for 3D velocity models, the feasibility test of the auto-
matically generated velocity model set is performed using
the 2D cross sections of the generated 3D velocity models.
As indicated by the good inversion results in the numerical
experiments, the proposed complex seismic velocity con-
struction algorithm could build a dataset that fulfills the
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FIGURE 1. Framework of building complex velocity models.
training requirement of seismic deep learning inversion.
Future extensions of this work is discussed in section IV and
conclusions are summarized in section V.
II. SEISMIC VELOCITY MODEL CONSTRUCTION
In this section, we aim at developing an algorithm to auto-
matically build numerous 3D velocity models with common
geologic structures, such as folding layers, faults and salt
bodies. As shown in Fig. 1, we start by building a folded
model of size NX × NY × NZ in the three dimensional space
(X, Y, Z) and then add faults or salt bodies on it to form
a complex structural model. Then, arbitrary velocity values
within a predefined range will be set on different geologic
structures to present the final 3D velocity models. In this
work, limited by the memory cost of training a deep learning
inversion network, we set the target model size as nx = ny =
nz = 100. Generally, geological structures are formed by the
deformation and dislocation of rock layers. By extending grid
layers outside the target model area, we can simulate the layer
movement in a larger space and the middle area gives the
target structural model. Thus in this article, we use the model
size of NX = NY = NZ = 160 with EL = 30 extended
layers for the illustration of model construction procedures.
By following the conventions in seismic exploration, recom-
mendations about model construction parameter settings are
made in grid points. They are empirical and should be further
adjusted appropriately for different situations.
A. FOLDED MODELS
In structural geology, folding layers are usually formed via
a permanent deformation of flat strata, where the rock is
deformed by bending rather than breaking. Thus, when build-
ing folding layers numerically, we assume they constitute a
FIGURE 2. (a) A structural model with seven folding layers and (b) a
cut-away view of the folded model. The colors here only denote different
layers and velocity values will be assigned later.
fold belt with straight hinge line denoted by equation (1) and
the fold shape can be described by trigonometric functions
shown in the equation (2). Actually, we use cosine function
here mainly because of its continuous undulation, which is
controllable by period and amplitude. For the folding layer
with a reference point (Xref, Yref, Zref) on it, we have
H(X, Y) = (X − Xref) + a(Y − Yref). (1)
S(X, Y) =





