CN112578431B - Method and system for storing full waveform inversion wave field optimization in finite state - Google Patents
Method and system for storing full waveform inversion wave field optimization in finite state Download PDFInfo
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Abstract
The invention provides a method and a system for optimally storing a full waveform inversion wave field in a finite state, and belongs to the field of seismic inversion imaging of wave equations. Obtaining an optimal buffer number according to the time sampling points of full waveform inversion, and then determining the distribution of a stored wave field and a calculated wave field by using the optimal buffer number and the time sampling points of full waveform inversion; the stored wave field refers to a wave field stored at a monitoring point; the calculated wavefield refers to the wavefield that is being transmitted from the stored wavefield. The invention can obtain the optimized buffer number (namely the optimal value), when the buffer number is larger than the optimal value, the calculation efficiency is not obviously improved although a large storage space is increased; when the number of caches is smaller than the optimum value, the calculation efficiency is greatly reduced as the number of caches is reduced. Meanwhile, the calculation efficiency is greatly improved by utilizing the storage strategy determined by the optimized monitoring point technology.
Description
Technical Field
The invention belongs to the field of seismic inversion imaging based on wave equation, and particularly relates to a method and a system for storing full waveform inversion wave fields in a finite state.
Background
The full waveform inversion synthesizes the seismic data by adopting a wave equation numerical simulation mode, so that the calculated amount is large, and the memory requirement is high. The gradient quasi-full waveform inversion technology can be obtained by carrying out time domain correlation on calculation of gradients by utilizing wave field errors in a back-pass mode and a wave field of forward modeling through a conjugate state method, so that the wave field of forward modeling needs to be stored. For large models, especially three-dimensional problems, it is not possible to store the wavefield at all times. However, if the wavefield at each time instant is obtained by propagating from the time instant when the time is equal to zero, the calculation amount is intolerable. When the storage amount is reduced, the calculated amount needs to be increased, and the calculation efficiency is reduced; as the computational efficiency increases, storage needs to be increased as support. Reverse time migration of acoustic wave media has thus also developed various approaches to addressing storage and computational efficiency, with a desire to balance storage and computational efficiency. Clapp proposes a boundary storage strategy for storing only the wave field within the boundary range, and using this as a boundary condition to obtain the forward wave field by the wave field counter-time propagation, thereby reducing the storage capacity of the wave field without increasing the calculation amount. Clapp then proposes that the storage of the extra wavefield can be reduced by using random boundaries, but this random boundary storage approach also introduces noise. The optimization monitoring point technology realizes the balance of calculation efficiency and wave field storage under certain memory conditions, but the method does not consider the problem of memory utilization, so that the problem that the full-waveform inversion wave field storage method cannot achieve the optimal calculation efficiency and wave field storage exists.
Disclosure of Invention
The invention aims to solve the problems in the prior art, and provides a method and a system for optimally storing a full waveform inversion wave field in a finite state, so as to realize optimal balance of calculation efficiency and wave field storage, improve the adaptability of full waveform inversion to mass data calculation and further promote the practical process.
The invention is realized by the following technical scheme:
the method obtains the optimal buffer number according to the time sampling points of full waveform inversion, and then utilizes the optimal buffer number and the time sampling points of full waveform inversion to determine the distribution of the stored wave field and the calculated wave field;
the stored wave field refers to a wave field stored at a monitoring point;
the calculated wavefield refers to the wavefield that is being transmitted from the stored wavefield.
The method comprises the following steps:
(1) Determining the number n of time sampling points of full waveform inversion;
(2) Numbering the time sampling points;
(3) Calculating the optimal cache number;
(4) Determining the number of the wave field stored in the first step;
(5) The wave field at each time sampling point is calculated starting from the wave field with the largest number.
The operation of step (2) comprises:
the n time sampling points are numbered in sequence from 0, and the maximum number is n-1.
The operation of step (3) comprises:
the optimal number of caches s is calculated using the following equation:
the operation of step (4) comprises:
determining the number of the wave field stored in the first step by utilizing an optimized monitoring technology according to the number n of the time sampling points and the number of the monitoring points, namely the number of the time sampling points of the wave field stored in each monitoring point;
and the number of the monitoring points adopts the optimized cache number s. The operation of step (5) comprises:
calculating the wavefield at each time sample point starting from the time sample point numbered n-1:
firstly, forward transmission of wave fields is carried out from wave fields at t(s) moments stored in the s-th monitoring point to obtain wave fields at n-1 moments, and gradient values at n-1 moments are obtained through cross correlation; (t(s) represents the wave field stored at the s-th monitoring point, t(s) is one of the wave fields of n time-sampled points, the number of which is calculated according to the optimization monitoring technique.)
