CN110568498B - Time shift correction method in well shock matching - Google Patents
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Abstract
The invention discloses a time shift correction method in well shock matching, which comprises the following steps: inputting an actual well side seismic record, and a synthetic seismic record obtained by convolution of reflection coefficients and seismic wavelets; establishing an objective function on the amount of time shift; giving a reference model; calculating a first derivative of the objective function at the reference model position with respect to the time shift amount; calculating a second derivative of the objective function at the reference model position with respect to the time shift amount; according to the Gaussian-Newton method principle, a new time shift amount is calculated by using an iterative inversion equation of the time shift amount; judging whether the new time shift quantity meets the iteration stop condition, if so, stopping the iteration, and obtaining the inversion result as the final time shift quantity; otherwise, setting the inversion result as an initial model, and returning to loop iteration until the iteration stopping condition is met; and obtaining the synthesized record after time shift correction by using an interpolation method. Compared with the prior art, the time shift inversion method has the advantages of high convergence rate and high calculation efficiency.
Description
Technical Field
The invention relates to the field of oil and gas geophysical exploration, in particular to a time shift correction method in well shock matching.
Background
With the improvement of the interpretation precision of three-dimensional seismic data, the development of reservoir geophysics and reservoir management and the progress of joint inversion technology, the matching problem of seismic exploration data and logging data becomes more and more important. The well logging curve and the seismic exploration data respectively represent the on-line and on-plane distribution characteristics of reservoir parameters, the well logging data can accurately provide reservoir parameter information of various underground rock formations, the accurate information can be extrapolated to an inter-well area by combining the seismic exploration data, and the organic combination of the two is the premise and key for carrying out fine scribing and lithology interpretation on the oil and gas reservoir parameters. However, there are many variations between the log and the seismic data that must be processed and corrected for before the extrapolation of the information between wells can be performed, so that they can be matched accurately.
In the well earthquake matching, firstly, a reflection coefficient is calculated according to logging data, a synthetic earthquake record is obtained through convolution of the reflection coefficient and earthquake wavelets, then, the synthetic record is corrected by taking an actual well side earthquake record as a reference, so that the synthetic record and the well side record reach a more accurate matching state, wherein the most important is time matching and real-time shift correction. The common manual correction method requires a great deal of man-machine interaction and has low efficiency; the window cross-correlation method has a certain requirement on window selection, if the time shift changes quickly, a narrower window needs to be selected, but the robustness can be reduced, and if the window is enlarged to improve the stability, the correction result can be inaccurate.
Therefore, there is a need to develop an intelligent, stable, accurate method for correcting time shift in well shock matching.
Disclosure of Invention
The invention aims to solve the defects in the prior art and provides a time shift correction method in well shock matching, which can accurately calculate the time shift between the synthesized record at each sampling point and the actual record beside the well and then obtain the corrected synthesized record through interpolation.
In order to achieve the above purpose, the invention is implemented according to the following technical scheme:
a time shift correction method in well shock matching comprises the following steps:
S1, inputting an actual well side seismic record and a synthetic seismic record obtained by convolution of reflection coefficients and seismic wavelets;
S2, establishing an objective function about the time shift amount;
S3, giving a reference model;
S4, calculating a first derivative of the objective function at the position of the reference model with respect to the time shift amount;
s5, calculating a second derivative of the objective function at the position of the reference model with respect to the time shift amount;
s6, calculating a new time shift amount by using an iterative inversion equation of the time shift amount according to the Gaussian-Newton method principle;
S7, judging whether the new time shift quantity meets an iteration stop condition, if so, stopping iteration, wherein the inversion result is the final time shift quantity, and executing a step S8; otherwise, setting the inversion result as an initial model, and returning to the step S3 to carry out loop iteration until the iteration stopping condition is met;
s8, obtaining the synthesized record after time shift correction by using an interpolation method.
