CN112255671A - Method and device for forward modeling of seismic waves between two points - Google Patents
Method and device for forward modeling of seismic waves between two points Download PDFInfo
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- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
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Abstract
The invention discloses a forward modeling method and a forward modeling device for seismic waves between two points, wherein the method comprises the following steps: simulating a ray path by using an optimized ray tracing method according to positions of a shot point and a detection point to obtain a nonlinear equation set of intersection point coordinates; determining a minimized parameter range of a nonlinear equation set by using a simulated annealing method, taking the minimized parameter range as an initial solution of an improved Newton method phase, and solving the nonlinear equation set; and determining intersection point coordinates according to the solution of the nonlinear equation system, and performing forward modeling on the seismic waves. The invention introduces a simulated annealing method to determine the global minimum parameter range, and then uses an improved Newton method to convert the nonlinear equation set into a linear equation to solve from the parameter ranges, thereby improving the solving precision of different stratum cross points of seismic waves.
Description
Technical Field
The invention belongs to the technical field of seismic exploration, and particularly relates to a forward modeling method and device for seismic waves between two points.
Background
The geophysical model can be divided into a construction model and a speed model, wherein the construction model mainly describes the stratum attitude; the velocity model is mainly used for prestack depth migration and time-depth conversion of seismic data. The model is constructed so that there are distinct layer-to-layer velocity interfaces, the formation is divided into layers, and the propagation velocities at each layer are different. In the data processing process of seismic exploration, the stratum structure is analyzed and processed, and the path track which takes the shortest time to pass through the multilayer stratum structure from a shot point to a demodulator probe is searched.
In the domestic and foreign researches in recent years, the ray tracing method is considered to be the method for researching the track, the result is used as the high-frequency approximate solution of the wave equation, the method avoids directly solving a high-order partial differential wave equation set, and the method is a quick and effective differential wave equation solving mode. The two-point method in ray operation is a common test method, and related rays can be transmitted to a wave detection point through a shot point by using the relation among an incidence angle, a reflection angle and a refraction angle through intersection points on different stratums. Since the stratigraphic structures are not of the same trend, the determination of the intersection points is an important part of various kinds of research, and the accuracy of solving the intersection points in the prior art is still to be improved.
Disclosure of Invention
The invention aims at solving the problem of solving a plurality of intersection points involved in the calculation of the ray path of the multilayer reflection interface in the ray tracing method between two points, and provides a method for solving the problem by combining a simulated annealing method and an improved Newton method, thereby achieving the purpose of realizing the forward modeling of seismic waves.
In a first aspect of the present invention, a method for forward modeling seismic waves between two points includes:
simulating a ray path by using an optimized ray tracing method according to positions of a shot point and a detection point to obtain a nonlinear equation set of intersection point coordinates;
determining a minimized parameter range of a nonlinear equation set by using a simulated annealing method, taking the minimized parameter range as an initial solution of an improved Newton method phase, and solving the nonlinear equation set;
and determining intersection point coordinates according to the solution of the nonlinear equation system, and performing forward modeling on the seismic waves.
Preferably, before the simulating the ray path by using the optimized ray tracing method, the method further includes:
simulating a stratum interface structure by cubic spline interpolation, and setting an interface function expression of a j section of an interface as follows:
zj(x)＝S(xj)＝ajx3+bjx2+cjx+dj
wherein a isj、bj、cj、djIs a constant.