Then, the wave field forward transmission is carried out from the wave field at the time t(s) stored in the s-th monitoring point, the wave field at the time n-2 is obtained, and the gradient value at the time n-2 is obtained through cross correlation;
and the like, until the calculation of the forward wave field at the time t(s) is started, the forward wave field calculation is not performed any more, and the wave field at the time t(s) is directly extracted from the s-th monitoring point;
when the forward wave field at the time t(s) -1 needs to be calculated, the wave field forward transmission is carried out from the wave field at the time t (s-1) stored in the s-1 monitoring point until the forward wave field at the time t(s) -1 is calculated, and the s-1 monitoring point is vacated at the moment and is used for storing t between t (s-1) and t(s) -1 s A wave field at a moment;
the positive transmission field at time t(s) -1 is stored from the s-th monitoring point at the time t s The wave field at the moment starts to be obtained through wave field forward transmission;
and so on until the calculation of the positive wavefield at all times is completed, and the final gradient values are obtained at the same time.
The operation of obtaining gradient values by cross-correlation includes: multiplying the positive transmission wave field value and the inverse transmission wave field value at the moment to obtain a gradient value at the moment;
the operation of obtaining the final gradient value includes: and superposing the gradient values at all the moments to obtain a final gradient value.
The t is s The time of day is determined using an optimization monitoring technique.
The invention also provides a finite-state full-waveform inversion wave field optimal storage system, which comprises:
the time sampling point number determining module is used for determining the time sampling point number n of full waveform inversion;
the numbering module is connected with the time sampling point number determining module and is used for numbering time sampling points according to the time sampling point number n;
the optimal cache number calculation module is connected with the time sampling point number determination module and is used for calculating the optimal cache number by utilizing the time sampling point number n determination module;
the first step of storing number determining module is respectively connected with the time sampling point number determining module, the number module and the optimal cache number calculating module and is used for determining the number of the wave field stored in the first step;
the wave field calculation module is respectively connected with the numbering module and the first step storage numbering determination module and is used for calculating wave fields of all time sampling points from the wave field with the largest number.
The present invention also provides a computer-readable storage medium storing at least one program executable by a computer, which when executed by the computer, causes the computer to perform the steps in the finite state full waveform inversion wavefield optimization storage method of the present invention.
Compared with the prior art, the invention has the beneficial effects that: the invention can obtain the optimized buffer number (namely the optimal value), when the buffer number is larger than the optimal value, the calculation efficiency is not obviously improved although a large storage space is increased; when the number of caches is smaller than the optimum value, the calculation efficiency is greatly reduced as the number of caches is reduced. Meanwhile, the calculation efficiency is greatly improved by utilizing the storage strategy determined by the optimized monitoring point technology.
Drawings
FIG. 1 is a block diagram of the steps of the method of the present invention;
FIG. 2 is a first step of monitoring point distribution when the time sampling points are 20;
FIG. 3 shows the wave field calculation process at each moment when the time sampling point is 20;
fig. 4 shows a relationship between the repetition rate and the number of buffers when the time sampling point is 10000 (the abscissa indicates the number of buffers s, and the ordinate indicates the repetition rate RCR);
FIG. 5 is a graph showing the relationship between the repeated calculation amount and the maximum back propagation step length t and the buffer memory when the time sampling point is 10000;
fig. 6 (a) shows the relationship between the repetition rate and the number of buffers when the time sampling point is 1501 (the abscissa indicates the number of buffers s, and the ordinate indicates the repetition rate RCR);
fig. 6 (b) shows the relationship between the repetition rate and the number of buffers (the abscissa indicates the number of buffers s, and the ordinate indicates the repetition rate RCR) at the time sampling point 2001;
FIG. 7 is a schematic diagram of the intersection of the solutions of equation (4) and equation (12);
fig. 8 is a block diagram of the system of the present invention.
