A method for tracing two-dimensional ray forward seismic traces

Abstract

The application provides a two-dimensional ray forward seismic trace tracking method, which comprises the following steps: establishing a mathematical physical model corresponding to incident and reflected rays; tracking from a surface ray exit angle β0 to the underground, tracking layer by layer downward according to Snell's law of refraction, calculating an incident point of the incident ray and the incident stratum interface, and calculating the travel time of the incident ray in each layer; tracking layer by layer from Snell's law of refraction to the surface according to the reflection law, calculating the intersection of the reflected ray and each stratum interface, and calculating the travel time of the reflected ray in each layer; tracking normal rays of each layer corresponding to common midpoint trace sets and pre-stack trace imaging rays; determining the common midpoint trace set according to the surface incident point, the stratum reflection point, the surface exit point and the normal ray passing through the common midpoint; and determining the seismic pre-stack trace set according to the imaging ray and the equal offset incident and reflected trace. A more complex and more realistic stratum model is established, and a more in-depth study on the seismic wave velocity forward simulation is carried out.

Description

Technical Field

[0001] This invention relates to the field of exploration geophysics, and more particularly to a method for tracking two-dimensional ray forward modeling seismic gathers. Background Technology

[0002] Before the 1990s, the ray method was the primary means for exploration geophysicists to understand and interpret reflected waves observed on reflection seismic profiles, and it was widely used in oil exploration and development. The ray method, short for the asymptotic ray method, can be seen in exploration seismology as a tool for simulating forward dynamic wave equations. In the ray method, the entire wavefield is decomposed into individual "fundamental waves," each ray being a fundamental wave. Many rays may be traced between a specific source and detector, and the entire wavefield is constructed by superimposing the fundamental waves. The fundamental wave (i.e., the pulse along the studied ray) can be represented by the source parameters obtained along the traced rays. The ray method can replace various integral and finite difference methods, and its most important characteristics are simplicity and intuitiveness. The first and second derivatives of the travel time curve include the ray direction and wavefront curvature of the outgoing wave, partially reflecting the duality of ray and wave theory. Although rays cannot adequately describe diffraction phenomena and low-frequency wave interference phenomena, and cannot accurately give the cause of vibration and wave motion, the ray method is the most effective means of solving forward and inverse problems of seismic wave travel time and velocity.

[0003] Because time migration is largely based on the theory of seismic wave diffraction, the role of ray theory in interpreting reflected wave time migration has long been overlooked. Normal rays describe unmigrated stacked data, while imaging rays describe time-migrated data. The relationship between migration velocity and imaging rays is analogous to the relationship between stacking velocity and normal rays. In oil exploration and development, subsurface reflection layer information is constructed by the incident and reflected data from the source and receiver, and velocity models are obtained through seismic gathers. Before the widespread adoption of digital seismic migration technology, exploration geophysicists used a given stratigraphic model to simulate the ray travel time between the source and receiver to forward model seismic wave velocity. Past stratigraphic models were relatively simple and primarily based on hand-drawn diagrams, resulting in insufficient precision and depth in quantitative research on seismic wave velocity forward modeling. This invention establishes a more complex model that more closely approximates real stratigraphy, utilizing modern advanced computer technology and software to conduct more in-depth quantitative research on seismic wave velocity forward modeling. Summary of the Invention

[0004] In view of the above problems, the present invention is proposed to provide a method for tracking two-dimensional ray forward modeling seismic gathers that overcomes or at least partially solves the above problems.

[0005] According to one aspect of the present invention, a method for tracing two-dimensional ray forward modeling seismic gathers is provided, the tracing method comprising:

[0006] Step S1: Establish mathematical and physical models corresponding to incident and reflected rays;

[0007] Step S2: Starting from the surface ray emission angle β0, trace the ray downwards layer by layer according to Snell's law of refraction, calculate the incident point at the interface between the incident ray and the incident stratum, and calculate the travel time of the incident ray in each layer.

[0008] Step S3: Based on the law of reflection and Snell's law of refraction, perform ray tracing layer by layer towards the Earth's surface, calculate the intersection points of the reflected rays with the interfaces of each stratum, and calculate the travel time of the reflected rays in each layer;

[0009] Step S4: Trace the normal rays of each layer corresponding to the common center point gather according to Snell's law of refraction;

[0010] Step S5: Track the imaging ray according to Snell's law of refraction;

[0011] Step S6: Determine the common midpoint gather based on the surface incident point, stratum reflection point, surface exit point, and the normal ray passing through the common midpoint. Determine the pre-stack gather based on the imaging ray and the equidistant incident and reflection traces.

[0012] Optionally, step S1: establishing the mathematical and physical model corresponding to the incident and reflected rays specifically includes:

[0013] Establish mathematical and physical models corresponding to incident and reflected rays based on the coordinates, dip angle, depth, and layer velocity of the given strata;

[0014] The dip angle of the first stratigraphic interface is θ1, and the slope is L1 = tgθ1. Given the coordinates (x, y) of a point on the first stratigraphic interface... d1 ,y d1 The equation for determining the first stratigraphic interface is:

[0015] y = L1(xx d1 )+y d1 (1-1)

[0016] The dip angle of the second stratigraphic interface is θ2, and the slope is L2 = tgθ2. Given the coordinates (x, y) of a point on the second stratigraphic interface... d2 ,y d2 The equation for determining the second stratigraphic interface is:

[0017] y = L2(xx) d2 )+y d2 (1-2)

[0018] The dip angle of the third stratigraphic interface is θ3, and the slope is L3 = tgθ3. Given the coordinates (x, y) of a point on the third stratigraphic interface... d3 ,y d3 The equation for the third stratigraphic interface is determined as follows:

[0019] y = L3(xx) d3 )+y d3 (1-3)

[0020] ...

[0021] The dip angle of the Nth stratigraphic interface is θ N The slope is L N =tgθ N Given the coordinates (x, y) of a point on the Nth stratigraphic interface. dN ,y dN The equation for determining the Nth stratigraphic interface is:

[0022] y = L N (xx dN )+y dN (1-4)

[0023] Given the layer velocities of layers 1, 2, 3, ..., N as V1, V2, V3, ..., V... N .

[0024] Optionally, in step S1, establishing the incident ray mathematical-physical model based on the established geological model through which the incident ray passes further includes:

[0025] Based on the given layer velocity V and Snell's law of refraction for each layer in the stratigraphic model, the relationship between the incident angle α and the refraction angle β is established, and the slope of the incident ray at the next interface is obtained based on the relationship.

[0026]

[0027]

[0028]

[0029] ...

[0030]

[0031]

[0032] The incident ray ends, β is not calculated. N V1, V2, V3, ..., V N These represent the layer velocities of layers 1, 2, 3, ..., N; θ1, θ2, θ3, ..., θ NThese are the dip angles of the 1st, 2nd, 3rd, ..., Nth stratigraphic interfaces; ε1, ε2, ε3, ..., ε N These are the dip angles of the normals at the interfaces of the 1st, 2nd, 3rd, ..., Nth strata.

[0033] Optionally, in step S1, establishing the geological model through which the reflected rays pass further includes:

[0034] For reflected rays, when a ray incident from the ground is reflected at a certain interface, the reflected ray exits in the direction of the ground and is incident below each interface.

[0035] In the reflection path, based on the dip angle θ of the two-dimensional stratigraphic interface and the coordinates (x, y) of a point on the stratigraphic interface... d ,y d Establish a mathematical and physical model for reflected rays;

[0036] The dip angle of the (N+1)th stratigraphic interface is θ N+1 =θ N-1 The slope is L N+1 =tgθ N+1 Given the coordinates (x, y) of a point on the (N+1)th stratigraphic interface. d(N+1) ,y d(N+1) ), x d(N+1) =x d(N-1) ,y d(N+1) =y d(N-1) The equation for determining the (N+1)th stratigraphic interface is as follows:

[0037] y = L N+1 (xx d(N+1) )+y d(N+1) (1-10)

[0038] The dip angle of the (N+2)th stratigraphic interface is θ N+2 =θ N-2 The slope is L N+2 =tgθ N+2 Given the coordinates (x, y) of a point on the (N+2)th stratigraphic interface. d(N+2) ,y d(N+2) ), x d(N+2) =x d(N-2) y d(N+2) =y d(N-2) The equation for the (N+2)th stratigraphic interface is determined as follows:

[0039] y = L N+2 (xx d(N+2) )+y d(N+2) (1-11)

[0040] The dip angle of the (N+3)th stratigraphic interface is θ N+3 =θ N-3 The slope is LN+3 =tgθ N+3 Given the coordinates (x, y) of a point on the (N+3)th stratigraphic interface. d(N+3) ,y d(N+3) ), x d(N+3) =x d(N-3) y d(N+3) =y d(N-3) Determine the equation for the (N+3)th stratigraphic interface.

