CN109655888B - Quantitative selection method and system for smooth floating reference surface in seismic data processing - Google Patents
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Abstract
The invention provides a quantitative selection method and a system of a smooth floating reference surface in seismic data processing, wherein the method comprises the following steps: establishing and minimizing a target functional of a smooth floating datum plane; determining a maximum smoothing factor; determining a minimum smoothing factor; and selecting any value between the maximum smoothness factor and the minimum smoothness factor to obtain the smooth floating reference surface. The invention provides a quantitative calculation formula for the construction of the smooth floating reference surface, so that the construction of the smooth floating reference surface is more scientific. In addition, the invention provides a smooth factor selection basis and a determined selection range of the smooth floating reference surface, so that the selection of the smooth floating reference surface is more reasonable.
Description
Technical Field
The invention belongs to the field of petroleum geophysical exploration, and relates to seismic data processing of petroleum geophysical exploration. And more particularly to selection and static correction of a smooth floating datum for exploration seismic prestack depth migration processing.
Background
As a reference plane for prestack migration imaging and velocity modeling, the selection of a smooth floating datum plane is crucial. Generally, the maximum migration aperture of observation data can be empirically selected to be obtained by obtaining the elevation of a smooth surface with a radius, or speed modeling and comparative analysis of migration effects are performed on different smooth radii in experiments, and the smooth surface with the best migration effect is selected as a smooth floating datum plane, but the selection of the smooth floating datum plane has no quantitative basis.
A quantitative smooth floating reference surface selection method is provided, and a quantitative selection basis is provided according to the resolution of offset imaging.
Disclosure of Invention
The invention aims to solve the problems in the existing smooth floating datum plane selection technology, realize a quantitative calculation method of a datum plane by establishing and minimizing a target functional of the smooth floating datum plane, determine the maximum smoothness factor and the minimum smoothness factor through the limitation of the longitudinal minimum imaging resolution lambda/4 of an earthquake, further enable the selection of the smooth floating datum plane to have a quantitative and reliable basis, and provide a basis for subsequent velocity analysis and offset imaging processing.
According to one aspect of the invention, there is provided a method of quantitative selection of a smooth floating reference plane in seismic data processing, the method comprising:
establishing and minimizing a target functional of a smooth floating datum plane;
determining a maximum smoothing factor;
determining a minimum smoothing factor;
and selecting any value between the maximum smoothness factor and the minimum smoothness factor to obtain the smooth floating reference surface.
Further, the minimized smooth floating datum target functional is expressed as follows:
where h represents the true surface elevation, hsRepresenting a smooth floating datum plane, wherein the first part on the right in the formula (1) is an approximate term of the smooth floating datum plane and a real earth surface, the second term and the third term are second-order partial derivatives of the smooth floating datum plane in the x and y directions respectively, αxAnd αyCalled the smoothing factor in the x, y direction, Dxx，DyyRepresenting a matrix of second order partial derivatives.
Further, for hsThe derivation is done and made zero, yielding the following:
wherein I is an identity matrix.
Further, according to the maximum high-frequency static correction value and the near-surface speed, the allowable maximum elevation correction value max (h-h) is calculateds) Thus, the maximum smoothing factor α is determined such that the elevation correction values for all of the probe points on the surface are less than the maximum elevation correction value.
Further, the high frequency static correction amount of the shot point is expressed as:
wherein, Delta Tshot_recFor high frequency static correction of current seismic trace, Vs(x)shotFor smooth surface shot velocity, Vs(x)recSpeed of smooth surface pickup point, h (x)shotTrue surface elevation of shot point, hs(x)shotSmooth surface elevation of shot h (x)recTrue surface elevation of the probe point, hs(x)recThe survey points smooth the elevation of the earth's surface.
Further, a minimum smoothing factor is determined based on the interpolation requirements of the travel time field such that the difference between the interpolated travel time and the travel time calculated for the real surface does not exceed T/4.
Further, an arbitrary value between the maximum smoothness factor and the minimum smoothness factor is selected, and the smooth floating reference surface h is obtained by using the formula (3)s。
According to another aspect of the present invention, there is provided a system for quantitative selection of a smooth floating reference plane in seismic data processing, the system comprising:
a memory storing computer-executable instructions;
a processor executing computer executable instructions in the memory to perform the steps of:
establishing and minimizing a target functional of a smooth floating datum plane;
determining a maximum smoothing factor;
determining a minimum smoothing factor;
and selecting any value between the maximum smoothness factor and the minimum smoothness factor to obtain the smooth floating reference surface.