Detailed Description
The invention is described in further detail below with reference to the attached drawing figures:
the invention aims at determining an optimized buffer number, theoretically calculating the optimized buffer number according to full waveform inversion time sampling points and a memory space provided by a computer, and determining the distribution of a stored wave field and a calculated wave field by using the buffer number and the total time sampling points of full waveform inversion time.
The principle of the method of the invention is as follows:
the full waveform inversion method of the gradient class carries out back transmission on the wave field error and is obtained by correlating the wave field error with the wave field of the forward modeling in a time domain, so that the wave field of the forward modeling needs to be stored. For large models, especially three-dimensional problems, it is not possible to store the wavefield at all sample points. However, if the wavefield for each sample point is obtained by propagating from the moment when the time is equal to zero, the calculation amount is intolerable. It can be said that there is a complementary relationship between storage and computational efficiency. When the storage amount is reduced, the calculated amount needs to be increased, and the calculation efficiency is reduced; as the computational efficiency increases, storage needs to be increased as support.
Defining a wave field repetition rate (RCR: recomputation ratio):
the repetition rate of the conventional method (LTBM: last time back propagation method) using stored last time wavefield back transfer is: rcr=2.0; when the memory is large enough, there is rcr=1.0 when the wavefield at all times can be stored.
The number of wavefields that can be stored simultaneously is also called the number of buffers, assuming a number of buffers s and a total number of time samples (time steps) (the total number of samples and the time step are the same concept) of n. The number of time steps of maximum back propagation for one monitoring point is t, and the number of time samples calculated with minimum additional increase is p (n, s):
p(n,s)＝tn-η(s+1,t-1) (2)
wherein the method comprises the steps of
And t is the only positive integer that requires the following conditions to be satisfied:
η(s,t-1)＜n≤η(s,t) (4)
then there are:
under the condition that t and n are certain, the first derivative of the equation pair s is obtained:
due to
So there are:
indicating that the number of additional computation steps decreases as the number of caches increases, as a monotonically decreasing function.
Further calculate its second derivative:
due to
Thus (2)
The second derivative is constantly less than zero, so the first derivative value decreases as the number of caches increases. According to the characteristic that the first derivative is also constantly smaller than zero, the absolute value thereof increases with the increase of the number of caches, i.e. the rate of change is increased.
Meanwhile, the total time step is fixed, and the relation between t and the buffer number s is examined. When the buffer number s is increased to s+m, the corresponding existence relationship
η(s+m,t m -1)＜n≤η(s+m,t m ) (12)
Wherein t is m The maximum allowable back propagation time step number for each monitoring point state corresponding to the buffer number s+m. Since η (s, t) is an increasing function of both s and t, when t m At > t, eta (s, t m ) > η (s, t); when m is greater than or equal to 1, eta (s+m, t) > eta (s, t).
As shown in FIG. 7, in order to satisfy both the formulas (4) and (12), η (s+1, t-1) < η (s, t). The deduction can be carried out: when m=1, then there is t < =s+1; when m is more than 1, the number of the groups is more than 1,
as the value of s increases, i.e. the value of m increases,the increase, but the t value can be satisfied within a certain increase range. Meanwhile, the smaller the t value is, the larger the s value is, so that s reaches an optimal value at the critical points of t=1 and t=2. Derived optimized cache numberThe purpose is as follows:
where int represents rounding.
The optimized monitoring point technique proposed by Griewank in 2000 (Griewank A, walther A. Algorithm 799:Revolve:An implementation of checkpointing for the reverse or adjoint mode of computational differentiation[J ]. ACM Transactions on Mathematical Software,2000,26 (1): 19-45.) has two implications: when the time sampling point number n and the buffer memory number s are fixed, the repeated calculation rate RCR corresponding to the optimized monitoring point strategy is the lowest; the number of caches s used to optimize the watch point strategy is minimal when the number of time samples n and the repetition rate RCR are fixed.
The invention obtains the optimized buffer number through the formula (13), and can realize double optimized full-waveform inversion wave field storage under the limited storage state by combining with the optimized monitoring point technology proposed by Griewank in 2000.
As shown in fig. 1, the method of the present invention is specifically as follows:
in the full waveform inversion, the time sampling point number is determined through a speed model (how to determine the time sampling point number through the speed model is an existing method is not repeated here), and the time sampling point number is numbered, the optimal buffer number s is obtained through calculation according to the invention, then the number of the wave field stored in the first step is determined through an optimal monitoring point technology, and then the wave field at each moment is calculated according to the sequence from the time sampling number to the time sampling number (as shown in fig. 1). And further provides a forward wavefield for velocity update gradient cross-correlation calculations for full waveform inversion. The method of the invention will now be described by taking time-sampling points 20 as an example.