Further, in the step S2, the objective function of the time shift amount is composed of a data error term, a smoothing term, and a model constraint term, as shown in the following formula (1):
Wherein: the symbol of the two norms; s 0 represents a well side record, s represents a synthetic record, and t represents a sampling time; τ represents the amount of time shift between two seismic records, An objective function representing the amount of time shift τ; the s 0(t)-s(t-τ)||2、||Lτ||2、||τ-τ0||2 represents a data error term, a smoothing term and a model constraint term respectively; the coefficient lambda 2、ε2 before the smoothing term and the model constraint term represents the weight occupied by the term; τ 0 is a reference model, and aims to constrain the value range of τ; l is a smoothing operator, L is a derivative operator of first order or second order, and expressions of the derivative operator are shown in the following (2) and (3) respectively:
further, the specific steps of the step S4 are as follows:
calculating the derivative of s (t- τ) with respect to τ in formula (1), let x=t- τ, and then the derivative of s (t- τ) with respect to τ is expressed as shown in formula (4) below:
Assuming that the number of sampling points is n, the expression of s (x) is written as: s (x) = [ s 1s2…sn]T, the expression of x is written as: x= [ x 1x2…xn]T ] then The expression of (2) is as shown in the following expression (5):
Calculating each element of the matrix in the formula (5) by adopting a first-order center difference method to enable (I=1, 2, …, n; j=1, 2, …, n), the calculation formula of which is shown in the following formula (6):
combining the formulas (4), (5) and (6), calculating to obtain the derivative of s (t-tau) with respect to tau, and then calculating an objective function Regarding the first derivative g (τ) of the time shift amount τ, the following expression (7) shows:
Wherein the superscript T denotes the transposed symbol and I denotes the identity matrix.
Further, an objective function is calculated in the step S5Regarding the second derivative H (τ) of the time shift amount τ, the following expression (8) shows:
Wherein the superscript T denotes the transposed symbol and I denotes the identity matrix.
Further, the specific steps of the step S6 are as follows:
The first derivative g (tau (0)) of the objective function at the position tau (0) with respect to the time shift amount is calculated according to the formula (7), the second derivative H (tau (0)) of the objective function at the position tau (0) with respect to the time shift amount is calculated according to the formula (8), and after one iteration calculation, the expression of the time shift amount tau is shown as the following formula (9):
τ＝τ(0)-H-1(τ(0))g(τ(0))(9)。
Further, the specific steps of the step S7 are as follows: after τ is obtained through calculation according to the formula (9), judging whether τ - τ (0) is small enough or whether the set maximum iteration number is reached, if so, stopping the iteration, wherein τ is the required final time shift amount; otherwise, setting the value of tau as an initial model, and returning to S3 for loop iteration until the condition of iteration stopping is met.
Compared with the prior art, the method can accurately calculate the time shift amount between the synthesized record at each sampling point and the actual record beside the well, and then obtain the corrected synthesized record through interpolation; the smooth term and the model constraint term in the objective function can provide regularization constraint, so that inversion is not easy to sink into local minima; the parameter setting is less, the use is convenient, and the parameters to be adjusted in the inversion only have the weight coefficients of the smooth term and the model constraint term.
Drawings
Fig. 1 is a process flow diagram of the present invention.
Fig. 2a shows the actual recording, the composite recording and the corrected recording in the theoretical model data test.
Fig. 2b shows the amplitude difference between the composite record and the corrected record and the actual record, respectively, in the theoretical model data test.
Fig. 3 is a graph showing the amount of time shift calculated in the theoretical model data test.
FIG. 4a is a well side actual record, synthetic record and corrected record in field data testing.
Fig. 4b shows the amplitude difference between the composite record and the corrected record and the actual record at the well side, respectively, in the field data test.
Fig. 5 is a graph showing the amount of time shift calculated in the field data test.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. The specific embodiments described herein are for purposes of illustration only and are not intended to limit the invention.