[0041] y = L N+3 (xx d(N+3) )+y d(N+3) (1-12)

[0042] ...

[0043] The dip angle of the (N+i)th stratigraphic interface is θ N+i =θ N-i The slope is L N+i =tgθ N+i Given the coordinates (x, y) of a point on the (N+i)th stratigraphic interface. d(N+i) ,y d(N+i) ), x d(N+i) =x d(N-i) ,y d(N+i) =y d(N-i) The equation for determining the (N+i)th stratigraphic interface is as follows:

[0044] y = L N+i (xx d(N+i) )+y d(N+i) (1-13)

[0045] Where i = 1, 2, 3, ..., N.

[0046] Optionally, step S1, establishing the mathematical and physical model of the reflected ray, further includes:

[0047] Based on the given layer velocity V and Snell's law of refraction for each layer in the stratigraphic model, the relationship between the incident angle α and the refraction angle β is established, and the slope of the incident ray at the next interface is obtained based on the relationship.

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] The incident ray ends, β is not calculated.N+i V N+1 V N+2 V N+3 ... V N+i These are the layer velocities of layers N+1, N+2, N+3, ..., N+i, respectively; θ N+1 θ N+2 θ N+3 、……、θ N+i ε represents the dip angle of the (N+1), (N+2), (N+3), ..., (N+i)th stratigraphic interfaces; N+1 ε N+2 ε N+3 ... ε N+i These are the normal dip angles of the N+1, N+2, N+3, ..., N+i stratigraphic interfaces, respectively.

[0054] Optionally, in step S2, tracing the ray from the surface at the emission angle β0 downwards, and following Snell's law of refraction layer by layer, the point of incidence at the interface between the incident ray and the incident stratum is calculated, and the travel time of the incident ray in each layer is calculated, specifically including:

[0055] (1) Incident rays at the first stratigraphic interface

[0056] The dip angle γ1 of the incident ray at the first stratigraphic interface and the coordinates (x0, y0) of the ground starting point determine the incident ray at the first stratigraphic interface.

[0057] Normal dip angle of the first stratigraphic boundary The incident angle of the first stratigraphic interface is α1 = β0 - ε1;

[0058] Inclination angle corresponding to the incident ray When the incident ray slope is K1 = tanγ1, the equation of the incident ray at the first stratigraphic interface is...

[0059] y = K1(x - x0) + y0 (1-19)

[0060] By combining equations (1-1) and (1-19), the intersection point of the incident ray and the first stratigraphic interface is determined to be (x1, y1).

[0061]

[0062] When the angle of inclination of the corresponding incident ray At that time, the intersection point of the incident ray from the first stratigraphic interface and the first stratigraphic interface is (x1, y1).

[0063]

[0064] The distance between points (x1, y1) and (x0, y0) is S1, and the travel time is Δt1.

[0065]

[0066] (2) Incident rays at the second stratigraphic interface

[0067] The incident ray at the second stratigraphic interface is determined by the dip angle γ2 of the incident ray at the second stratigraphic interface and the intersection point (x1, y1) of the incident ray at the first stratigraphic interface with the first stratigraphic interface.

[0068] Normal dip angle of the second stratigraphic boundary The angle of refraction at the first stratigraphic interface The incident angle of the second stratigraphic interface is α2 = β1 + ε1 - ε2;

[0069] Inclination angle corresponding to the incident ray The incident ray equation for the second stratigraphic interface corresponds to the incident ray slope K2 = tanγ2.

[0070] y = K2(x - x1) + y1 (1-23)

[0071] By combining equations (1-2) and (1-23), the intersection point of the incident ray at the second stratigraphic interface and the second layer interface is determined to be (x2, y2).

[0072]

[0073] When the angle of inclination of the corresponding incident ray At that time, the intersection point of the incident ray from the second stratigraphic interface and the second stratigraphic interface is (x2, y2).

[0074]

[0075] The distance between points (x2, y2) and (x1, y1) is S2, and the travel time is Δt2.

[0076]

[0077] (3) Incident rays at the third stratigraphic interface

[0078] The incident ray at the third stratigraphic interface is determined by the dip angle γ3 of the incident ray at the third stratigraphic interface and the intersection point (x2, y2) of the incident ray at the second stratigraphic interface.

[0079] Normal dip angle of the third stratigraphic boundary The angle of refraction at the second stratigraphic interface The incident angle of the third stratigraphic interface is α3 = β2 + ε2 - ε3;

[0080] Inclination angle corresponding to the incident ray The incident ray equation for the third stratigraphic interface corresponds to the incident ray slope K3 = tanγ3.

[0081] y = K3(x - x2) + y2 (1-27)

[0082] By combining equations (1-3) and (1-27), the intersection point of the incident ray and the third stratigraphic interface is determined to be (x3, y3).

[0083]

[0084] When the angle of inclination of the corresponding incident ray At that time, the intersection point of the incident ray from the third stratigraphic interface and the third stratigraphic interface is (x3, y3).

[0085]

[0086] The distance between points (x2, y2) and (x3, y3) is S3, and the travel time is Δt3.

[0087]

[0088] ...

[0089] (N) Incident rays at the Nth stratigraphic interface

[0090] The dip angle γ of the incident ray at the Nth stratigraphic interface N The intersection point (x) of the incident ray from the (N-1)th stratigraphic interface with the (N-1)th stratigraphic interface. N-1 ,y N-1 Determine the incident ray at the Nth stratigraphic interface;

[0091] normal dip angle of the Nth stratigraphic boundary The angle of refraction at the (N-1)th stratigraphic interface The incident angle α at the Nth stratigraphic interface N =β N-1 +ε N-1 -ε N ;

[0092] Inclination angle corresponding to the incident ray Corresponding incident ray slope K N =tanγ N The equation of the incident ray at the Nth stratigraphic interface

[0093] y = K N (xx N-1 )+y N-1 (1-31)

[0094] By combining equations (1-4) and (1-31), the intersection point of the incident ray at the Nth stratigraphic interface and the Nth stratigraphic interface is obtained as (x). N ,y N )

[0095]

[0096] When the angle of inclination of the corresponding incident ray At that time, the intersection point of the incident ray from the Nth stratigraphic interface and the Nth stratigraphic interface is (x N ,y N )

[0097]

[0098] Point (x) N-1 ,y N-1 ) and (x N ,y N The distance between them is S. N The travel time is Δt N

[0099]

[0100] Optionally, step S3: performing ray tracing layer by layer towards the Earth's surface according to the law of reflection and Snell's law of refraction, calculating the intersection points of the reflected rays with the interfaces of each stratum, and calculating the travel time of the reflected rays in each layer specifically includes:

[0101] (1) Incident rays at the (N+1)th stratigraphic interface

[0102] The dip angle γ of the incident ray at the (N+1)th stratigraphic interface N+1 The intersection point (x) of the incident ray from the Nth stratigraphic interface with the Nth stratigraphic interface. N ,y N Determine the incident ray at the (N+1)th stratigraphic interface;

[0103] normal dip angle of the N+1th stratigraphic boundary The incident angle α of the (N+1)th stratigraphic interface N+1 =ε N -α N -ε N+1 ;

[0104] Corresponding incident ray tilt angle Corresponding incident ray slope K N+1 =tanγ N+1 The equation of the incident ray at the (N+1)th stratigraphic interface

[0105] y = K N+1 (xx N )+y N(1-35)

[0106] By combining equation (1-35) and equation (1-10) of the (N+1)th stratigraphic interface, the intersection point of the incident ray and the (N+1)th stratigraphic interface is found to be (x). N+1 ,y N+1 )

[0107]

[0108] When the angle of inclination of the corresponding incident ray At that time, the intersection point of the incident ray from the (N+1)th stratigraphic interface and the (N+1)th stratigraphic interface is (x N+1 ,y N+1 )

[0109]

[0110] Point (x) N+1 ,y N+1 ) and (x N ,y N The distance between them is S. N+1 The travel time is Δt N+1

[0111]