A1 cos(2πH/T1) − A1 H ≤ T̂1
Ai cos(2πH/Ti) − Ai T̂i−1 < H ≤ T̂i
An cos(2πH/Tn) − An H > T̂n−1.
(2)
Here, X and Y denote the horizontal directions, H(X, Y)
denotes the hinge line of a folding layers, whose direction
is determined by the parameter a. S(X, Y) is in the vertical
Z direction denoting the fluctuation of the layers. We use
Ti and Ai, i = 1, . . . , n, to control the folding layer shape
(period and amplitude, respectively). That is, for every point
H(X, Y) in the interval (T̂i−1, T̂i), where T̂i =
Pk=i
k=1 Tk,
we build a folding layer according to the function with the
parameter Ti and Ai, whose values can be randomly selected
from predetermined ranges. In fact, we use a 1D Brownian
motion to determine both parameters respectively and A1 <
T1/10 is recommended to avoid sharp fluctuation of the
layers.
Once a curved layer is obtained, a dipping term D(X, Y)
is introduced to further complicate the layer with a dipping
angle. The dipping term D(X, Y) is defined as a linear func-
tion with randomly selected parameter b1 and b2.
D(X, Y) = b1(X − Xref) + b2(Y − Yref). (3)
Then, one can place the folding layers in the 3D model
area based on a series of randomly selected reference points
(Xk, Yk, Zk). For the model with N folding layers, we rec-
ommend to choose the location of the first layer Z1 > 10 to
avoid a very shallow layer and the location of the last layer
ZN < nz − 5 to avoid a very deep layer at the model bottom.
The reference points of deeper layers can be determined
iteratively according to (Xk, Yk, Zk) = (Xk−1 + 1X, Yk−1 +
1Y, Zk−1 + 1Z) with random shifting value 1X ∈ [−5, 5],
1Y ∈ [−5, 5] and 1Z > 5. Here, the vertical shift 1Z is
used to mainly control the layer depth and we set it with a
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Algorithm 1 Folded Model Construction Process
Notations:
Model array M of size NX × NY × NZ; Total number of
layers N; Rounding function R(·).
Outputs:
Model array m of size nx × ny × nz.
Construction process:
1: Init: Randomly set model construction parameters a,
{Ti}, {Ai}, b1, b2 and reference points {(Xk, Yk, Zk)};
2: Init: M ← ones(NX, NY, NZ)
3: for k = 1 : N do
4: Xref = Xk, Yref = Yk
5: for i = 1 : NX, j = 1 : NY do
6: calculate hinge line H via equation (1)
7: calculate curved surface S via equation (2)
8: calculate dipping terms D via equation (3)
{Generate N curved layers}
9: Ẑ(i, j, k) ← R(S(i, j) + D(i, j) + Zk)
{Place the curved layers in the model}
10: M(i, j, Ẑ(i, j, k) : end) ← k + 1
{Assign identification numbers}
11: end for
12: end for
13: m ← remove the extended layers of M
large value to avoid thin layers, which could be difficult to
invert due to the resolution limitation of seismic inversion.
In fact, with the given values of the vertical shift 1Z as well
as Z1 and ZN , the depth component of the remaining reference
points can be determined as
Zk = 1Z(k − 1) +
Rk−1
sum(R)
F, k = 2, 3, . . . , N − 1,
F = nz − Z1 − ZN − 1Z × (N − 1). (4)
Here, R is a sequence of (N − 2) random numbers, and Ri is
the ith element of R. F denotes the number of grid rows that
can be assigned as reference points. In the end, placing the
folding layers based on the reference points outputs the final
folded models. Moreover, each layer will be assigned an iden-
tification number for the convenience of velocity assignment
(see Fig. 2 for example). The corresponding algorithm can be
found in Alg. 1 for detailed model construction procedures.
B. FAULT MODELS
In order to simulate a complex velocity model, we further add
faulting structures based on the constructed folded model.
Considering that one of the most common fault types are
planar, we use linear functions, including strike and dip
angle, to describe faults. Here, by assuming a flat fault plane,
the governing equation is defined by the equation (5) and a
reference point (Xref, Yref, Zref).
c1(X − Xref) + c2(Y − Yref) + c3(Z − Zref) = 0. (5)
In fact, as shown in Fig. 3, by setting φ ∈ [0, 2π) and
θ ∈ (0, π/2) as the strike and dip angle, respectively, we can
relate the parameters c1, c2 and c3 to the local normal vector
[0, 0, 1]T via the rotation matrix R [39] in (7).


c1
c2
c3

 = R


0
0
1

 =


cos φ sin θ
sin φ sin θ
− cos θ

 . (6)
R =


sin φ cos φ cos θ cos φ sin θ
cos φ − sin φ cos θ sin φ sin θ
0 sin θ − cos θ

 . (7)
Thus, by randomly selecting a pair of strike and dip angles,
we can determine a fault plane passing the reference point
(Xref, Yref, Zref). Furthermore, by randomly defining the dis-
placement d = [dα, dβ, 0]T in the local coordinate system
(α, β, γ ), we use the rotation matrix to derive the correspond-
ing displacement in the global coordinate system (X, Y, Z)
as