Example 1
As shown in fig. 1, the time shift correction method in the well shock matching of the embodiment specifically includes the following correction processes:
S1, inputting an actual parawell seismic record S 0, and a synthetic seismic record S obtained by convolution of a reflection coefficient and a seismic wavelet;
s2, establishing an objective function about the time shift amount: assuming that the time sequence corresponding to the seismic record is t, the time shift amount between the actual record and the synthesized record is τ, and an objective function shown in the following formula (1) is constructed based on the principle of least squares:
Wherein: the symbol of the two norms; s 0 represents a well side record, s represents a synthetic record, and t represents a sampling time; τ represents the amount of time shift between two seismic records, An objective function representing the amount of time shift τ; the s 0(t)-s(t-τ)||2、||Lτ||2、||τ-τ0||2 represents a data error term, a smoothing term and a model constraint term respectively; the coefficient lambda 2、ε2 before the smoothing term and the model constraint term represents the weight occupied by the term; τ 0 is a reference model, and aims to constrain the value range of τ; l is a smoothing operator, L is a derivative operator of first order or second order, and expressions of the derivative operator are shown in the following (2) and (3) respectively:
S3, giving a reference model;
S4, calculating the derivative of S (t- τ) with respect to τ in the formula (1), and letting x=t- τ, where the derivative of S (t- τ) with respect to τ is expressed as the form shown in the following formula (4):
Assuming that the number of sampling points is n, the expression of s (x) is written as: s (x) = [ s 1s2…sn]T, the expression of x is written as: x= [ x 1x2…xn]T ] then The expression of (2) is as shown in the following expression (5):
Calculating each element of the matrix in the formula (5) by adopting a first-order center difference method to enable (I=1, 2, …, n; j=1, 2, …, n), the calculation formula of which is shown in the following formula (6):
combining the formulas (4), (5) and (6), calculating to obtain the derivative of s (t-tau) with respect to tau, and then calculating an objective function Regarding the first derivative g (τ) of the time shift amount τ, the following expression (7) shows:
Wherein the superscript T represents the transposed symbol and I represents the identity matrix;
S5, recalculating an objective function Regarding the second derivative H (τ) of the time shift amount τ, the following expression (8) shows:
Wherein the superscript T represents the transposed symbol and I represents the identity matrix;
S6, according to the Gaussian-Newton method principle, calculating a new time shift amount by using an iterative inversion equation of the time shift amount: the first derivative g (tau (0)) of the objective function at the position tau (0) with respect to the time shift amount is calculated according to the formula (7), the second derivative H (tau (0)) of the objective function at the position tau (0) with respect to the time shift amount is calculated according to the formula (8), and after one iteration calculation, the expression of the time shift amount tau is shown as the following formula (9):
τ＝τ(0)-H-1(τ(0))g(τ(0))(9)；
S7, after the initial model tau (0) is used for calculating tau according to the formula (9), judging whether tau-tau (0) is small enough or whether the number of iterations reaches the set maximum number of iterations, if so, stopping the iteration, wherein tau is the calculated time shift; otherwise, setting the value of tau as an initial model, and returning to the step S3 to carry out loop iteration until the condition of iteration stopping is met;
S8, after the time shift amount tau is calculated, the time sequence corresponding to the well side record S 0 is t, the time sequence corresponding to the synthesized record is t-tau, and then the corrected synthesized record is obtained through interpolation.
As shown in fig. 2, fig. 2a shows an actual record and a composite record generated by a theoretical model simulation, and a corrected record obtained by using the present embodiment, respectively; in fig. 2b, the amplitude difference between the composite record and the actual record, and the amplitude difference between the corrected record and the actual record obtained in this embodiment are shown, respectively. It is obvious that the correction result of the composite record and the actual record are almost completely overlapped after the technology of the invention is used, the amplitude difference between the two is almost zero, and the correction effect is very good. The accurate time shift amounts at the four waveform positions in fig. 2a are 4ms, -6ms, 4ms and-4 ms in sequence, and fig. 3 shows that the time shift correction amount obtained by using the method has good matching effect with the accurate result.