Preferably, the determining the minimized parameter range of the nonlinear equation set by using the simulated annealing method specifically includes: let the known shot point O (x)0,z0) And a detection point R (x)2Jz2J) Selecting the variation range of the unknown parameters of the nonlinear equation set as (x)0,x2J) Within this range, take x0′＝x0As the initial model parameters, the corresponding function values S (x) are calculated0′)；
For the current model parameter x0' perturbation is performed to generate a new model parameter x1', calculating the corresponding function value S (x)1') to obtain Δ S ═ S (x)1′)-S(x0') to a host; if Δ S<0, representing that the model parameter is accepted, otherwise the parameter x of the model1' accept with probability P ═ exp (- Δ S/T), T is temperature;
when the model is accepted, x is1' assign to x0' iterative operation as initial point until convergence condition is satisfied, determining unknown parameter x1′；
For the same reason, x1' determining x as an initial value2', until the minimized parameter range (x) of all unknowns is found1′,x2′,…,x2J-1′)。
Preferably, the solving the nonlinear equation system by taking the minimized parameter range as an initial solution of the modified newton's law phase is specifically as follows:
converting the solving problem of the nonlinear equation set into the minimum value problem of the multi-element real value function so as to ensure that
h(x)＝f(x)Tf(x)＝f1(x)2+f2(x)2+...+fn(x)2
And taking the minimum parameter range searched by the simulated annealing method as an initial solution of a Newton method, calculating gradient and searching direction, judging whether a convergence condition is reached, if not, calculating a next Hessen matrix by adopting a DFP method, and updating the gradient and the searching direction until the convergence condition is reached.
In a second aspect of the present invention, a device for forward modeling seismic waves between two points is provided, the device comprising:
a path simulation module: simulating a ray path by using an optimized ray tracing method according to positions of a shot point and a detection point to obtain a nonlinear equation set of intersection point coordinates;
an equation system solving module: determining a minimized parameter range of a nonlinear equation set by using a simulated annealing method, taking the minimized parameter range as an initial solution of an improved Newton method phase, and solving the nonlinear equation set;
the seismic wave forward modeling module: and determining intersection point coordinates according to the solution of the nonlinear equation system, and performing forward modeling on the seismic waves.
The invention has the beneficial effects that:
the invention introduces a simulated annealing method to determine the global minimum parameter range, and then uses an improved Newton method to convert the nonlinear equation set into a linear equation to solve from the parameter ranges, thereby overcoming the problem that the Newton method is easy to fall into local optimization and improving the solving precision of different stratum cross points of seismic waves.
Drawings
In order to more clearly illustrate the technical solution of the present invention, the drawings needed to be used in the technical description of the present invention will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a diagram of a simulated stratigraphic model;
FIG. 2 is a flow chart of a simulated annealing process;
FIG. 3 is a flow chart based on a simulated annealing method and a modified Newton method;
FIG. 4 is a stratigraphic model diagram of a tilted reflecting interface;
FIG. 5 is a ray trend graph of a forward process under the tilted reflecting interface of FIG. 4;
FIG. 6 is a stratigraphic model diagram of a single-curved reflective interface;
FIG. 7 is a ray diagram of the forward process under the single-curved reflective interface of FIG. 6;
FIG. 8 is a stratigraphic model diagram of a curved reflective interface;
fig. 9 is a ray diagram of the forward process under the curved reflective interface of fig. 8.
Detailed Description
In order to make the objects, features and advantages of the present invention more obvious and understandable, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the embodiments described below are only a part of the embodiments of the present invention, but not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The representation form of the complex stratum structure function can be obtained by a cubic spline interpolation method, and the interface function of the j section of the interface can be written as formula 1:
zj(x)＝S(xj)＝ajx3+bjx2+cjx+dj (1)
in the treatment of the stratigraphic structure as shown in FIG. 1, at a known shot point O (x)0,z0) And a detection point R (x)2J,z2J) In the case of (2), the ray path is simulated by means of an optimized ray tracing method, the ray reaches the detection point by means of correlated reflection and refraction through the multiple strata and according to the corresponding intersection point coordinates such as (x)1,z1)、(x2,z2)…(x2J-2,z2J-2)、 (x2J-1,z2J-1) Obtaining corresponding nonlinear equations, finally forming a nonlinear equation set, obtaining the coordinates of the intersection point under the condition of shortest time, and finally obtaining the coordinates of the intersection pointSo as to obtain the ray track of the forward process through the intersection coordinates. How to solve the nonlinear system of equations is the key to implementing the forward process.