DX
DY
DZ

 = R


dα
dβ
0

 =


dα sin φ + dβ cos φ cos θ
dα cos φ − dβ sin φ cos θ
dβ sin θ

 . (8)
Therefore, moving the model block on the right of the fault
plane will add the faulting structure on the curved layer
model. Recommendation about the displacement values are
within [5, 15] grid points. Particularly, as shown in Fig. 4,
setting dα = 0, dβ > 0 and dα = 0, dβ < 0 leads to a
normal dip-slip fault and reverse dip-slip fault, respectively,
and dβ = 0, dα > 0 and dβ = 0, dα < 0 corresponds
to a left lateral strike-slip fault and a right lateral strike-slip
fault, respectively. According to the desired number of faults,
repeating the aforementioned operations based on the refer-
ence points from left to right will result in a velocity model
with multiple faults.
C. SALT MODELS
Another option for building a complex geological model is to
add salt bodies on the constructed folded model. In this work,
we focus on one of the most common types of salt bodies,
namely salt dome, and we assume the salt body grows from
a layer deeper than the model bottom. In the process of salt
dome rising, the layers above the salt dome will be topped
up, yielding changes in layer shapes. To simply simulate the
changes, the salt dome and the geological layer affected by
the vertically upward intrusion of the salt body are assumed
to follow a 2D Gaussian function (9) with a reference location
(Xref, Yref). Generally speaking, the 2D Gaussian function can
be considered to be close to the shape of the salt dome, and
the function parameters can also be adjusted to approximate
the fluctuation of the upper interface.
G(X, Y) = A exp(−(d1(X − Xref)2
+ d3(Y − Yref)2
+2d2(X − Xref)(Y − Yref))), (9)
where
d1 =
cos2 ϕ
2σ2
X
+
sin2
ϕ
2σ2
Y
,
63770 VOLUME 9, 2021