[0112] (2) Incident rays at the (N+2)th stratigraphic interface

[0113] The dip angle γ of the incident ray at the (N+2)th stratigraphic interface N+2 The intersection point (x) of the incident ray from the (N+1)th stratigraphic interface with the (N+1)th stratigraphic interface. N+1 ,y N+1 Determine the incident ray at the N+2th stratigraphic interface;

[0114] normal dip angle of the (N+2)th stratigraphic boundary The angle of refraction at the (N+1)th stratigraphic interface The incident angle α of the (N+2)th stratigraphic interface N+2 =β N+1 +ε N+1 -ε N+2 ;

[0115] Corresponding incident ray tilt angle Corresponding incident ray slope K N+2 =tanγ N+2 The equation of the incident ray at the N+2th stratigraphic interface

[0116] y = K N+2 (xx N+1 )+y N+1 (1-39)

[0117] By combining equation (1-39) and equation (1-11) of the (N+2)th stratigraphic interface, the intersection point of the incident ray and the (N+2)th stratigraphic interface is found to be (x). N+2 ,y N+2 )

[0118]

[0119] When the angle of inclination of the corresponding incident ray The intersection point of the incident ray at the (N+2)th stratigraphic interface and the (N+2)th stratigraphic interface is (x N+2 ,y N+2 )

[0120]

[0121] Point (x) N+2 ,y N+2 ) and (x N+1 ,y N+1 The distance between them is S. N+2 The travel time is Δt N+2

[0122]

[0123] (3) Incident rays at the (N+3)th stratigraphic interface

[0124] The dip angle γ of the incident ray at the (N+3)th stratigraphic interface N+3 The intersection point (x) of the incident ray from the N+2th stratigraphic interface with the N+2th stratigraphic interface. N+2 ,y N+2 Determine the incident ray at the N+3rd stratigraphic interface;

[0125] Normal dip angle of the (N+3)th stratigraphic boundary The angle of refraction at the (N+2)th stratigraphic interface The incident angle α of the (N+3)th stratigraphic interface N+3 =β N+2 +ε N+2 -ε N+3

[0126] Corresponding incident ray tilt angle Corresponding incident ray slope L N+3 =tanγ N+3 The equation of the incident ray at the (N+3)th stratigraphic interface

[0127] y = K N+3 (xx N+2 )+y N+2 (1-43)

[0128] By combining equation (1-43) and equation (1-12) of the (N+3)th stratigraphic interface, the intersection point of the incident ray and the (N+3)th stratigraphic interface is found to be (x). N+3 ,y N+3 )

[0129]

[0130] When the angle of inclination of the corresponding incident ray The intersection point of the incident ray at the (N+3)th stratigraphic interface and the (N+3)th stratigraphic interface is (x N+3 ,y N+3 )

[0131]

[0132] Point (x) N+2 ,y N+2 ) and (x N+3 ,y N+3 The distance between them is S. N+3 The travel time is Δt N+3

[0133]

[0134] ...

[0135] (N+i) Incident ray at the N+i-th stratigraphic interface

[0136] The dip angle γ of the incident ray at the (N+i)th stratigraphic interface N+i The intersection point (x) of the incident ray from the N+i-1th stratigraphic interface with the N+i-1th stratigraphic interface. N+(i-1) ,y N+(i-1) Determine the incident ray at the (N+i)th stratigraphic interface;

[0137] Normal dip angle of the (N+i)th stratigraphic interface The angle of refraction at the (N+i-1)th stratigraphic interface The incident angle α of the N+i-th stratigraphic interface N+i =β N+(i-1) +ε N+(i-1) -ε N+i ;

[0138] Corresponding incident ray tilt angle Corresponding incident ray slope K N+i =tanγ N+i The equation of the incident ray at the N+i-th stratum interface

[0139] y = K N+i (xx N+(i-1) )+y N+(i-1)(1-47)

[0140] By combining equation (1-47) and equation (1-13) of the (N+i)th stratigraphic interface, the intersection point of the incident ray and the (N+i)th stratigraphic interface is obtained as (x N+i ,y N+i )

[0141]

[0142] When the angle of inclination of the corresponding incident ray The intersection point of the incident ray at the (N+i)th stratigraphic interface and the (N+i)th stratigraphic interface is (x N+i ,y N+i )

[0143]

[0144] Point (x) N+i ,y N+i ) and (x N+(i-1) ,y N+(i-1) The distance between them is S. N+i The travel time is Δt N+i

[0145]

[0146] For reflected rays, when a ray incident from the ground is reflected at a specific interface, the reflected ray exits towards the ground and is incident below each interface. For a stratum with N interfaces, reflection occurs at the Nth interface, and the dip angle of the reflected ray at the Nth interface is the same as the dip angle γ of the incident ray at the (N+1)th stratum interface. N+1 =ε N -α N (i=1), the incident angle α of the (N+1)th stratigraphic interface N+1 =ε N -α N -ε N+1 (i=1); When the reflected ray enters the (N+2)th stratigraphic interface (i≥2) γ N+i =β N+(i-1) +ε N+(i-1) ,α N+i =β N+(i-1) +ε N+(i-1) -ε N+i Here, i = 2, 3, ..., N.

[0147] Optionally, in step S4, tracing the normal rays of each layer corresponding to the common center point gather according to Snell's law of refraction specifically includes:

[0148] To obtain the normal ray from the Nth stratigraphic interface, we first use this normal ray as the initial incident ray for reverse tracing. According to Snell's law of refraction, we perform ray tracing layer by layer towards the surface. The normal ray is traced back towards the surface, incident below the stratigraphic interface, and exits towards the surface at an exit angle of β0. The slope of the initial incident normal ray is determined by the exit angle β0. The coordinates (x, y, y) of the CMP point in the common center point (CMP) gather are then used. m ,y m Using this as the starting point of the initial incident ray, we trace it back to the Nth stratigraphic interface.

[0149] According to step S3, the normal ray from the Nth stratigraphic interface is traced back to the surface. Here, the incident angle α and refraction angle β of each layer are calculated based on the mathematical and physical model of reflected rays established in step S1, and finally the normal ray exit angle β0 of the Nth stratigraphic interface is calculated. During the process of the normal ray from the Nth stratigraphic interface tracing back to the surface, the incident ray from the (N+1)th stratigraphic interface is the starting ray for the normal ray to trace back to the surface, and it exits at the (N+i)th stratigraphic interface, where 1≤i≤N;

[0150] This determines the normal ray emission angle β0 at the Nth stratigraphic interface.

[0151]

[0152] γ N+i ε is the dip angle of the incident ray at the (N+i)th stratum interface in the ray reflection path. N+i It is the dip angle of the normal to the (N+i)th stratum interface.

[0153] The coordinates (x, y) of the CMP point in the common center point (CMP) gather. m ,y m Using β0 obtained from the above process as the starting point of the initial incident ray, and β0 as the inclination angle of the initial incident ray, the ray is traced to the Nth stratigraphic interface according to the established stratigraphic model and incident ray mathematical and physical model, and the normal ray of the Nth stratigraphic interface is obtained.

[0154] Optionally, in step S5, tracing the imaging ray according to Snell's law of refraction specifically includes:

[0155] On a horizontal surface, with coordinates A and an exit angle β0 = 0, an imaging ray is obtained by using the geological model of the incident ray, the mathematical and physical model of the incident ray, and the ray tracing algorithm established in step 1 above. The intersection of the imaging ray with each geological interface is the imaging point.

[0156] Optionally, in step S6, determining the common midpoint gather based on the surface incident point, stratum reflection point, surface exit point, and the normal ray passing through the common midpoint, and determining the pre-stack gather from the imaging rays and the equidistant incident and reflection traces specifically includes:

[0157] Based on the above steps S2 (from the surface incident point and the stratigraphic interface reflection point) and S3 (from the stratigraphic interface reflection point and the common center point with the surface), a set of common center point gather travel time information is determined to determine the shot-receiver distance; based on step S4 (from the reflection interface normal to the surface, the normal ray exiting the surface at the exit angle β0 is recorded), and then at the common center point position, the ray is traced downwards at the exit angle β0 to the reflection interface, and the normal ray of the reflection interface in this set of gathers is determined;

[0158] On the horizontal surface, to determine the coordinate position point A, according to step S5, trace an imaging ray downwards at a departure angle β0 = 0. The intersection of the imaging ray with each stratum interface is the imaging point. Treat the imaging point as a secondary seismic source, and trace it back to the surface according to step S3. The two initial rays that trace back from the imaging point to the surface and have an equal angle with the normal of the initial interface constitute a pair of incident and reflected rays of the initial interface. Only the reflection of seismic waves is considered, and the diffraction of seismic waves is not considered. Therefore, the incident and reflected rays at the imaging point are unique.