The invention provides a forward modeling method for seismic waves between two points, which comprises the following steps:
simulating a ray path by using an optimized ray tracing method according to positions of a shot point and a detection point to obtain a nonlinear equation set of intersection point coordinates;
determining a minimized parameter range of a nonlinear equation set by using a simulated annealing method, taking the minimized parameter range as an initial solution of an improved Newton method phase, and solving the nonlinear equation set;
and determining intersection point coordinates according to the solution of the nonlinear equation system, and performing forward modeling on the seismic waves.
At present, solving a nonlinear equation is more complicated than solving a linear equation, and a method which is commonly used for solving the nonlinear equation is to linearize the nonlinear equation, namely, a nonlinear problem is converted into a linear problem to be solved, and the solution of a thread equation set is used as an approximate solution of the nonlinear equation set.
A nonlinear equation set is set:
using a system of linear equations f' (x)k)(x-xk)+f′(xk) The solution for 0 is:
xk+1＝xk-[f′(xk)]-1f(xk) (3)
the equation (3) is used as an approximate solution of the nonlinear equation system (2) to construct a matrix HkBy HkApproximation of the Jacobian matrix f' (x) of a non-linear system of equationsk) The inverse of the matrix of (a) is,
xk+1＝xk-Hkf(xk) (4)
Hkthe condition that the matrix should satisfy modified Newton's method is Hk+1(f(xk+1)-f(xk))＝xk+1- xkBy using DSolving for H by FP methodk。
In order to overcome the problem that the Newton method is easy to fall into local optimization, a simulated annealing method is introduced to determine a global minimum parameter range, and then from the parameter range, an improved Newton method is used for converting a nonlinear equation set into a linear equation to solve.
Referring to fig. 2, a schematic diagram of determining a global minimization parameter range by a simulated annealing method is shown.
Let the known shot point O (x)0,z0) And a detection point R (x)2Jz2J) Selecting the variation range of the unknown parameters of the nonlinear equation set as (x)0,x2J) Within this range, take x0′＝x0As the initial model parameters, the corresponding function values S (x) are calculated0′)；
For the current model parameter x0' perturbation is performed to generate a new model parameter x1', calculating the corresponding function value S (x)1') to obtain Δ S ═ S (x)1′)-S(x0') to a host; if Δ S<0, representing that the model parameter is accepted, otherwise the parameter x of the model1' accept with probability P ═ exp (- Δ S/T), T is temperature;
when the model is accepted, x is1' assign to x0' iterative operation as initial point until convergence condition is satisfied, determining unknown parameter x1′；
For the same reason, x1' determining x as an initial value2', until the minimized parameter range (x) of all unknowns is found1′,x2′,…,x2J-1′)。
For the nonlinear equation system (2), the solving problem can be converted into a minimal value problem of a multi-element real-value function, and then
h(x)＝f(x)Tf(x)＝f1(x)2+f2(x)2+...+fn(x)2 (5)
A sufficient requirement for f (x) to be 0 is that s (x) is 0 because
Therefore, minh (x) ≧ 0, so that any minimum value for h (x) ≧ 0 must be the solution for equation set f (x) ≧ 0.
Minimizing the parameter range (x) for the unknowns determined by the simulated annealing algorithm1′,x2′,…,x2J-1') as the initial solution of the quasi-Newton method, calculating the gradient and the search direction, judging whether the convergence condition is reached, if not, adopting a DFP method to calculate the next Hessen matrix, updating the gradient and the search direction until the convergence condition is reached, and obtaining the respective optimal solution.
In particular, with x1' for the initial solution, the function values and the gradient of the initial solution are calculated, and the gradient direction p in which s (x) is decreased is shifted by one step λpWhere λ is the step factor, 0<λ<1, obtaining a new starting point x1＝x1′+λpFind the appropriate λ such that h (x)t)<h(xt') and finally h (x)t)＝ minh(x1′+λp) Further obtain the optimal solution x1；
Similarly, x searched by the simulated annealing method2' As an initial solution, x is determined according to the same procedure2Sequentially determining to x2J-1Thereby determining all coordinate points.