Step one: determining that the number of time sampling points is 20, namely, the time step n=20;
step two: the 20 time sampling points are numbered in sequence from 0, and the maximum number is 19;
step three: the method calculates the optimized buffer memory number:
i.e. 4 monitoring points are used in this embodiment.
Step four: determining the number of the first step of stored wave fields according to an optimized monitoring point technology: 0. 5, 11, 16 (i.e., monitoring points 1, 2, 3, 4 store wavefields at time points 0, 5, 11, 16, respectively), as shown in fig. 2. The calculation refers to the method proposed by Griewank in 2000, and the parameter n and the number of monitoring points s are needed when the Griewank method is used for calculation.
Step five: the wave field at each time sampling point is calculated starting from the wave field with the largest number (i.e. the wave field with number 19) (wave field is calculated using wave equation finite difference numerical forward method, which is well known in the art of forward modeling of seismic waves and is not described here in detail):
when the forward process reaches the last moment, the gradient value of the 19 th moment can be directly obtained, namely, the 19 th moment positive transmission wave field and the 19 th moment error inverse transmission wave field are multiplied to obtain the 19 th moment gradient value;
as shown in fig. 3, the wave field value at time 18 is being transferred from time 16 stored in the 4 th monitoring point to time 18;
the wave field value at the 17 th moment is transferred from the 16 th moment to the 17 th moment through 1 step;
the wave field value of the wave field at the 16 th moment is directly obtained from the monitoring point;
the wave field value at the 15 th moment is transmitted from the 11 th moment to the 15 th moment, meanwhile, since the data at the 16 th moment is not used any more, the 4 th monitoring point is used for storing the wave field at the 13 th moment, namely the data at the 16 th moment is used completely and is not needed any more, so the 4 th monitoring point originally storing the 16 th moment is used for storing the wave field at the 13 th moment, and the method for determining which monitoring point stores which moment is described in detail in the method of Griewank2000, and the detailed description is omitted herein;
the wave field value at the 14 th moment is obtained from the 13 th moment through 1 step positive transmission;
the wave field value of the wave field at 13 th moment is directly obtained from the monitoring point;
the wave field value at the 12 th moment is obtained from the 11 th moment through 1 step positive transmission;
the wave field value of the wave field at the 11 th moment is directly obtained from the monitoring point;
the 10 th time wave field value is being transferred from the 5 th time to the 10 th time, and the 3 rd and 4 th monitoring points are used for storing the 6 th and 8 th wave fields;
the wave field value at the 9 th moment is obtained from the 8 th moment through 1 step positive transmission;
the wave field value of the wave field at the 8 th moment is directly obtained from the monitoring point;
the wave field value at the 7 th moment is obtained by 1 step positive transmission from the 6 th moment;
the wave field values of the wave fields at the 6 th and 5 th moments are directly obtained from the monitoring points;
the wave field value at the 4 th moment is positively transmitted from the 0 th moment, and the 2 nd, 3 rd and 4 th monitoring points are used for storing wave fields at the 1 st, 2 nd and 3 rd moments;
the wave field values of the wave fields at the 3 rd, 2 nd and 1 st moments are directly obtained from the monitoring points.
The calculation of the forward wavefield at all times is completed, and the cross-correlation with the error wavefield is completed at the same time: the positive transmission wave field value and the inverse transmission wave field value at the corresponding moment are multiplied to obtain the gradient value at the corresponding moment, and the gradient values at all the moments are overlapped to form the final gradient value.
As shown in FIG. 8, the present invention also provides a finite state full waveform inversion wavefield optimization storage system, comprising:
the time sampling point number determining module 10 is used for determining the time sampling point number n of the full waveform inversion;
the numbering module 20 is connected with the time sampling point number determining module 10 and is used for numbering time sampling points according to the time sampling point number n;
the optimal buffer number calculating module 30 is connected with the time sampling point number determining module 10 and is used for calculating the optimal buffer number by utilizing the time sampling point number n determining module;
the first step of storing number determining module 40 is respectively connected with the time sampling point number determining module 10, the numbering module 20 and the optimal buffer number calculating module 30, and is used for determining the number of the wave field stored in the first step;
the wave field calculation module 50 is connected to the numbering module 20 and the first step storage numbering determination module 40, respectively, and is configured to calculate the wave field at each time sampling point from the wave field with the largest number.