FIGURE 3. (a) A fault plane is defined by randomly choosing a reference point (Xref, Yref, Zref) and angle parameters φ and θ.
(b) Displacement of the hanging wall gives the final fault model (c). Different layers are denoted by different colors.
FIGURE 4. Examples of (a) normal dip-slip fault, (b) reverse dip-slip fault,
(c) left lateral strike-slip fault and (d) right lateral strike-slip fault.
d2 = −
sin 2ϕ
4σ2
X
+
sin 2ϕ
4σ2
Y
,
d3 =
sin2
ϕ
2σ2
X
+
cos2 ϕ
2σ2
Y
. (10)
Here, the height of salt body or the vertical intrusion influence
is defined by the amplitude parameter A in grid points. More-
over, we use the variance parameters σ2
X and σ2
Y to control the
size. The strike is determined by the clockwise rotation angle
ϕ. Similarly as before, all these parameters can be randomly
selected from a preferred range. In this work, we choose the
σX and σY from [5, 20], a range that is appropriate for our
model scale, and the rotation angle ϕ from [0, 2π].
We use Fig. 5 to further demonstrate the construction
process of salt models, which involves two major steps:
a) change the geological layer shape under the influence of
the salt body intrusion and b) add salt body. For the first
step, the 2D Gaussian function with amplitude A is used
to control the shape change of geological layers near the
reference location (Xref, Yref). Specifically speaking, on the
basis of the constructed folded model, an influence zone of
salt dome upward intrusion is defined on the bottom h grid
layers. Here, h is randomly set from [Amax + 5, Amax + 15]
and Amax ∈ [20, 40] denotes the largest amplitude of the salt
intrusion influence. Considering that the salt intrusion influ-
ence increases with depth, the corresponding amplitudes for
different layers are generated as components of the linearly
spaced vector A = {A(k)}h
k=1 ← linspace(Amax, 1, h) and
Amax is the largest among {A(k)}. Thus, for a shallower layer
k in the influence zone, the corresponding Gaussian function
of that layer will have a smaller amplitude A(k). In other
words, wherever the geological layer is in the influence zone,
the corresponding salt intrusion influence is determined by
the 2D Gaussian with a predefined amplitude A correspond-
ing to that layer. The structures above the influence zone
will remain unchanged. In the second step, feeding the 2D
Gaussian function with a given amplitude value hsalt leads to
a salt body and placing it based on the same reference point
outputs the final salt model. In addition, when the deepest
folding layers are close to the model bottom, the salt body
will penetrate through these layers. To include this scenario
in our salt models, we set the salt body height hsalt =
Amax+rand[0, 10]. Examples of this special case can be found
in Fig. 6.
In this way, by reassigning a new layer identification
number based on the reshaped folding layers and the salt
body, one could obtain a complex salt model. We provide the
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FIGURE 5. Based on the folded model (a), layers within the influence zone, which is marked in gray in (a), are further bended to simulate
the salt intrusion influence shown in (b). Placing the salt body based on the same reference points outputs the final salt body shown in (c).
Different structures are denoted by different colors and the color brown is used to denote the salt body.
FIGURE 6. An example showing that the salt body penetrates some
folding layers.
FIGURE 7. Examples of the models with both fault and salt structures.
corresponding algorithm in Alg. 2 for detailed construction
steps.
In addition, as shown in Fig 1, one can further add faulting
structures on the built salt models by following the instruc-
tions in the above Section II-B and we show some exam-
ples in Fig. 7. However, this is only a preliminary study
on the model construction to assist deep learning inversion
and the coexistence of salt and fault within one model may
TABLE 1. A Summary of Model Generation Parameters for Different
Geological Structures.
not entirely obey geological rules. In fact, as pointed out
by many researchers, the interaction between faults and salt
bodies is complex and salt bodies could have major impact on
the development of faults [42]–[44]. Thus, in the following
data validation test using deep learning inversion networks,
we neglect this type of models and put folded models, pure
fault models and pure salt models in the experiment dataset.
D. VELOCITY ASSIGNMENT
We have demonstrated the construction process of a com-
plex geological model with common geological structures
including folding layers, faults and salt bodies. The model
generation parameters are summarized in Table 1. All these
parameters take values from predetermined ranges. A random
choice of these parameters defines a unique geological struc-
tural model. Moreover, by sequentially adding several faults
and/or salt bodies, one can get a complex geological model
with multiple faults and salt bodies.
To build a rich dataset for training a seismic velocity inver-
sion network, the final step is to assign velocity values for
different structures based on the layer identification number.
Actually, by following some basic rules based on the target
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Algorithm 2 Salt Model Construction Process
Notations:
Folding-layer array L of size NX × NY × N; Total num-
ber of layers N; 2D Gaussian function G(·); Rounding
function R(·).
Outputs:
Salt model array m of size nx × ny × nz.
Construction process:
1: Init: Randomly set model construction parameters Amax,
ϕ, σX , σY , h, hsalt and reference point (Xref, Yref);
2: Init: Msalt ← ones(NX, NY, NZ),
Z ← zeros(NX, NY, NZ), Zsalt ← zeros(NX, NY),
Lsalt ← zeros(NX, NY, N);
3: linearly spaced vector A ← linspace(Amax, 1, h)
{Calculate amplitude A = {A(k)}h
k=1}
4: for i = 1 : NX, j = 1 : NY do
5: for k = 1 : h do
6: Z(i, j, NZ − k) ← G(i, j, A(k))
{Calculate salt intrusion influence}
7: end for
8: Zsalt(i, j) ← G(i, j, hsalt) {Calculate salt body}
9: end for
10: for i = 1 : NX, j = 1 : NY do
11: for l = 1 : N do
12: Lsalt(i, j, l) ← R(L(i, j, l) − Z(i, j, L(i, j, l)))
{Relocate the reshaped folding layers}
13: Msalt(i, j, Lsalt(i, j, l) : end) = l + 1
{Reassign ID number for the folding layers}
14: end for
15: Lsalt(i, j, N + 1) ← R(NZ − Zsalt(i, j))
{Place the salt body in the model}
16: Msalt(i, j, Lsalt(i, j, N + 1) : end) = N + 2
{Assign ID number for the salt body}
17: end for
18: m ← remove the extended layers of Msalt
model type, the velocity assignment is quite straightforward
to achieve. For example in this work, the target model type
is acoustic velocity model, so we set the following principles
for velocity assignment.
• The velocity values for folding layers are set in the range
of [1500 m/s, 4000 m/s], the velocity values for salt
bodies are set between 4300 m/s and 4500 m/s.
• The velocity value of a folding layer increases with
depth and the velocity difference between adjacent lay-
ers should be over 200 m/s.
• The velocity values are randomly selected from the pre-
defined range following an uniform distribution.
In Fig. 8, we use two folding-layer models, two fault models
and two salt models as examples to exhibit the outcome of
our velocity model construction framework. By adjusting
the value range of the model generation parameters shown
in Table 1 according to different velocity inversion tasks, one
can get an arbitrary number of 3D velocity models.
III. DATASET VALIDATION BASED ON DEEP LEARNING
INVERSION NETWORKS
The goal of this work is to build a rich dataset suitable
for training a deep learning inversion network by which the
complex velocity models can be estimated from the corre-
sponding seismic observation data. In this sense, the con-
structed velocity models are designed to contain common
geological structures like folding layers, faults and salt bod-
ies. Here, we simulate the geological structures by some
basic functions with randomly selected parameters, thereby
leading to a set of velocity models with rich features that
are potentially useful for the deep learning network training.
In addition, due to computing limitations, currently there are
no deep learning inversion codes available for estimating
3D velocity models. Thus, in this section, we will only use
one of the most recently published deep learning inversion
network, namely the SeisInvNet [33], to test the applica-
tion effect of models constructed by the proposed algorithm
in 2D.
A. DATASET PREPARATION
Based on the framework proposed above, we can automati-
cally generate hundreds of thousands of 3D complex velocity
models. Here, we assume that the dataset contains three kinds
of velocity models, i.e., folded models, fault models, and salt
models. The maximum layer number is set to be seven and
only one fault or salt body is contained in a single model.
Considering that the SeisInvNet can only deal with 2D veloc-
ity inversion problem, the 2D velocity models are obtained
by taking several 2D slices of the 3D velocity models at
random positions in both XOZ and YOZ planes. For folded
models, to maintain the diversity of geological structures,
we select three slices randomly from the XOZ and YOZ
planes respectively with an interval larger than ten grid points.
As for the fault models and salt models, only one or two
slices are selected from the faulting and salting areas in the 3D
model from each direction. In fact, the number of 2D slices
obtained from a 3D model is subject to model size and the
shape of geological structures and it may vary depending on
different situations.
Moreover, the seismic data is computed via numerical
simulation of acoustic wave propagating through the 2D
velocity models. The governing equation in 2D time-space
domain with a source term s(t, x, z) can be expressed
as
∂2p
∂t2
= v2
(x, z)