Referring to fig. 3, another embodiment of the present invention provides a modified newton method flow chart based on simulated annealing. After initialization, simulating the value of a parameter searched by an annealing method as an initial value, calculating a gradient and a Henssen matrix, calculating a new search direction and updating a current point; and calculating the difference value delta x between the parameter value searched by the simulated annealing method and the new current point, comparing the difference value delta x with a set threshold value, judging whether convergence occurs or not, if the convergence occurs, finishing the operation, and if the convergence does not occur, entering the next cycle until the convergence condition is reached.
The invention also provides a device for forward modeling seismic waves between two points, which comprises:
a path simulation module: simulating a ray path by using an optimized ray tracing method according to positions of a shot point and a detection point to obtain a nonlinear equation set of intersection point coordinates;
an equation system solving module: determining a minimized parameter range of a nonlinear equation set by using a simulated annealing method, taking the minimized parameter range as an initial solution of an improved Newton method phase, and solving the nonlinear equation set;
the seismic wave forward modeling module: and determining intersection point coordinates according to the solution of the nonlinear equation system, and performing forward modeling on the seismic waves.
The equation system solving module specifically comprises:
a range determination unit: let the known shot point O (x)0，z0) And a detection point R (x)2J，z2J) Selecting the variation range of the unknown parameters of the nonlinear equation set as (x)0，x2J) Within this range, take x0′＝x0As the initial model parameters, the corresponding function values S (x) are calculated0') to a host; for the current model parameter x0' perturbation is performed to generate a new model parameter x1', calculating the corresponding function value S (x)1') to obtain Δ S ═ S (x)1′)-S(x0') to a host; if Δ S<0, representing that the model parameter is accepted, otherwise the parameter x of the model1' accept with probability P ═ exp (- Δ S/T), T is temperature; when the model is accepted, x is1' assign to x0' iterative operation as initial point until convergence condition is satisfied, determining unknown parameter x1'; for the same reason, x1' determining x as an initial value2', until the minimized parameter range (x) of all unknowns is found1′，x2′，…，x2J-1′)；
An intersection solving unit: converting the solving problem of the nonlinear equation set into the minimum value problem of the multi-element real value function so as to ensure that
h(x)＝f(x)Tf(x)＝f1(x)2+f2(x)2+...+fn(x)2
And taking the minimum parameter range searched by the simulated annealing method as an initial solution of a Newton method, calculating gradient and searching direction, judging whether a convergence condition is reached, if not, calculating a next Hessen matrix by adopting a DFP method, and updating the gradient and the searching direction until the convergence condition is reached.
The above apparatus embodiments and method embodiments are in one-to-one correspondence, and reference may be made to the method embodiments for a brief point of the apparatus embodiments.
It can be clearly understood by those skilled in the art that for convenience and brevity of description, in the foregoing embodiments, descriptions of various embodiments have respective emphasis, and details or description of some embodiments may be referred to related descriptions of other embodiments, which are not repeated herein.
Although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and the modifications or the substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (6)
1. A method for forward modeling seismic waves between two points, the method comprising:
simulating a ray path by using an optimized ray tracing method according to positions of a shot point and a detection point to obtain a nonlinear equation set of intersection point coordinates;
determining a minimized parameter range of a nonlinear equation set by using a simulated annealing method, taking the minimized parameter range as an initial solution of an improved Newton method phase, and solving the nonlinear equation set;
and determining intersection point coordinates according to the solution of the nonlinear equation system, and performing forward modeling on the seismic waves.
2. The method for forward modeling seismic waves between two points according to claim 1, wherein said simulating ray paths using optimized ray tracing further comprises:
simulating a stratum interface structure by cubic spline interpolation, and setting an interface function expression of a j section of an interface as follows:
zj(x)＝S(xj)＝ajx3+bjx2+cjx+dj
wherein a isj、bj、cj、djIs a constant.