The effect of using the method of the present invention is shown below by way of example with a time-sampling point number of 10000. Fig. 4 shows the relationship between the repetition rate and the number of buffers in the case where the number of buffers is less than 1000, it can be seen that as the number of buffers increases, the repetition rate drops sharply and then drops slowly, and there is a distinct inflection point. There is a last inflection point between the cache numbers 100 and 200 after which the repetition rate can only slowly drop. The relation between p and t and s obtained by numerical calculation is shown in fig. 5, in which the maximum value is only 160 in order to more clearly show the relation between the additional calculation amount p and the buffer number s when the buffer number is small. Meanwhile, the corresponding value change trend is also shown in fig. 5, it can be seen that the s values corresponding to the inflection points of the t value and the p value are the same, s reaches the optimal value when t=1 and t=2 are critical points, and the numerical extraction result of fig. 5 is agreed with theoretical analysis. Meanwhile, the optimal cache number is calculated by a formula (13):
meanwhile, the optimal cache number obtained by numerical calculation (taking 20 sampling points as an example, selecting the value of the monitoring point s from 1 to 20 to perform calculation efficiency test of a monitoring point storage wave field for 20 times, and finally obtaining the data of a column of numerical reading in the table 1) is 139, and the numerical reading result is consistent with a theoretical derivation formula (12) of the invention (as shown in the table 1 and fig. 6), so that the theoretical calculation effect of the invention is further verified.
The calculated value and the numerical reading result pair of the invention are shown in the following table 1:
TABLE 1
As can be seen from both fig. 6 (a) and fig. 6 (b), when the number of caches is greater than the optimum value, the improvement in computational efficiency is not significant despite the addition of a large storage space; when the number of caches is smaller than the optimum value, the calculation efficiency is greatly reduced as the number of caches is reduced. The number of caches is optimal at the optimization point. Meanwhile, according to the wave field calculation mode of each moment when the time sampling point is 20 in the figure 3, when the number of caches is determined, the storage strategy determined by the optimized monitoring point technology is the most computationally efficient.
The invention derives a theoretical calculation formula of the optimized buffer number in theory, then utilizes the buffer number and the total time sampling point number of the full waveform inversion time to determine the distribution of the stored wave field (the stored wave field refers to the wave field with the monitoring points) and the calculated wave field (the calculated wave field refers to the wave field which is transmitted from the stored wave field) (the distribution refers to the wave field which is stored at which moment in the monitoring points in the step five), thereby realizing the optimal balance of the calculation efficiency and the wave field storage and further advancing the full waveform inversion practical process.
The foregoing technical solution is only one embodiment of the present invention, and various modifications and variations can be easily made by those skilled in the art based on the application methods and principles disclosed in the present invention, not limited to the methods described in the foregoing specific embodiments of the present invention, so that the foregoing description is only preferred and not in a limiting sense.
Claims (8)
1. A finite state full waveform inversion wave field optimal storage method is characterized in that: the method comprises the steps of obtaining the optimized cache number according to the time sampling points of full waveform inversion, and then determining the distribution of a stored wave field and a calculated wave field by utilizing the optimized cache number and the time sampling points of full waveform inversion;
the stored wave field refers to a wave field stored at a monitoring point;
the calculated wavefield refers to the wavefield that is being transmitted from the stored wavefield;
the method comprises the following steps:
(1) Determining the number n of time sampling points of full waveform inversion;
(2) Numbering the time sampling points;
(3) Calculating the optimized cache number;
(4) Determining the number of the wave field stored in the first step;
(5) Calculating the wave field of each time sampling point from the wave field with the largest number;
the operation of step (5) comprises:
calculating the wavefield at each time sample point starting from the time sample point numbered n-1:
firstly, forward transmission of wave fields is carried out from wave fields at t(s) moments stored in the s-th monitoring point to obtain wave fields at n-1 moments, and gradient values at n-1 moments are obtained through cross correlation; s is the optimized cache number;
then, the wave field forward transmission is carried out from the wave field at the time t(s) stored in the s-th monitoring point, the wave field at the time n-2 is obtained, and the gradient value at the time n-2 is obtained through cross correlation;
and the like, until the calculation of the forward wave field at the time t(s) is started, the forward wave field calculation is not performed any more, and the wave field at the time t(s) is directly extracted from the s-th monitoring point;
when the forward wave field at the time t(s) -1 needs to be calculated, the wave field forward transmission is carried out from the wave field at the time t (s-1) stored in the s-1 monitoring point until the forward wave field at the time t(s) -1 is calculated, and the s-1 monitoring point is vacated at the moment and is used for storing t between t (s-1) and t(s) -1 s A wave field at a moment;
the positive wave field at time t(s) -1 is from the s monitoring point at the momentStored t s The wave field at the moment starts to be obtained through wave field forward transmission;
and so on until the calculation of the positive wavefield at all times is completed, and the final gradient values are obtained at the same time.