Further, a maximum smoothing factor and a minimum smoothing factor are determined by the limitation of the seismic longitudinal minimum imaging resolution λ/4.
Further, a smooth floating reference surface h is obtained by using the formula (3)s：
Where h represents the true surface elevation, hsIndicating a smooth floating datum, αxAnd αyCalled the smoothing factor in the x, y direction, Dxx，DyyAnd (3) a matrix formed by second-order partial derivatives is shown, and I is an identity matrix.
The quantitative selection technology of the smooth floating datum plane in seismic data processing comprises the steps of firstly realizing quantitative expression of the smooth floating datum plane according to a minimum smooth floating datum plane target functional, then determining a maximum smooth factor and a minimum smooth factor according to the limitation of the seismic longitudinal minimum imaging resolution lambda/4, and giving any smooth factor between the maximum smooth factor and the minimum smooth factor to obtain the corresponding correction value of each point on the smooth floating datum plane.
Compared with the prior art, the invention provides a quantitative calculation formula for the construction of the smooth floating reference surface, so that the construction of the smooth floating reference surface is more scientific. In addition, the invention provides a smooth factor selection basis and a determined selection range of the smooth floating reference surface, so that the selection of the smooth floating reference surface is more reasonable. Therefore, the algorithm of the invention is scientific, easy to realize and high in calculation efficiency.
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The above and other objects, features and advantages of the present disclosure will become more apparent by describing in greater detail exemplary embodiments thereof with reference to the attached drawings, in which like reference numerals generally represent like parts throughout.
FIG. 1 shows a flow chart of a method for quantitative selection of a smooth floating datum in seismic data processing.
Fig. 2 shows a graphical elevation smoothing diagram (longitudinal units: meters, lateral position points) for different smoothing factors, the solid black lines on the way being the original elevations,
is the elevation at which the smoothing factor is 10,
is in elevation with a smoothing factor of 25.
FIG. 3 shows elevation corrected differential intents (longitudinal units: meters, lateral location points) for different smoothness factors, where
Is the elevation difference with a smoothing factor of 10,
for a smoothing factor of 25, it can be seen that as the smoothing factor increases, the datum level is smoother and the height difference is also greater.
FIG. 4 is a schematic diagram showing local elevations of travel time control points spaced 200 meters apart, A1A2The dotted line is a linear interpolation, B1B2B3B4B5As a true surface elevation curve, A1B'2A2Is a smooth floating datum curve.
Detailed Description
Preferred embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While the preferred embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
The invention aims at the difficult problem of quantitative selection of the conventional smooth floating reference surface, provides a quantitative calculation method of the smooth floating reference surface by establishing and minimizing a smooth floating reference surface target functional, determines the maximum smooth factor and the minimum smooth factor through the limitation of the longitudinal minimum imaging resolution lambda/4 of the earthquake, and provides any smooth factor between the maximum smooth factor and the minimum smooth factor to calculate the corresponding correction value of each point on the smooth floating reference surface, so that the selection of the smooth floating reference surface has quantitative and reliable basis, the construction of the smooth floating reference surface is more scientific, and a foundation is provided for subsequent velocity analysis and offset imaging processing.
As shown in fig. 1, the present disclosure proposes a method for providing a quantitative selection of a smooth floating reference plane in seismic data processing, the method comprising:
establishing and minimizing a target functional of a smooth floating datum plane;
determining a maximum smoothing factor;
determining a minimum smoothing factor;
and selecting any value between the maximum smoothness factor and the minimum smoothness factor to obtain the smooth floating reference surface.
The method of the invention aims at the quantitative selection problem of the smooth reference surface, establishes a target functional of the smooth floating reference surface to obtain the quantitative expression of the smooth floating reference surface, further determines the maximum smooth factor and the minimum smooth factor according to the limitation of the longitudinal minimum imaging resolution lambda/4 of the earthquake, and gives any smooth factor between the maximum smooth factor and the minimum smooth factor to calculate the corresponding correction value of each point on the smooth floating reference surface.
Specifically, the method comprises the following steps:
(1) a smooth floating datum target functional is established and minimized.
Assuming h represents the true surface elevation, a smooth floating datum level h is obtainedsWe expect hsTwo conditions are satisfied: firstly, the surface of the earth is as close as possible to the real earth surface, and secondly, the surface is as smooth as possible, namely, the second-order partial derivative is as small as possible and can pass through the matrix Dxx，DyyAnd (4) showing. The above problem can be solved by minimizing the following smooth floating datum target functional:
wherein, the first part on the right in the formula (1) is an approximate term of a smooth floating datum plane and a real earth surface, the second term and the third term are respectively second-order partial derivatives in x and y directions of the smooth floating datum plane, αxAnd αyA smoothing factor, referred to as the x, y direction, is generally takenαx＝αyThe larger the α, the base plane hsThe higher the smoothness.