[0159] This invention provides a tracing method for two-dimensional ray forward modeling seismic gathers. The tracing method includes: Step S1: Establishing a mathematical and physical model corresponding to incident and reflected rays; Step S2: Tracing rays from the surface at the emission angle β0 downwards, tracing layer by layer downwards according to Snell's law of refraction, calculating the incident point of the incident ray at the interface between the incident ray and the incident stratum, and calculating the travel time of the incident ray in each layer; Step S3: Tracing rays layer by layer towards the surface according to the law of reflection and Snell's law of refraction, calculating the intersection point of the reflected ray with each stratum interface, and calculating the travel time of the reflected ray in each layer; Step S4: Tracing the normal rays of each layer corresponding to the common midpoint gather according to Snell's law of refraction; Step S5: Tracing the imaging rays according to Snell's law of refraction; Step S6: Determining the common midpoint gather based on the surface incident point, stratum reflection point, surface emission point, and normal rays passing through the common midpoint, and determining the pre-stack seismic gather based on the imaging rays and the equidistant incident and reflected rays. It replaces the traditional method of manually drawing forward seismic gathers and can build more complex models that are closer to the real strata. With the help of modern advanced computer technology and software, it can conduct more in-depth research on forward modeling of seismic wave velocities, laying an important foundation for quantitative research on stacking velocity and pre-stack time migration velocity.

[0160] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0161] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0162] Figure 1 A flowchart illustrating a two-dimensional ray forward modeling seismic gather tracking method provided in an embodiment of the present invention;

[0163] Figure 2 A schematic diagram of a common center point gather for 10 reflective interfaces;

[0164] Figure 3 This is a schematic diagram of the pre-stack gather with 8 reflective interfaces. Detailed Implementation

[0165] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented 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.

[0166] The terms "comprising" and "having," and any variations thereof, in the specification, embodiments, claims, and drawings of this invention are intended to cover non-exclusive inclusion, such as including a series of steps or units.

[0167] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0168] like Figure 1 As shown, a method for tracing two-dimensional ray forward modeling seismic gathers includes:

[0169] In step 101, a mathematical and physical model corresponding to the incident and reflected rays is established based on the stratigraphic model used for forward modeling, including the coordinates, dip angle, depth, and layer velocity of the given strata.

[0170] The specific operating steps are as follows:

[0171] 2.1. Establishing a mathematical and physical model of the incident ray

[0172] (1) Based on the dip angle θ of the strata and the coordinates (x, y) of a point on the strata interface d ,y d Establish a mathematical and physical model of the incident ray.

[0173] The dip angle of the first stratigraphic interface is θ1, and the slope is L1 = tgθ1. Given the coordinates (x, y) of a point on the first stratigraphic interface... d1 ,y d1 The equation for determining the first stratigraphic interface is:

[0174] y = L1(xx d1 )+y d1 (1-1)

[0175] The dip angle of the second stratigraphic interface is θ2, and the slope is L2 = tgθ2. Given the coordinates (x, y) of a point on the second stratigraphic interface... d2 ,y d2 The equation for determining the second stratigraphic interface is:

[0176] y = L2(xx) d2 )+y d2 (1-2)

[0177] The dip angle of the third stratigraphic interface is θ3, and the slope is L3 = tgθ3. Given the coordinates (x, y) of a point on the third stratigraphic interface... d3 ,y d3 The equation for the third stratigraphic interface is determined as follows:

[0178] y = L3(xx) d3 )+y d3 (1-3)

[0179] ...

[0180] The dip angle of the Nth stratigraphic interface is θ N The slope is L N =tgθ N Given the coordinates (x, y) of a point on the Nth stratigraphic interface. dN ,y dN The equation for determining the Nth stratigraphic interface is:

[0181] y = L N (xx dN )+y dN (1-4)

[0182] Given the layer velocities of layers 1, 2, 3, ..., N as V1, V2, V3, ..., V... N .

[0183] (2) Based on the given layer velocity V and Snell's law of refraction for each layer in the stratigraphic model, establish the relationship between the incident angle α and the refraction angle β, and calculate the slope of the incident ray at the next interface based on the relationship.

[0184]

[0185]

[0186]

[0187] ...

[0188]

[0189]

[0190] The incident ray ends, β is not calculated. N V1, V2, V3, ..., V N These represent the layer velocities of layers 1, 2, 3, ..., N; θ1, θ2, θ3, ..., θ N These are the dip angles of the 1st, 2nd, 3rd, ..., Nth stratigraphic interfaces; ε1, ε2, ε3, ..., ε N These are the dip angles of the normals at the interfaces of the 1st, 2nd, 3rd, ..., Nth strata.

[0191] 2.2. Establishing a mathematical and physical model for reflected rays

[0192] (1) For reflected rays, when a ray incident from the ground is reflected at a certain interface, the reflected ray exits towards the ground and is incident below each interface. In the reflection path, based on the dip angle θ of the two-dimensional stratum interface and the coordinates (x, y) of a point on the stratum interface... d ,y d Establish a mathematical and physical model of reflected rays.

[0193] The dip angle of the (N+1)th stratigraphic interface is θ N+1 =θ N-1 The slope is L N+1 =tgθ N+1 Given the coordinates (x, y) of a point on the (N+1)th stratigraphic interface. d(N+1) ,y d(N+1) ), x d(N+1) =x d(N-1) ,y d(N+1) =y d(N-1) The equation for determining the (N+1)th stratigraphic interface is as follows:

[0194] y = L N+1 (xx d(N+1) )+y d(N+1) (1-10)

[0195] The dip angle of the (N+2)th stratigraphic interface is θ N+2 =θ N-2 The slope is L N+2 =tgθ N+2 Given the coordinates (x, y) of a point on the (N+2)th stratigraphic interface. d(N+2) ,y d(N+2) ), x d(N+2) =x d(N-2) y d(N+2) =y d(N-2) The equation for the (N+2)th stratigraphic interface is determined as follows:

[0196] y = L N+2 (xx d(N+2) )+y d(N+2) (1-11)

[0197] The dip angle of the (N+3)th stratigraphic interface is θ N+3 =θ N-3 The slope is L N+3 =tgθ N+3 Given the coordinates (x, y) of a point on the (N+3)th stratigraphic interface. d(N+3) ,y d(N+3) ), x d(N+3) =x d(N-3) y d(N+3) =y d(N-3) Determine the equation for the (N+3)th stratigraphic interface.

[0198] y = L N+3 (xx d(N+3) )+y d(N+3) (1-12)

[0199] ...

[0200] The dip angle of the (N+i)th stratigraphic interface is θ N+i =θ N-i The slope is L N+i =tgθ N+i Given the coordinates (x, y) of a point on the (N+i)th stratigraphic interface. d(N+i) ,y d(N+i) ), x d(N+i) =x d(N-i) ,y d(N+i) =y d(N-i) The equation for determining the (N+i)th stratigraphic interface is as follows:

[0201] y = L N+i (xx d(N+i) )+y d(N+i) (1-13)

[0202] Where i = 1, 2, 3, ..., N.

[0203] (2) Based on the given layer velocity V and Snell's law of refraction for each layer in the stratigraphic model, establish the relationship between the incident angle α and the refraction angle β, and calculate the slope of the incident ray at the next interface based on the relationship.

[0204]

[0205]

[0206]

[0207]

[0208]

[0209]

[0210] The incident ray ends, β is not calculated. N+i V N+1 V N+2 V N+3 ... V N+i These are the layer velocities of layers N+1, N+2, N+3, ..., N+i, respectively; θ N+1 θ N+2 θ N+3 、……、θ N+i ε represents the dip angle of the (N+1), (N+2), (N+3), ..., (N+i)th stratigraphic interfaces; N+1 ε N+2 ε N+3 ... ε N+i These are the normal dip angles of the N+1, N+2, N+3, ..., N+i stratigraphic interfaces, respectively.

[0211] The process proceeds to step 102.

[0212] In step 102, the ray is traced underground from the surface outgoing angle β0 (the angle between the incident ray at the first underground layer interface and the surface normal), and then traced downwards layer by layer according to Snell's law of refraction. The incident point of the incident ray and the incident layer interface is calculated, and the travel time of the ray in each layer is calculated.