∂2p
∂x2
+
∂2p
∂z2

+ s. (11)
Here, x and z denote the horizontal and vertical axes, respec-
tively. t denotes time, p(t, x, z) denotes the acoustic wave
field and v(x, z) represents the 2D acoustic velocity model.
We apply the seismic acquisition system similar to the Seis-
InvNet paper, which involves 20 seismic sources and 32
receivers evenly distributed on the top layer of the velocity
model. The wavefield at every time step and every receiver
points for all seismic sources of 15 Hz dominant frequency
VOLUME 9, 2021 63773

FIGURE 8. Examples of the generated velocity models, which include two folding-layer models, two fault models and two salt models.
will be saved as the recorded data. The recorded data and
its corresponding velocity model construct a pair of training
dataset for SeisInvNet.
In this experiment, 13,600 pairs of data will be generated
as the training dataset of SeisInvNet and the validation set
and test set contain 1,360 data pairs, respectively. Moreover,
in each dataset, the number of each type of geological model
is approximately the same.
B. DEEP LEARNING INVERSION NETWORK SETUPS
The deep learning inversion based on SeisInvNet belongs
to a supervised learning, which requires seismic observation
data as the network input and the corresponding 2D velocity
models as labels. Similarly to the SeisInvNet paper, the loss
function is defined based on the L2 norm and MSSIM [45] of
the predicted and the true velocity. In this way, data features
can be captured in the aspects of velocity values and geo-
logical structure similarities, respectively. Moreover, since
SeisInvNet has achieved a recognized inversion effect on
simple models, the similar network architecture and param-
eter setups as the SeisInvNet paper [33] is also used in this
experiment.
Specifically, the learning rate is set to decay exponen-
tially from 5 × 10−5 to zero and the Adam optimizer
with a batch size of 20 is used for training the net-
work parameters. In addition, 200 epochs of training will
be carried out and the network parameters that perform
best on the validation set will be selected to build the
final network. We use the validation and test dataset to
demonstrate the inversion performance of the constructed
models.
FIGURE 9. Loss curves in deep learning inversion on (a) training dataset
and (b) validation dataset.
C. DEEP LEARNING INVERSION RESULTS
After training, validating and testing the SeisInvNet on a
computer with a single NVIDIA TITAN RTX GPU card
for about 19 hours, we obtained the deep learning inversion
result with loss curves shown in Fig. 9. Generally speaking,
the rapid and stable convergence of the SeisInvNet indicate
a good inversion effect on the generated velocity models.
Moreover, network predictions are randomly selected from
the test dataset as examples to further evaluate the deep
learning inversion effect. As shown in Fig. 10, virtual com-
parisons between the network predictions and their corre-
sponding ground-truth solutions indicate that the generated
velocity models can satisfy the requirement of deep learn-
ing network in the task of velocity inversion. In addition,
as demonstrated in the comparison of vertical velocity pro-
files, the trained network can accurately invert the 2D veloc-
ity distribution, especially for the folding layers and salt
models.
63774 VOLUME 9, 2021