Example 2
As shown in fig. 1, the time shift correction method in the well shock matching of the embodiment specifically includes the following correction processes:
S1, inputting an actual parawell seismic record S 0, and a synthetic seismic record S obtained by convolution of a reflection coefficient and a seismic wavelet;
s2, establishing an objective function about the time shift amount: assuming that the time sequence corresponding to the seismic record is t, the time shift amount between the actual record and the synthesized record is τ, and an objective function shown in the following formula (1) is constructed based on the principle of least squares:
Wherein: the symbol of the two norms; s 0 represents a well side record, s represents a synthetic record, and t represents a sampling time; τ represents the amount of time shift between two seismic records, An objective function representing the amount of time shift τ; the s 0(t)-s(t-τ)||2、||Lτ||2、||τ-τ0||2 represents a data error term, a smoothing term and a model constraint term respectively; the coefficient lambda 2、ε2 before the smoothing term and the model constraint term represents the weight occupied by the term; τ 0 is a reference model, and aims to constrain the value range of τ; l is a smoothing operator, L is a derivative operator of first order or second order, and expressions of the derivative operator are shown in the following (2) and (3) respectively:
S3, giving a reference model;
S4, calculating the derivative of S (t- τ) with respect to τ in the formula (1), and letting x=t- τ, where the derivative of S (t- τ) with respect to τ is expressed as the form shown in the following formula (4):
Assuming that the number of sampling points is n, the expression of s (x) is written as: s (x) = [ s 1s2…sn]T, the expression of x is written as: x= [ x 1x2…xn]T ] then The expression of (2) is as shown in the following expression (5):
Calculating each element of the matrix in the formula (5) by adopting a first-order center difference method to enable (I=1, 2, …, n; j=1, 2, …, n), the calculation formula of which is shown in the following formula (6):
combining the formulas (4), (5) and (6), calculating to obtain the derivative of s (t-tau) with respect to tau, and then calculating an objective function Regarding the first derivative g (τ) of the time shift amount τ, the following expression (7) shows:
Wherein the superscript T represents the transposed symbol and I represents the identity matrix;
S5, recalculating an objective function Regarding the second derivative H (τ) of the time shift amount τ, the following expression (8) shows:
Wherein the superscript T represents the transposed symbol and I represents the identity matrix;
S6, according to the Gaussian-Newton method principle, calculating a new time shift amount by using an iterative inversion equation of the time shift amount: the first derivative g (tau (0)) of the objective function at the position tau (0) with respect to the time shift amount is calculated according to the formula (7), the second derivative H (tau (0)) of the objective function at the position tau (0) with respect to the time shift amount is calculated according to the formula (8), and after one iteration calculation, the expression of the time shift amount tau is shown as the following formula (9):
τ＝τ(0)-H-1(τ(0))g(τ(0))(9)；
S7, after the initial model tau (0) is used for calculating tau according to the formula (9), judging whether tau-tau (0) is small enough or whether the number of iterations reaches the set maximum number of iterations, if so, stopping the iteration, wherein tau is the calculated time shift; otherwise, setting the value of tau as an initial model, and returning to the step S3 to carry out loop iteration until the condition of iteration stopping is met;
S8, after the time shift amount tau is calculated, the time sequence corresponding to the well side record S 0 is t, the time sequence corresponding to the synthesized record is t-tau, and then the corrected synthesized record is obtained through interpolation.
As shown in fig. 4, fig. 4a shows a well-side actual record and a synthesized record obtained by field data acquisition, and a corrected record obtained by using the embodiment; in fig. 4b, the amplitude difference between the composite record and the actual record and the amplitude difference between the corrected record and the actual record obtained by the present embodiment are respectively shown. It can be seen that there is not only a time difference but also an amplitude difference between the synthesized recording and the actual recording, and after the technique of the present invention is used, the time shift between the synthesized recording and the actual recording is corrected well; the correlation coefficients between the synthesized record before and after correction and the actual record are 0.8864 and 0.9282 respectively, and the correlation coefficient between the two is obviously improved after time shift correction. Fig. 5 shows the amount of time shift correction obtained using the present invention.
The results of the above two examples show that: the technology of the invention is used for carrying out inversion and time shift correction of the time shift amount on the synthesized record in well earthquake matching, and a more accurate result can be obtained.