In order to solve the above functional minimum, h needs to be calculatedsThe derivation is done and made zero, yielding the following:
thereby obtaining:
(3) the formula is a typical linear equation system, and can be directly solved by a general solution method such as a conjugate gradient method, a least square orthogonal decomposition method and the like, wherein α is usedxAnd αyAs a regularization term, which adds to the identity matrix I, actually serves a smoothing function, αxAnd αyThe degree of smoothing is represented and the result obtained is the smoothed floating reference surface.
(2) Determining a maximum smoothing factor
The determination of the maximum smoothing factor is analyzed from the angle of the longitudinal resolution of the offset imaging, and the selection principle of the smoothing factor is that the in-phase superposition of reflected waves in an imaging channel set is not influenced by the correction of the high wave number time difference of the reflected waves introduced by the smooth floating reference surface, namely the accurate position and the imaging energy of the offset imaging are not changed. In seismic exploration, the longitudinal minimum imaging resolution of seismic imaging is lambda/4, lambda is the wavelength corresponding to seismic wave main frequency, the maximum static correction value of reflected waves obtained according to the longitudinal minimum imaging resolution is required to be smaller than T/4, T is the period corresponding to the seismic wave main frequency, and the following relational expression is satisfied:
ΔTshot_rec<T/4 (4)
ΔTshot_recis the high-frequency static correction value of the wave detection point. The high-frequency static correction value between the real ground surface and the smooth floating reference surface at any position x is expressed as:
wherein H (x) is the low speed belt thickness; v (x) is the ground surface true velocity; vs(x) For surface smoothness velocities, in fact, the surface true velocity is unknown, so it is generally assumed that the near-surface model created by near-surface tomography is accurate, i.e., has V (x) approximately equal to Vs(x) In that respect Thus, the high frequency static correction amount at this time of the shot point can be expressed as:
wherein, Delta Tshot_recFor high frequency static correction of current seismic trace, Vs(x)shotFor smooth surface shot velocity, Vs(x)recSpeed of smooth surface pickup point, h (x)shotTrue surface elevation of shot point, hs(x)shotSmooth surface elevation of shot h (x)recTrue surface elevation of the probe point, hs(x)recThe survey points smooth the elevation of the earth's surface.
Considering that the high-frequency static correction quantity expressed in the formula (6) is not only related to the near-surface speed but also related to the surface elevation correction difference caused by the smoothing factor, when the near-surface speed V is useds(x) Under the determined condition, the high-frequency static correction amount is only matched with the smooth floating reference surface hsIt is related.
Maximum elevation correction max (h-h)s) Is the maximum value of the difference between the true surface and the smooth surface corresponding to all shot points and demodulator probes, different smoothing factors α produce different smooth surfaces hsThe larger the smoothness factor α, the more slippery surface h is producedsThe smoother the maximum elevation correction max (h-h)s) The larger. The high-frequency static correction value delta T of any seismic channel can be obtained by bringing the elevation difference of all shot and geophone points into the formula (6)shot_recA smooth reference surface h for ensuring that the high-frequency static correction amount is equal to T/4sThe corresponding smoothing factor is the maximum smoothing factor.
(3) Determining a minimum smoothing factor
The determination of the minimum smoothing factor is determined from the interpolation requirements of the travel time field. In the migration method of Kirchhoff product classification, calculation of a control point travel time field is required before migration is performed, and the interval of the travel time field in a plane space is generally from several tens of meters to several hundreds of meters. When the gather is shifted, the travel time fields of the shot point and the demodulator probe need to be interpolated according to the travel time of the control point. The method can be obtained by interpolating positions of a control point travel time field and a shot point demodulator probe, the interpolation is generally linear interpolation, and if the difference between the travel time obtained by interpolation and the travel time calculated by the real earth surface exceeds T/4, the minimum smoothing factor needs to be performed on the real earth surface, so that the difference between the travel time obtained by interpolation and the travel time calculated by the real earth surface does not exceed T/4.