[0213] The specific operating steps are as follows:

[0214] (1) Incident rays at the first stratigraphic interface

[0215] The dip angle γ1 of the incident ray at the first stratigraphic interface and the coordinates (x0, y0) of the ground starting point determine the incident ray at the first stratigraphic interface.

[0216] Normal dip angle of the first stratigraphic boundary The incident angle of the first stratigraphic interface is α1 = β0 - ε1;

[0217] Inclination angle corresponding to the incident ray When the incident ray slope is K1 = tanγ1, the equation of the incident ray at the first stratigraphic interface is...

[0218] y = K1(x - x0) + y0 (1-19)

[0219] By combining equations (1-1) and (1-19), the intersection point of the incident ray and the first stratigraphic interface is determined to be (x1, y1).

[0220]

[0221] When the angle of inclination of the corresponding incident ray At that time, the intersection point of the incident ray from the first stratigraphic interface and the first stratigraphic interface is (x1, y1).

[0222]

[0223] The distance between points (x1, y1) and (x0, y0) is S1, and the travel time is Δt1.

[0224]

[0225] (2) Incident rays at the second stratigraphic interface

[0226] The incident ray at the second stratigraphic interface is determined by the dip angle γ2 of the incident ray at the second stratigraphic interface and the intersection point (x1, y1) of the incident ray at the first stratigraphic interface with the first stratigraphic interface.

[0227] Normal dip angle of the second stratigraphic boundary The angle of refraction at the first stratigraphic interface The incident angle of the second stratigraphic interface is α2 = β1 + ε1 - ε2;

[0228] Inclination angle corresponding to the incident ray The incident ray equation for the second stratigraphic interface corresponds to the incident ray slope K2 = tanγ2.

[0229] y = K2(z-x1) + y1 (1-23)

[0230] By combining equations (1-2) and (1-23), the intersection point of the incident ray at the second stratigraphic interface and the second layer interface is determined to be (x2, y2).

[0231]

[0232] When the angle of inclination of the corresponding incident ray At that time, the intersection point of the incident ray from the second stratigraphic interface and the second stratigraphic interface is (x2, y2).

[0233]

[0234] The distance between points (x2, y2) and (x1, y1) is S2, and the travel time is Δt2.

[0235]

[0236] (3) Incident rays at the third stratigraphic interface

[0237] The incident ray at the third stratigraphic interface is determined by the dip angle γ3 of the incident ray at the third stratigraphic interface and the intersection point (x2, y2) of the incident ray at the second stratigraphic interface.

[0238] Normal dip angle of the third stratigraphic boundary The angle of refraction at the second stratigraphic interface The incident angle of the third stratigraphic interface is α3 = β2 + ε2 - ε3;

[0239] Inclination angle corresponding to the incident ray The incident ray equation for the third stratigraphic interface corresponds to the incident ray slope K3 = tanγ3.

[0240] y = K3(x - x2) + y2 (1-27)

[0241] By combining equations (1-3) and (1-27), the intersection point of the incident ray and the third stratigraphic interface is determined to be (x3, y3).

[0242]

[0243] When the angle of inclination of the corresponding incident ray At that time, the intersection point of the incident ray from the third stratigraphic interface and the third stratigraphic interface is (x3, y3).

[0244]

[0245] The distance between points (x2, y2) and (x3, y3) is S3, and the travel time is Δt3.

[0246]

[0247] ...

[0248] (N) Incident rays at the Nth stratigraphic interface

[0249] The dip angle γ of the incident ray at the Nth stratigraphic interface NThe intersection point (x) of the incident ray from the (N-1)th stratigraphic interface with the (N-1)th stratigraphic interface. N-1 ,y N-1 Determine the incident ray at the Nth stratigraphic interface;

[0250] normal dip angle of the Nth stratigraphic boundary The angle of refraction at the (N-1)th stratigraphic interface The incident angle α at the Nth stratigraphic interface N =β N-1 +ε N-1 -ε N ;

[0251] Inclination angle corresponding to the incident ray Corresponding incident ray slope K N =tanγ N The equation of the incident ray at the Nth stratigraphic interface

[0252] y = K N (xx N-1 )+y N-1 (1-31)

[0253] By combining equations (1-4) and (1-31), the intersection point of the incident ray at the Nth stratigraphic interface and the Nth stratigraphic interface is obtained as (x). N ,y N )

[0254]

[0255] When the angle of inclination of the corresponding incident ray At that time, the intersection point of the incident ray from the Nth stratigraphic interface and the Nth stratigraphic interface is (x N ,y N )

[0256]

[0257] Point (x) N-1 ,y N-1 ) and (x N ,y N The distance between them is S. N The travel time is Δt N

[0258]

[0259] The process proceeds to step 103.

[0260] In step 103, ray tracing is performed layer by layer towards the Earth's surface according to the law of reflection and Snell's law of refraction. The intersection points of the reflected rays with the interfaces of each stratum are calculated, and the travel time of the reflected rays in each layer is calculated.

[0261] The specific operating steps are as follows:

[0262] (1) Incident rays at the (N+1)th stratigraphic interface

[0263] The dip angle γ of the incident ray at the (N+1)th stratigraphic interface N+1 The intersection point (x) of the incident ray from the Nth stratigraphic interface with the Nth stratigraphic interface. N ,y N Determine the incident ray at the (N+1)th stratigraphic interface;

[0264] normal dip angle of the N+1th stratigraphic boundary The incident angle α of the (N+1)th stratigraphic interface N+1 =ε N -α N -ε N+1 ;

[0265] Corresponding incident ray tilt angle Corresponding incident ray slope K N+1 =tanγ N+1 The equation of the incident ray at the (N+1)th stratigraphic interface

[0266] y = K N+1 (xx N )+y N (1-35)

[0267] By combining equation (1-35) and equation (1-10) of the (N+1)th stratigraphic interface, the intersection point of the incident ray and the (N+1)th stratigraphic interface is found to be (x). N+1 ,y N+1 )

[0268]

[0269] When the angle of inclination of the corresponding incident ray At that time, the intersection point of the incident ray from the (N+1)th stratigraphic interface and the (N+1)th stratigraphic interface is (x N+1 ,y N+1 )

[0270]

[0271] Point (x) N+1 ,y N+1 ) and (x N ,y N The distance between them is S. N+1 The travel time is Δt N+1

[0272]

[0273] (2) Incident rays at the (N+2)th stratigraphic interface

[0274] The dip angle γ of the incident ray at the (N+2)th stratigraphic interface N+2 The intersection point (x) of the incident ray from the (N+1)th stratigraphic interface with the (N+1)th stratigraphic interface. N+1 ,y N+1 Determine the incident ray at the N+2th stratigraphic interface;

[0275] normal dip angle of the (N+2)th stratigraphic boundary The angle of refraction at the (N+1)th stratigraphic interface The incident angle α of the (N+2)th stratigraphic interface N+2 =β N+1 +ε N+1 -ε N+2 ;

[0276] Corresponding incident ray tilt angle Corresponding incident ray slope K N+2 =tanγ N+2 The equation of the incident ray at the N+2th stratigraphic interface

[0277] y = K N+2 (xx N+1 )+y N+1 (1-39)

[0278] By combining equation (1-39) and equation (1-11) of the (N+2)th stratigraphic interface, the intersection point of the incident ray and the (N+2)th stratigraphic interface is found to be (x). N+2 ,y N+2 )

[0279]

[0280] When the angle of inclination of the corresponding incident ray The intersection point of the incident ray at the (N+2)th stratigraphic interface and the (N+2)th stratigraphic interface is (x N+2 ,y N+2 )

[0281]

[0282] Point (x) N+2 ,y N+2 ) and (x N+1 ,y N+1 The distance between them is S. N+2 The travel time is Δt N+2

[0283]

[0284] (3) Incident rays at the (N+3)th stratigraphic interface

[0285] The dip angle γ of the incident ray at the (N+3)th stratigraphic interface N+3 The intersection point (x) of the incident ray from the N+2th stratigraphic interface with the N+2th stratigraphic interface. N+2 ,y N+2 Determine the incident ray at the N+3rd stratigraphic interface;

[0286] Normal dip angle of the (N+3)th stratigraphic boundary The angle of refraction at the (N+2)th stratigraphic interface The incident angle α of the (N+3)th stratigraphic interface N+3 =β N+2 +ε N+2 -ε N+3

[0287] Corresponding incident ray tilt angle Corresponding incident ray slope K N+3 =tanγ N+3 The equation of the incident ray at the (N+3)th stratigraphic interface

[0288] y = K N+3 (xx N+2 )+y N+2 (1-43)

[0289] By combining equation (1-43) and equation (1-12) of the (N+3)th stratigraphic interface, the intersection point of the incident ray and the (N+3)th stratigraphic interface is found to be (x). N+3 ,y N+3 )

[0290]

[0291] When the angle of inclination of the corresponding incident ray The intersection point of the incident ray at the (N+3)th stratigraphic interface and the (N+3)th stratigraphic interface is (x N+3 ,y N+3 )

[0292]

[0293] Point (x) N+2 ,y N+2 ) and (x N+3 ,y N+3 The distance between them is S. N+3 The travel time is Δt N+3

[0294]

[0295] ...