The technical scheme of the invention is not limited to the specific embodiment, and all technical modifications made according to the technical scheme of the invention fall within the protection scope of the invention.
Claims (5)
1. A time shift correction method in well shock matching is characterized by comprising the following steps:
S1, inputting an actual well side seismic record and a synthetic seismic record obtained by convolution of reflection coefficients and seismic wavelets;
S2, establishing an objective function about the time shift amount;
the objective function of the time shift amount is composed of a data error term, a smoothing term, and a model constraint term, as shown in the following formula (1):
Wherein: the symbol of the two norms; s 0 represents a well side record, s represents a synthetic record, and t represents a sampling time; τ represents the amount of time shift between two seismic records, An objective function representing the amount of time shift τ; the s 0(t)-s(t-τ)||2、||Lτ||2、||τ-τ0||2 represents a data error term, a smoothing term and a model constraint term respectively; the coefficient lambda 2、ε2 before the smoothing term and the model constraint term represents the weight occupied by the term; τ 0 is a reference model, and aims to constrain the value range of τ; l is a smoothing operator, L is a derivative operator of first order or second order, and expressions of the derivative operator are shown in the following (2) and (3) respectively:
S3, giving a reference model;
S4, calculating a first derivative of the objective function at the position of the reference model with respect to the time shift amount;
s5, calculating a second derivative of the objective function at the position of the reference model with respect to the time shift amount;
s6, calculating a new time shift amount by using an iterative inversion equation of the time shift amount according to the Gaussian-Newton method principle;
S7, judging whether the new time shift quantity meets an iteration stop condition, if so, stopping iteration, wherein the inversion result is the final time shift quantity, and executing a step S8; otherwise, setting the inversion result as an initial model, and returning to the step S3 to carry out loop iteration until the iteration stopping condition is met;
s8, obtaining the synthesized record after time shift correction by using an interpolation method.
2. The method for time shift correction in well shock matching according to claim 1, wherein: the specific steps of the step S4 are as follows:
calculating the derivative of s (t- τ) with respect to τ in formula (1), let x=t- τ, and then the derivative of s (t- τ) with respect to τ is expressed as shown in formula (4) below:
Assuming that the number of sampling points is n, the expression of s (x) is written as: s (x) = [ s 1 s2…sn]T, the expression of x is written as: x= [ x 1x2…xn]T ] then The expression of (2) is as shown in the following expression (5):
Calculating each element of the matrix in the formula (5) by adopting a first-order center difference method to enable (I=1, 2, …, n; j=1, 2, …, n), the calculation formula of which is shown in the following formula (6):
combining the formulas (4), (5) and (6), calculating to obtain the derivative of s (t-tau) with respect to tau, and then calculating an objective function Regarding the first derivative g (τ) of the time shift amount τ, the following expression (7) shows:
Wherein the superscript T denotes the transposed symbol and I denotes the identity matrix.
3. The method for time shift correction in well shock matching according to claim 2, wherein: calculating an objective function in said step S5Regarding the second derivative H (τ) of the time shift amount τ, the following expression (8) shows:
Wherein the superscript T denotes the transposed symbol and I denotes the identity matrix.
4. A method of time shift correction in well shock matching according to claim 3, wherein: the specific steps of the step S6 are as follows:
The first derivative g (tau (0)) of the objective function at the position tau (0) with respect to the time shift amount is calculated according to the formula (7), the second derivative H (tau (0)) of the objective function at the position tau (0) with respect to the time shift amount is calculated according to the formula (8), and after one iteration calculation, the expression of the time shift amount tau is shown as the following formula (9):
τ＝τ(0)-H-1(τ(0))g(τ(0)) (9)。
5. The method for time shift correction in borehole seismic matching as recited in claim 4 where: the specific steps of the step S7 are as follows: after τ is obtained through calculation according to the formula (9), judging whether τ - τ (0) is small enough or whether the set maximum iteration number is reached, if so, stopping the iteration, wherein τ is the required final time shift amount; otherwise, setting the value of tau as an initial model, and returning to S3 for loop iteration until the condition of iteration stopping is met.
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