FIG. 4 is a schematic view of local elevations at 200 m intervals of control points during travel, A1A2The dotted line is a linear interpolation curve, B1B2B3B4B5As a true surface elevation curve, A1B'2A2Is a smooth floating datum curve. A. the1，A2Calculating the elevation position of the control point for travel, B1，B2，B3，B4，B5The travel time interpolation points that need to be calculated. With B2Taking a point as an example, if B2Elevation difference B to linear interpolation curve2B”2The correction value of the caused time difference does not exceed T/4, which shows that the price ratio of the local elevation change is flat, and the smoothing of the minimum smoothing factor is not needed, namely the minimum smoothing factor is zero. If B is present2Elevation difference B to linear interpolation curve2B”2The amount of correction of the resulting time difference exceeds T/4, then B2The travel time field obtained by interpolation has larger error, and further affects the in-phase superposition of in-phase axes, at the moment, the smoothness of the minimum smooth factor is needed to be carried out on the local elevation, and the smooth result is B2Point moving to B'2To ensure B'2B”2And (3) the correction value of the caused elevation time difference does not exceed T/4, and the specific calculation method of the elevation time difference refers to the formula (6), so that the selection method of the minimum smooth factor is obtained.
(4) Calculation of smooth reference surface
After the maximum smoothness factor and the minimum smoothness factor are determined, any value between the maximum smoothness factor and the minimum smoothness factor can be selected, and then the smooth floating reference surface h is obtained by utilizing the formula (3)sAnd finishing the calculation of the smooth reference surface.
According to another embodiment of the present invention, there is provided a system for quantitative selection of a smooth floating reference plane in seismic data processing, the system comprising:
a memory storing computer-executable instructions;
a processor executing computer executable instructions in the memory to perform the steps of:
establishing and minimizing a target functional of a smooth floating datum plane;
determining a maximum smoothing factor;
determining a minimum smoothing factor;
and selecting any value between the maximum smoothness factor and the minimum smoothness factor to obtain the smooth floating reference surface.
Further, a maximum smoothing factor and a minimum smoothing factor are determined by the limitation of the seismic longitudinal minimum imaging resolution λ/4.
Further, a smooth floating reference surface h is obtained by using the formula (3)s：
Where h represents the true surface elevation, hsIndicating a smooth floating datum, αxAnd αyCalled the smoothing factor in the x, y direction, Dxx，DyyAnd (3) a matrix formed by second-order partial derivatives is shown, and I is an identity matrix.
The invention provides a quantitative calculation formula for the construction of the smooth floating reference surface, so that the construction of the smooth floating reference surface is more scientific. In addition, the invention provides a smooth factor selection basis and a determined selection range of the smooth floating reference surface, so that the selection of the smooth floating reference surface is more reasonable. Therefore, the algorithm of the invention is scientific, easy to realize and high in calculation efficiency.
To facilitate understanding of the solution of the embodiments of the present invention and the effects thereof, a specific application example is given below. It will be understood by those skilled in the art that this example is merely for the purpose of facilitating an understanding of the present invention and that any specific details thereof are not intended to limit the invention in any way.
Fig. 2-3 depict one embodiment of the present invention, fig. 2 showing elevation smoothness plots (longitudinal units: meters, lateral location points) for different smoothness factors, where the solid black lines are the original elevations,
for a smooth surface elevation with a smoothing factor of 10,
for a smooth surface elevation with a smoothing factor of 25, it can be seen that the greater the smoothing factor, the smoother the surface. FIG. 3 is a schematic diagram of elevation correction values (in units of meters in longitudinal direction, lateral position points) for two different smoothing factors
Is the elevation difference with a smoothing factor of 10,
the elevation difference is an elevation difference with a smoothing factor of 25, the maximum elevation correction value of the smooth earth surface is 40m when the smoothing factor is 10, and the maximum elevation correction value of the smooth earth surface is 47m when the smoothing factor is 25. Assuming that the near-surface velocity is 1000m/s and the T/4 of the seismic wave is 80ms, the maximum allowable height difference is 40m, and the smoothing factor 10 is the maximum smoothing factor.
FIG. 4 is a schematic view of local elevations at 200 m intervals of control points during travel, A1A2The dotted line is a linear interpolation curve, B1B2B3B4B5As a true surface elevation curve, A1B'2A2Is a smooth floating datum curve. A. the1，A2Calculating the elevation position of the control point for travel, B1，B2，B3，B4，B5The travel time interpolation points that need to be calculated. With B2Taking a point as an example, if B2Elevation difference B to linear interpolation curve2B”2The correction value of the caused time difference does not exceed T/4, which shows that the price ratio of the local elevation change is flat, and the smoothing of the minimum smoothing factor is not needed, namely the minimum smoothing factor is zero. If B is present2Elevation difference B to linear interpolation curve2B”2The amount of correction of the resulting time difference exceeds T/4, then B2The travel time field obtained by interpolation has larger error, and further affects the in-phase superposition of in-phase axes, at the moment, the smoothness of the minimum smooth factor is needed to be carried out on the local elevation, and the smooth result is B2Point moving to B'2To ensure B'2B”2And (3) the correction value of the caused elevation time difference does not exceed T/4, and the specific calculation method of the elevation time difference refers to the formula (6), so that the selection method of the minimum smooth factor is obtained.