[0296] (N+i) Incident ray at the N+i-th stratigraphic interface

[0297] The dip angle γ of the incident ray at the (N+i)th stratigraphic interface N+i The intersection point (x) of the incident ray from the N+i-1th stratigraphic interface with the N+i-1th stratigraphic interface. N+(i-1) ,y N+(i-1) Determine the incident ray at the (N+i)th stratigraphic interface;

[0298] Normal dip angle of the (N+i)th stratigraphic interface The angle of refraction at the (N+i-1)th stratigraphic interface The incident angle α of the N+i-th stratigraphic interface N+i =β N+(i-1) +ε N+(i-1) -ε N+i ;

[0299] Corresponding incident ray tilt angle Corresponding incident ray slope K N+i =tanγ N+i The equation of the incident ray at the N+i-th stratum interface

[0300] y = K N+i (xx N+(i-1) )+y N+(i-1) (1-47)

[0301] By combining equation (1-47) and equation (1-13) of the (N+i)th stratigraphic interface, the intersection point of the incident ray and the (N+i)th stratigraphic interface is obtained as (x N+i ,y N+i )

[0302]

[0303] When the angle of inclination of the corresponding incident ray The intersection point of the incident ray at the (N+i)th stratigraphic interface and the (N+i)th stratigraphic interface is (x N+i ,y N+i )

[0304]

[0305] Point (x) N+i ,y N+i ) and (x N+(i-1) ,y N+(i-1) The distance between them is S. N+i The travel time is Δt N+i

[0306]

[0307] For reflected rays, when a ray incident from the ground is reflected at a specific interface, the reflected ray exits towards the ground and is incident below each interface. For a stratum with N interfaces, reflection occurs at the Nth interface, and the dip angle of the reflected ray at the Nth interface is the same as the dip angle γ of the incident ray at the (N+1)th stratum interface. N+1 =ε N -α N (i=1), the incident angle α of the (N+1)th stratigraphic interface N+1 =ε N -α N -ε N+1 (i=1); When the reflected ray enters the (N+2)th stratigraphic interface (i≥2) γ N+i =β N+(i-1) +ε N+(i-1) ,α N+i =β N+(i-1) +ε N+(i-1) -ε N+i Here, i = 2, 3, ..., N.

[0308] The process proceeds to step 104.

[0309] In step 104, the normal rays of each layer corresponding to the common center point gather are traced according to Snell's law of refraction.

[0310] The specific operating steps are as follows:

[0311] To obtain the normal ray from the Nth stratigraphic interface, we first use this normal ray as the initial incident ray for reverse tracing. According to Snell's law of refraction, we perform ray tracing layer by layer towards the surface. The normal ray is traced back towards the surface (equivalent to reflection of the normal ray), incident below the stratigraphic interface, and exiting towards the surface at an exit angle of β0. The slope of the initial incident normal ray is determined by the exit angle β0. The coordinates (x, y, y) of the CMP point in the common center point (CMP) gather are then used. m ,y m Using this as the starting point of the initial incident ray, we trace back to the Nth stratigraphic interface.

[0312] Based on the reverse tracing of the normal ray from the Nth stratigraphic interface back to the Earth's surface (equivalent to the reflection of the normal ray), the incident angle α and refraction angle β of each layer are calculated using the mathematical and physical model of the reflected ray established in step S1. Finally, the exit angle β0 of the normal ray from the Nth stratigraphic interface is calculated. During the reverse tracing of the normal ray from the Nth stratigraphic interface back to the Earth's surface (equivalent to the reflection of the normal ray), the incident ray from the (N+1)th stratigraphic interface is the starting ray for the reverse tracing of the normal ray back to the Earth's surface.

[0313] (1) Incident rays at the (N+1)th stratigraphic interface

[0314] The dip angle γ of the incident ray at the (N+1)th stratigraphic interface N+1 The intersection point (x) of the incident ray from the Nth stratigraphic interface with the Nth stratigraphic interface. N ,y N Determine the incident ray at the (N+1)th stratigraphic interface;

[0315] normal dip angle of the N+1th stratigraphic boundary The incident angle α of the (N+1)th stratigraphic interface N+1 =ε N -α N -ε N+1 ;

[0316] Corresponding incident ray tilt angle Corresponding incident ray slope K N+1 =tanγ N+1 The equation of the incident ray at the (N+1)th stratigraphic interface

[0317] y = K N+1 (xx N )+y N (1-35)

[0318] By combining equation (1-35) and equation (1-10) of the (N+1)th stratigraphic interface, the intersection point of the incident ray and the (N+1)th stratigraphic interface is found to be (x). N+1 ,y N+1 )

[0319]

[0320] When the angle of inclination of the corresponding incident ray At that time, the intersection point of the incident ray from the (N+1)th stratigraphic interface and the (N+1)th stratigraphic interface is (x N+1 ,y N+1 )

[0321]

[0322] Point (x) N+1 ,y N+1 ) and (x N ,y N The distance between them is S. N+1 The travel time is Δt N+1

[0323]

[0324] (2) Incident rays at the (N+2)th stratigraphic interface

[0325] The dip angle γ of the incident ray at the (N+2)th stratigraphic interfaceN+2 The intersection point (x) of the incident ray from the (N+1)th stratigraphic interface with the (N+1)th stratigraphic interface. N+1 ,y N+1 Determine the incident ray at the N+2th stratigraphic interface;

[0326] normal dip angle of the (N+2)th stratigraphic boundary The angle of refraction at the (N+1)th stratigraphic interface The incident angle α of the (N+2)th stratigraphic interface N+2 =β N+1 +ε N+1 -ε N+2 ;

[0327] Corresponding incident ray tilt angle Corresponding incident ray slope K N+2 =tanγ N+2 The equation of the incident ray at the N+2th stratigraphic interface

[0328] y = K N+2 (cx N+1 )+y N+1 (1-39)

[0329] By combining equation (1-39) and equation (1-11) of the (N+2)th stratigraphic interface, the intersection point of the incident ray and the (N+2)th stratigraphic interface is found to be (x). N+2 ,y N+2 )

[0330]

[0331] When the angle of inclination of the corresponding incident ray The intersection point of the incident ray at the (N+2)th stratigraphic interface and the (N+2)th stratigraphic interface is (x N+2 ,y N+2 )

[0332]

[0333] Point (x) N+2 ,y N+2 ) and (x N+1 ,y N+1 The distance between them is S. N+2 The travel time is Δt N+2

[0334]

[0335] (3) Incident rays at the (N+3)th stratigraphic interface

[0336] The dip angle γ of the incident ray at the (N+3)th stratigraphic interface N+3The intersection point (x) of the incident ray from the N+2th stratigraphic interface with the N+2th stratigraphic interface. N+2 ,y N+2 Determine the incident ray at the N+3rd stratigraphic interface;

[0337] Normal dip angle of the (N+3)th stratigraphic boundary The angle of refraction at the (N+2)th stratigraphic interface The incident angle α of the (N+3)th stratigraphic interface N+3 =β N+2 +ε N+2 -ε N+3

[0338] Corresponding incident ray tilt angle Corresponding incident ray slope K N+3 =tanγ N+3 The equation of the incident ray at the (N+3)th stratigraphic interface

[0339] y = K N+3 (xx N+2 )+y N+2 (1-43)

[0340] By combining equation (1-43) and equation (1-12) of the (N+3)th stratigraphic interface, the intersection point of the incident ray and the (N+3)th stratigraphic interface is found to be (x). N+3 ,y N+3 )

[0341]

[0342] When the angle of inclination of the corresponding incident ray The intersection point of the incident ray at the (N+3)th stratigraphic interface and the (N+3)th stratigraphic interface is (x N+3 ,y N+3 )

[0343]

[0344] Point (x) N+2 ,y N+2 ) and (x N+3 ,y N+3 The distance between them is S. N+3 The travel time is Δt N+3

[0345]

[0346] ...