2. The finite state full waveform inversion wavefield optimization storage method of claim 1, wherein: the operation of step (2) comprises:
the n time sampling points are numbered in sequence from 0, and the maximum number is n-1.
3. The finite state full waveform inversion wavefield optimization storage method of claim 2, wherein: the operation of step (3) comprises:
the optimal number of caches s is calculated using the following equation:
4. a finite state full waveform inversion wavefield optimization storage method of claim 3, wherein: the operation of step (4) comprises:
determining the number of the wave field stored in the first step by utilizing an optimized monitoring technology according to the number n of the time sampling points and the number of the monitoring points, namely the number of the time sampling points of the wave field stored in each monitoring point;
and the number of the monitoring points adopts the optimized cache number s.
5. The finite state full waveform inversion wavefield optimization storage method of claim 4, wherein: the operation of obtaining gradient values by cross-correlation includes: multiplying the positive transmission wave field value and the inverse transmission wave field value at the moment to obtain a gradient value at the moment;
the operation of obtaining the final gradient value includes: and superposing the gradient values at all the moments to obtain a final gradient value.
6. The finite state full waveform inversion wavefield optimization storage method of claim 5, wherein: the t is s The time of day is determined using an optimization monitoring technique.
7. The utility model provides a full wave form inversion wave field optimization memory system of finite state which characterized in that: the system comprises: the time sampling point number determining module is used for determining the time sampling point number n of full waveform inversion;
the numbering module is connected with the time sampling point number determining module and is used for numbering time sampling points according to the time sampling point number n;
the optimization cache number calculation module is connected with the time sampling point number determination module and is used for calculating the optimization cache number by utilizing the time sampling point number n determination module;
the first step of storing number determining module is respectively connected with the time sampling point number determining module, the number module and the optimizing cache number calculating module and is used for determining the number of the wave field stored in the first step;
the wave field calculation module is respectively connected with the numbering module and the first step storage numbering determination module and is used for calculating wave fields of all time sampling points from the wave field with the largest number;
the wave field calculation module performs the following operations:
calculating the wavefield at each time sample point starting from the time sample point numbered n-1:
firstly, forward transmission of wave fields is carried out from wave fields at t(s) moments stored in the s-th monitoring point to obtain wave fields at n-1 moments, and gradient values at n-1 moments are obtained through cross correlation; s is the optimized cache number;
then, the wave field forward transmission is carried out from the wave field at the time t(s) stored in the s-th monitoring point, the wave field at the time n-2 is obtained, and the gradient value at the time n-2 is obtained through cross correlation;
and the like, until the calculation of the forward wave field at the time t(s) is started, the forward wave field calculation is not performed any more, and the wave field at the time t(s) is directly extracted from the s-th monitoring point;
when the forward wave field at the time t(s) -1 needs to be calculated, the wave field forward transmission is carried out from the wave field at the time t (s-1) stored in the s-1 monitoring point until the forward wave field at the time t(s) -1 is calculated, and the s-1 monitoring point is vacated at the moment and is used for storing t between t (s-1) and t(s) -1 s A wave field at a moment;
the positive transmission field at time t(s) -1 is stored from the s-th monitoring point at the time t s The wave field at the moment starts to be obtained through wave field forward transmission;
and so on until the calculation of the positive wavefield at all times is completed, and the final gradient values are obtained at the same time.
8. A computer-readable storage medium, characterized by: the computer readable storage medium stores at least one program executable by a computer, which when executed by the computer, causes the computer to perform the steps in the finite state full waveform inversion wavefield optimization storage method of any one of claims 1-6.
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