Having described embodiments of the present disclosure, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen in order to best explain the principles of the embodiments, the practical application, or improvements made to the technology in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.
Claims (4)
1. A method for quantitative selection of a smooth floating reference plane in seismic data processing, the method comprising:
establishing and minimizing a target functional of a smooth floating datum plane;
determining a maximum smoothing factor;
determining a minimum smoothing factor;
selecting any value between the maximum smooth factor and the minimum smooth factor to obtain a smooth floating reference surface;
wherein, the minimized smooth floating datum plane target functional is expressed as follows:
where h represents the true surface elevation, hsRepresenting a smooth floating datum plane, wherein the first part on the right in the formula (1) is an approximate term of the smooth floating datum plane and a real earth surface, the second term and the third term are second-order partial derivatives of the smooth floating datum plane in the x and y directions respectively, αxAnd αyCalled the smoothing factor in the x, y direction, Dxx，DyyRepresenting a matrix of second partial derivatives;
wherein, the allowable maximum elevation correction value max (h-h) is calculated according to the maximum high-frequency static correction value and the near-surface speeds) Determining a maximum smoothing factor α so that the elevation correction values of all the detection points on the earth surface are smaller than the maximum elevation correction value;
determining a minimum smooth factor according to the interpolation requirement of the travel time field, so that the difference between the travel time obtained by interpolation and the travel time calculated by a real earth surface does not exceed T/4, wherein T is a period corresponding to the seismic wave dominant frequency;
wherein, for hsThe derivation is done and made zero, yielding the following:
wherein I is an identity matrix;
selecting any value between the maximum smoothness factor and the minimum smoothness factor, and solving the smooth floating reference surface h by using the formula (3)s。
2. The method of claim 1, wherein the high frequency static correction for the shot point is expressed as:
wherein, Delta Tshot_recFor high frequency static correction of current seismic trace, Vs(x)shotFor smooth surface shot velocity, Vs(x)recSpeed of smooth surface pickup point, h (x)shotTrue surface elevation of shot point, hs(x)shotSmooth surface elevation of shot h (x)recTrue surface elevation of the probe point, hs(x)recThe survey points smooth the elevation of the earth's surface.
3. A system for quantitative selection of a smooth floating reference surface in seismic data processing, the system comprising:
a memory storing computer-executable instructions;
a processor executing computer executable instructions in the memory to perform the steps of:
establishing and minimizing a target functional of a smooth floating datum plane;
determining a maximum smoothing factor;
determining a minimum smoothing factor;
selecting any value between the maximum smooth factor and the minimum smooth factor to obtain a smooth floating reference surface;
wherein, the minimized smooth floating datum plane target functional is expressed as follows:
where h represents the true surface elevation, hsRepresenting a smooth floating datum plane, wherein the first part on the right in the formula (1) is an approximate term of the smooth floating datum plane and a real earth surface, the second term and the third term are second-order partial derivatives of the smooth floating datum plane in the x and y directions respectively, αxAnd αyCalled the smoothing factor in the x, y direction, Dxx，DyyRepresenting a matrix of second partial derivatives;
wherein, according toCalculating the maximum allowable elevation correction value max (h-h) by the maximum high-frequency static correction value and the near-surface speeds) Determining a maximum smoothing factor α so that the elevation correction values of all the detection points on the earth surface are smaller than the maximum elevation correction value;
determining a minimum smooth factor according to the interpolation requirement of the travel time field, so that the difference between the travel time obtained by interpolation and the travel time calculated by the real earth surface does not exceed T/4;
wherein, for hsThe derivation is done and made zero, yielding the following:
wherein I is an identity matrix;
selecting any value between the maximum smoothness factor and the minimum smoothness factor, and solving the smooth floating reference surface h by using the formula (3)s。
4. A system for quantitative selection of a smooth floating reference surface in seismic data processing according to claim 3, wherein the maximum and minimum smoothing factors are determined by a constraint on the seismic longitudinal minimum imaging resolution λ/4, λ being the wavelength corresponding to the seismic wave dominant frequency.
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