FIGURE 10. Deep learning inversion results for folded models (the first row), fault models (the second row) and salt models (the third row).
Detailed comparison of the velocity at the black lines are provided to show the inversion accuracy.
FIGURE 11. The deep learning inversion results after fine-tuning the
network parameters. The corresponding data shown in the last column
are the noisy data with SNR equals to −4.0656 dB and −4.7565 dB
(calculated after removing the first arrival wave), respectively.
To verify the effectiveness of our method on noisy data,
we conduct the deep learning inversion via following the
experiment setup in [33]. we add random noise to 1,360 sets
of seismic data, i.e. one-tenth of our original data, and retrain
the network parameters for 40 epochs to achieve fine-tuning
on the noisy data. The test results for the noisy data are
shown in Fig.11. Despite the more complex signal, accurate
prediction results can be obtained as well.
IV. DISCUSSION
The ultimate goal of deep learning seismic inversion is to
invert a realistic observation data and obtain a good velocity
estimation that can be beneficial to the seismic community.
Since we currently focus on supervised learning networks,
one potential way to achieve this is via training on numerous
velocity models that best resemble the actual underground
geology. Inspired by works in seismic data denoising [24]
and structural interpretation [39], deep learning networks
trained on synthetic dataset may result in acceptable appli-
cation effect in realistic data. Thus, constructing a large-scale
realistic velocity models is still a strongly demanded research
topic.
In this work, we have proposed a novel framework to build
complex velocity models based on simplified assumptions
on the shape of geological structures, which are determined
mainly based on the relatively small-scale velocity mod-
els used in current deep learning inversion networks. This
framework can be easily extended to generate large-scale
realistic velocity models by adding or replacing some struc-
tural feature simulation functions. For example, instead of
a flat fault plane, one can further add some small perturba-
tions on it to obtain a more realistic simulation. Moreover,
the simulation functions of folding layers and salt bodies can
also be replaced with more complicated functions like Gaus-
sian functions, polynomials with different basis functions
or even actual geometrical data obtained from outcrops and
drilling. In fact, the simulation equation used in geological
model building varies according to the deep learning task.
For example, in the task of faulting structure interpretation,
Wu et al. [39] use Gaussian functions to simulate dense
folding layers with less undulations, which is potentially
VOLUME 9, 2021 63775