[0347] (N+i) Incident ray at the N+i-th stratigraphic interface

[0348] The dip angle γ of the incident ray at the (N+i)th stratigraphic interfaceN+i The intersection point (x) of the incident ray from the N+i-1th stratigraphic interface with the N+i-1th stratigraphic interface. N+(i-1) ,y N+(i-1) Determine the incident ray at the (N+i)th stratigraphic interface;

[0349] Normal dip angle of the (N+i)th stratigraphic interface The angle of refraction at the (N+i-1)th stratigraphic interface The incident angle α of the N+i-th stratigraphic interface N+i =β N+(i-1) +ε N+(i-1) -ε N+i ;

[0350] Corresponding incident ray tilt angle Corresponding incident ray slope K N+i =tanγ N+i The equation of the incident ray at the N+i-th stratum interface

[0351] y = K N+i (xx N+(i-1) )+y N+(i-1) (1-47)

[0352] By combining equation (1-47) and equation (1-13) of the (N+i)th stratigraphic interface, the intersection point of the incident ray and the (N+i)th stratigraphic interface is obtained as (x N+i ,y N+i )

[0353]

[0354] When the angle of inclination of the corresponding incident ray The intersection point of the incident ray at the (N+i)th stratigraphic interface and the (N+i)th stratigraphic interface is (x N+i ,y N+i )

[0355]

[0356] Point (x) N+i ,y N+i ) and (x N+(i-1) ,y N+(i-1) The distance between them is S. N+i The travel time is Δt N+i

[0357]

[0358] For reflected rays, when a ray incident from the ground is reflected at a specific interface, the reflected ray exits towards the ground and is incident below each interface. For a stratum with N interfaces, reflection occurs at the Nth interface, and the dip angle of the reflected ray at the Nth interface is the same as the dip angle γ of the incident ray at the (N+1)th stratum interface. N+1 =ε N -α N (i=1), the incident angle α of the (N+1)th stratigraphic interface N+1 =ε N -α N -ε N+1 (i=1); When the reflected ray enters the (N+2)th stratigraphic interface (i≥2) γ N+i =β N+(i-1) +ε N+(i-1) ,α N+i =β N+(i-1) +ε N+(i-1) -ε N+i Here, i = 2, 3, ..., N.

[0359] This determines the normal ray emission angle β0 at the Nth stratigraphic interface.

[0360]

[0361] γ N+i ε is the dip angle of the incident ray at the (N+i)th stratum interface in the ray reflection path. N+i It is the dip angle of the normal to the (N+i)th stratum interface.

[0362] The coordinates (x, y) of the CMP point in the common center point (CMP) gather. m ,y m Using β0 obtained from the above process as the starting point of the initial incident ray, and β0 as the inclination angle of the initial incident ray, the ray is traced to the Nth stratigraphic interface according to the established stratigraphic model and incident ray mathematical and physical model, and the normal ray of the Nth stratigraphic interface is obtained.

[0363] The process proceeds to step 105.

[0364] In step 105, the imaging ray is traced according to Snell's law of refraction.

[0365] On a horizontal surface, with coordinates A and an exit angle β0 = 0, an imaging ray is obtained by using the geological model of the incident ray, the mathematical and physical model of the incident ray, and the ray tracing algorithm established in step 1 above. The intersection of the imaging ray with each geological interface is the imaging point.

[0366] In step 106, the common midpoint gather is determined based on the surface incident point, the stratum reflection point, the surface exit point, and the normal ray passing through the common midpoint. The pre-stack gather is determined by the imaging ray and the equidistant incident and reflection traces.

[0367] The specific operating steps are as follows:

[0368] This step requires computer programming and specialized software. In the programming, the formation model parameters (Table 1) must first be specified. These parameters include:

[0369] The dip angles of the strata are θ1, θ2, θ3, ... θ N ,θ N+1 ,θ N+2 ,……θ N+i ;

[0370] coordinates (x) d1 ,y d1 ), (x d2 ,y d2 ), (x d3 ,y d3 ), ……,(x dN ,y dN ), (x d(N+1) ,y d(N+1) ), (x d(N+2) y d(N+2) ), (x d(N+i) ,y d(N+i) );

[0371] Formation velocities V1, V2, V3, ..., V N V N+1 V N+2 ,……,V N+i ;

[0372] i = 1, 2, 3, ..., N.

[0373] Input the coordinates (x0, y0) of the starting ray and the tilt angle β0 of the starting ray. Each pair of (x0, y0) and β0 determines the start of a ray.

[0374] Output (x1,y1), (x2,y2), (x3,y3), ..., (x N ,y N ),(x N+1 ,y N+1 ), (x N+2 ,y N+2 ), (x N+3 ,y N+3 ), ... (x) 2N ,y 2N Coordinates of each point;

[0375] Output S1 and Δt1, S2 and Δt2, S3 and Δt3, ..., S N and Δt N S N+1 and Δt N+1 S N+2 and Δt N+2 ... S 2N and Δt 2N ;

[0376] Output t=Δt1+Δt2+Δt3+…+Δt N +Δt N+1 +Δt N+2 +…+Δt 2N .

[0377] Table 1. Stratigraphic parameters (N=10)

[0378]

[0379] In Table 1, N is the total number of stratigraphic interfaces designed. When N = 10, then i = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

[0380] V N+i =V N-(i-1)

[0381] x d(N+i) =x d(N-i) ,x d0 =0

[0382] y d(N+i) =y d(N-i) ,y d0 =0

[0383] θ N+i =θ N-i

[0384] (1) Based on the above steps S2, determine the travel time information of a set of common center point gathers from the surface incident point and the stratigraphic interface reflection point, and the above steps S3, from the position of the stratigraphic interface reflection point and the common center point with the surface, and determine the shot-receiver distance; based on the above steps S4, trace the normal of the reflection interface back to the surface, record the exit angle β0 of the normal ray exiting the surface, and then trace it down to the ground at the common center point position with the exit angle β0, trace it to the reflection interface, and determine the normal ray of the reflection interface in this set of gathers.

[0385] (2) On the horizontal surface, determine the coordinate position point A, and according to step S5, trace an imaging ray downwards at a departure angle β0 = 0. The intersection of the imaging ray with each stratum interface is the imaging point. Treat the imaging point as a secondary seismic source, and trace it back to the surface according to step S3. The two initial rays that trace back from the imaging point to the surface and have equal angles with the normal of the initial interface constitute a pair of incident and reflected rays of the initial interface. Only the reflection of seismic waves is considered, and the diffraction of seismic waves is not considered. Therefore, the incident and reflected rays at the imaging point are unique.

[0386] Figure 2 This is a set of common center point (CMP) gathers in the forward model of this invention, which intuitively represents the ray tracing paths of 10 reflecting interfaces, and also tracks the normal rays incident from the CMP points to each interface.

[0387] Figure 3 This is a set of pre-stack gathers used in the forward modeling of this invention. The imaging ray traced from point A downwards into the ground (the imaging ray exits the surface and is perpendicular to point A on the horizontal surface) intersects the horizontal ground at point A, and then intersects with the 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th, 9th, and 10th stratigraphic interfaces at Q1, Q2, Q3, Q4, Q5, Q6, Q7, Q8, Q9, and Q1, respectively. 10 In pre-stack time migration of earthquakes, with point A as the center of the migration aperture, the reflection information from directly below point A is searched within the migration aperture range (e.g., by Kirchhoff integral summation migration). The coordinates of point A are recorded vertically below point A. However, the information recorded vertically below point A is not always directly below point A, especially when the dip angle of the strata is large and the velocity changes between upper and lower layers are large. In such cases, the imaging rays will bend significantly, and the reflection information recorded at point A will not be directly below point A.