3. The method for forward modeling seismic waves between two points according to claim 2, wherein the method for determining the minimized parameter range of the nonlinear equation set by using the simulated annealing method specifically comprises:
let the known shot point O (x)0，z0) And a detection point R (x)2J，z2J) Selecting the variation range of the unknown parameters of the nonlinear equation set as (x)0，x2J) Within this range, take x0′＝x0As the initial model parameters, the corresponding function values S (x) are calculated0′)；
For the current model parameter x0' perturbation is performed to generate a new model parameter x1', calculating the corresponding function value S (x)1') to obtain Δ S ═ S (x)1′)-S(x0') to a host; if Δ S < 0, the model parameter is accepted, otherwise the parameter x of the model is accepted1' accept with probability P ═ exp (- Δ S/T), T is temperature;
when the model is accepted, x is1' assign to x0' iterative operation as initial point until convergence condition is satisfied, determining unknown parameter x1′；
For the same reason, x1' determining x as an initial value2', until the minimized parameter range (x) of all unknowns is found1′，x2′，...，x2J-1′)。
4. The method for forward modeling seismic waves between two points according to claim 2, wherein the solving the system of nonlinear equations with the minimized parameter range as an initial solution of the modified newton's facies is specifically:
converting the solving problem of the nonlinear equation set into the minimum value problem of the multi-element real value function so as to ensure that
h(x)＝f(x)Tf(x)＝f1(x)2+f2(x)2+...+fn(x)2
And taking the minimum parameter range searched by the simulated annealing method as an initial solution of a Newton method, calculating gradient and searching direction, judging whether a convergence condition is reached, if not, calculating a next Hessen matrix by adopting a DFP method, and updating the gradient and the searching direction until the convergence condition is reached.
5. An apparatus for forward modeling of seismic waves between two points, the apparatus comprising:
a path simulation module: simulating a ray path by using an optimized ray tracing method according to positions of a shot point and a detection point to obtain a nonlinear equation set of intersection point coordinates;
an equation system solving module: determining a minimized parameter range of a nonlinear equation set by using a simulated annealing method, taking the minimized parameter range as an initial solution of an improved Newton method phase, and solving the nonlinear equation set;
the seismic wave forward modeling module: and determining intersection point coordinates according to the solution of the nonlinear equation system, and performing forward modeling on the seismic waves.
6. The device for forward modeling of seismic waves between two points according to claim 5, wherein the equation system solving module specifically comprises:
a range determination unit: let the known shot point O (x)0，z0) And a detection point R (x)2J，z2J) Selecting the variation range of the unknown parameters of the nonlinear equation set as (x)0，x2J) Within this range, take x0′＝x0As the initial model parameters, the corresponding function values S (x) are calculated0') to a host; for the current model parameter x0' perturbation is performed to generate a new model parameter x1', calculating the corresponding function value S (x)1') to obtain Δ S ═ S (x)1′)-S(x0') to a host; if Δ S < 0, the model parameter is accepted, otherwise the parameter x of the model is accepted1' accept with probability P ═ exp (- Δ S/T), T is temperature; when the model is accepted, x is1' assign to x0' iterative operation as initial point until convergence condition is satisfied, determining unknown parameter x1'; for the same reason, x1' determining x as an initial value2', until the minimized parameter range (x) of all unknowns is found1′，x2′，...，x2J-1′)；
An intersection solving unit: converting the solving problem of the nonlinear equation set into the minimum value problem of the multi-element real value function so as to ensure that
h(x)＝f(x)Tf(x)＝f1(x)2+f2(x)2+...+fn(x)2
And taking the minimum parameter range searched by the simulated annealing method as an initial solution of a Newton method, calculating gradient and searching direction, judging whether a convergence condition is reached, if not, calculating a next Hessen matrix by adopting a DFP method, and updating the gradient and the searching direction until the convergence condition is reached.
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