conducive to the identification of faulting structures. As for
the task of deep learning inversion, we use trigonometric
functions to simulate the folding layers with more ups and
downs and the Gaussian function is mainly used for the design
of salt mounds and influence zones in this study.
Currently we are simply creating as many and complex
geological models as possible mainly based on the shape
and position of the subsurface structures. When building
large-scale realistic models, the geodynamic characteristics
of the geological structures becomes an important factor
worth considering. By analyzing the dynamical formation
mechanisms of the geological structures, the constructed
model could be more geologically correct and therefore more
in line with the practical situations. For example, the geo-
logical structure design and velocity assignment assumptions
should be further studied to achieve the automatic construc-
tion of realistic models like Marmousi model, which would
be beneficial to the development of deep learning inversion
algorithms in real data cases.
In terms of deep learning inversion networks, limited by the
computing ability, we only demonstrate the inversion effect
of 2D versions of the constructed velocity models. Replacing
the 2D convolutions with 3D convolutions in the state-of-
the-art deep learning inversion networks is very expensive
with respect to memory requirements. Thus, extending cur-
rent seismic velocity inversion networks into 3D is a great
barrier on the way to practical applications. Inspired by the
image-based 3D reconstruction in computer vision commu-
nity [46], surface-based representations like meshes and point
clouds might be memory-efficient choices. However, this cat-
egory of techniques usually require non-conventional struc-
ture grids and might suffer from generalization constraints on
the topology of underground structures. Latest development
in seismic data classification called SeismicPatchNet [47]
has shown a promising reduction in CNN parameter storage,
which provides a new perspective in designing a computa-
tionally efficient deep learning inversion network that could
be feasible for estimating 3D velocity distributions.
In addition to seismic deep learning inversion, the auto-
matic construction of complex geological structural models
can be applied in other deep learning tasks like subsur-
face structural interpretation [39], [40] or other geological
problems in electric and electromagnetic fields [48], [49].
Besides the application in deep learning, seismic velocity
models play an important role in the study of seismic for-
ward modeling, imaging and inversion techniques [50]. For
example, by setting the model building parameters manually,
one can generate a series of models indicating the growth of
salt body, which facilitates the study of time-lapse imaging
techniques.
V. CONCLUSION
In this work, we have designed a novel framework to automat-
ically build a large database of complex seismic velocity mod-
els that can be used to train deep learning inversion networks.
The generated 3D models can include common geological
structures like folding layers, faults and salt bodies. To test
the usability of the generated velocity dataset, one of the latest
deep learning inversion network called SeisInvNet is trained
based on the 2D sections of the generated 3D models. The
good inversion effect shown in the numerical experiments
indicate the effectiveness of the proposed velocity model
construction method. In the end, future extension of this work
are briefly discussed in terms of designing more realistic
models and computationally efficient network architecture
for inverting 3D models.
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YUXIAO REN received the bachelor’s degree in
mathematics from Shandong University, China,
in 2014, and the master’s degree in mathematics
from Loughborough University, U.K., in 2015.
He is currently pursuing the Ph.D. degree in civil
engineering with Shandong University. He then
came back to Shandong University. He is currently
a Visiting Scholar with the Georgia Institute of
Technology under the supervision of Prof. Felix
Herrmann. His research interests include seismic
modeling and imaging, full-waveform inversion, and deep-learning based
geophysical inversion.
LICHAO NIE received the Ph.D. degree from the
Geotechnical and Structural Engineering Research
Center, Shandong University, China, in 2014.
He is currently an Associate Professor with the
School of Civil Engineering, Shandong University.
His current research interests include geophysical
forward and inversion theory and method, and
geological forward-prospecting method and tech-
nology in tunnels and tunnel boring machine with
forward-prospecting systems and its engineering
application.
SENLIN YANG received the bachelor’s degree
in engineering from Shandong University, China,
in 2017, where he is currently pursuing the
Ph.D. degree. His research interest includes
deep-learning based geophysical data processing
and inversion.
VOLUME 9, 2021 63777

PENG JIANG (Member, IEEE) received the
B.S. and Ph.D. degrees in computer science and
technology from Shandong University, China,
in 2010 and 2016, respectively. He is currently
a Research Assistant with the School of Qilu
Transportation, Shandong University. His research
interests include computer vision, image pro-
cessing, machine learning, and deep learning.
He has published many works on top-tier venues,
including ICCV, NeurIPS(NIPS), and the IEEE
TRANSACTIONS ON IMAGE PROCESSING (TIP). Recently, he is focusing on deep
learning-based geophysical inversion.
YANGKANG CHEN received the B.S. degree
in exploration geophysics from the China Uni-
versity of Petroleum, Beijing, in 2012, and the
Ph.D. degree in geophysics from The University
of Texas at Austin, in 2015, under the supervision
of Prof. Sergey Fomel. In 2015, he joined the
Oak Ridge National Laboratory as a Distinguished
Postdoctoral Research Associate and conducted
research on global adjoint tomography. He is cur-
rently an Assistant Professor with Zhejiang Uni-
versity. He has published more than 100 internationally renowned journal
articles and more than 80 international conference papers. His research
interests include seismic signal analysis, seismic modeling and inversion,
simultaneous-source data deblending and imaging, global adjoint tomogra-
phy, and machine learning.
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