[0388] like Figure 3 In the image, the imaging ray is perpendicular to the horizontal surface at point A, intersecting the 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, and 8th stratigraphic interfaces at points D1, D2, D3, D4, D5, D6, D7, and D8, respectively. D6, D7, and D8 deviate significantly from the vertical direction of point A. However, in actual seismic data processing, D6, D7, and D8 are recorded on the vertical line from point A using their respective travel-time depths. This is clearly an inaccurate imaging method, failing to account for the curvature of the imaging ray. The imaging ray traces from point A to the 8th stratigraphic interface, but due to total internal reflection, it stops tracing downwards. Figure 3Given the stratigraphic model and stratigraphic velocity, the imaging ray terminates at the 8th stratigraphic interface after tracing from point A on the surface. In fact, when the stratigraphic dip angle is small and the velocity variation between layers is small, the bending of the imaging ray is minimal, and the deviation from the vertical direction of point A is small, resulting in relatively small imaging errors. This is because seismic wave energy always returns to the seismic receiver from a large area [10 square wavelength (Woods, 1975)] on the subsurface interface; it does not originate from a point-like excitation or return, nor does it propagate within an infinitely thin ray tube surrounding a central ray. The aforementioned small deviations can be covered by the seismic wave energy reflected from a large area [10 square wavelength (Woods, 1975)] on the corresponding subsurface reflecting interface. However, the deviations of points D6, D7, and D8 relative to the vertical direction of point A cannot be ignored.

[0389] exist Figure 3 The study also tracked the gun-receiver distances and reflection paths of D1, D2, D3, D4, D5, D6, D7, D8, and their corresponding S1D1G1, S2D2G2, S3D3G3, S4D4G4, S5D5G5, S6D6G6, S7D7G7, and S8D8G8.

[0390] Beneficial effects: The method of forward modeling seismic gathers based on two-dimensional ray tracing in this invention replaces the previous method of manually drawing forward seismic gathers. It can establish more complex models that are closer to the real strata and use modern advanced computer technology and software to conduct more in-depth research on forward modeling of seismic wave velocities, laying an important foundation for quantitative research on stacking velocity and pre-stack time migration velocity.

[0391] The above specific embodiments further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for tracing two-dimensional ray forward modeling seismic gathers, characterized in that, The tracking method includes: Step S1: Establish mathematical and physical models corresponding to incident and reflected rays; Step S2: Angle of emission of rays from the Earth's surface β Tracing downwards from 0, according to Snell's law of refraction, the incident ray is traced layer by layer downwards to calculate the point of incidence at the interface between the incident ray and the incident stratum, and the travel time of the incident ray in each layer is calculated. Step S3: Based on the law of reflection and Snell's law of refraction, perform ray tracing layer by layer towards the Earth's surface, calculate the intersection points of the reflected rays with the interfaces of each stratum, and calculate the travel time of the reflected rays in each layer; Step S4: Trace the normal rays of each layer corresponding to the common center point gather according to Snell's law of refraction; Step S5: Tracing the imaging ray according to Snell's law of refraction, including: On a horizontal surface, determine the coordinate location point A and the angle of incidence. β 0=0 According to the geological model of the incident ray, the mathematical and physical model of the incident ray established in step S1 above, and the ray tracing algorithm in step S2, an imaging ray is obtained. The intersection of the imaging ray with each geological interface is the imaging point. Step S6: Determine the common midpoint gather based on the surface incident point, stratigraphic reflection point, surface exit point, and the normal ray passing through the common midpoint. Determine the pre-stack gather from the imaging rays and the equidistant incident and reflection traces, including: Based on the above steps S2 (from the surface incident point and the stratigraphic interface reflection point) and S3 (from the stratigraphic interface reflection point and the common midpoint of the exit point and the surface), a set of travel time information for the common midpoint gather is determined to determine the shot-receiver distance; based on step S4 (from the normal of the reflection interface back to the surface), the exit angle of the normal ray exiting the surface is recorded. β 0, and then at the common center point with the angle of departure. β Tracing downwards to the underground, the reflection interface is located, and the normal ray of the reflection interface is determined. On a horizontal surface, determine the coordinate position of point A, and according to step S5, determine the angle of departure. β 0=0 traces an imaging ray downwards to determine an imaging ray. The intersection of the imaging ray with the interface of each stratum is the imaging point. The imaging point is regarded as a secondary seismic source, and it is traced backwards to the surface according to step S3. The two initial rays that trace backwards from the imaging point to the surface and have equal angles with the normal of the initial interface constitute a pair of incident and reflected rays of the initial interface. Only the reflection of seismic waves is considered, and the diffraction of seismic waves is not considered. Therefore, the incident and reflected rays at the imaging point are unique.

2. The method for tracing two-dimensional ray forward modeling seismic gathers according to claim 1, characterized in that, Step S1: Establishing the mathematical and physical models corresponding to the incident and reflected rays specifically includes: Establish mathematical and physical models corresponding to incident and reflected rays based on the coordinates, dip angle, depth, and layer velocity of the given strata; The dip angle of the first stratigraphic boundary is θ 1. The slope is Given the coordinates of a point on the first stratigraphic interface ( x d1 , y d1 The equation for determining the first stratigraphic interface is as follows: (1-1) The dip angle of the second stratigraphic boundary is θ 2, the slope is Given the coordinates of a point on the second stratigraphic interface ( x d2 , y d2 The equation for determining the second stratigraphic interface is as follows: (1-2) The dip angle of the third stratigraphic boundary is θ 3, the slope is Given the coordinates of a point on the third stratigraphic interface ( x d3 , y d3 The equation for determining the third stratigraphic interface is as follows: (1-3) …… No. N The dip angle of each stratigraphic interface is θ N The slope is Given the first N The coordinates of a point on a stratigraphic interface ( x dN , y dN ), determine the first N The equations for each stratigraphic interface are: (1-4) Given the 1st, 2nd, 3rd, ... N The layer velocities are respectively V 1. V 2. V 3, ... V N .

3. The tracking method for two-dimensional ray forward modeling seismic gathers according to claim 1 The method, characterized in that, In step S1, establishing the mathematical and physical models corresponding to the incident and reflected rays also includes: Based on the layer velocities given in each layer of the stratigraphic model V Using Snell's law of refraction, establish the angle of incidence. α and angle of refraction β Based on the relationship between the two, the slope of the incident ray at the next interface can be determined. (1-5) (1-6) (1-7) …… , (1-8) , , (1-9) The incident ray ends, no calculation is performed. β N ; V 1. V 2. V 3, ... V N They are respectively the 1st, 2nd, 3rd, ... N Layer velocity; θ 1. θ 2. θ 3, ... θ N They are respectively the 1st, 2nd, 3rd, ... N The dip angle of each stratigraphic interface; ε 1. ε 2. ε 3、……、ε N They are respectively the 1st, 2nd, 3rd, ... N The dip angle of the normal to each stratigraphic interface.

4. A tracking method for two-dimensional ray forward modeling seismic gathers according to claim 1 The method, characterized in that, In step S1, establishing the geological model through which the reflected rays pass also includes: For reflected rays, when a ray incident from the ground is reflected at a certain interface, the reflected ray exits in the direction of the ground and is incident below each interface. Based on the dip angle of the two-dimensional stratigraphic interface in the reflection path. θ and the coordinates of a point on the stratigraphic interface ( x d , y d Establish a mathematical and physical model for reflected rays; No. N The dip angle of +1 stratigraphic interface is The slope is Given the first N +1 coordinates of a point on a geological boundary ( x d(N+1) , y d(N+1) ), , , determine the first N The equation for +1 formation interface is: (1-10) No. N The dip angles of the two stratigraphic interfaces are: The slope is , Given the first N + Coordinates of a point on two stratigraphic interfaces ( x d(N+2) , y d(N+2) ), , Determine the first N The equations for the two formation interfaces are: (1-11) No. N The dip angles of the three stratigraphic interfaces are: The slope is Given the first N + Coordinates of a point on 3 stratigraphic interfaces ( x d(N+3) , y d(N+3) ), , Determine the first N Equations for +3 stratigraphic interfaces (1-12) …… No. N + i The dip angle of each stratigraphic interface is The slope is Given the first N + i The coordinates of a point on a stratigraphic interface ( x d(N+i) , y d(N+i) ), , , determine the first N + i The equations for each stratigraphic interface are: (1-13) in, i =1, 2, 3, ..., N .

5. A tracking method for two-dimensional ray forward modeling seismic gathers according to claim 1. The method, characterized in that, Step S1, establishing the mathematical and physical model of the reflected ray, further includes: Based on the layer velocities given in each layer of the stratigraphic model V Using Snell's law of refraction, establish the angle of incidence. α and angle of refraction β Based on the relationship between the two, the slope of the incident ray at the next interface can be determined. , , , (1-14) , , , (1-15) , , , (1-16) , , (1-17) , , (1-18) The incident ray ends, no calculation is performed. β N+i ; V N+1 , V N+2 , V N+3 ... V N+i The first N +1、 N +2、 N +3、……、 N + i Layer velocity; θ N+1 , θ N+2 , θ N+3 ... θ N+i The first N +1、 N +2、 N +3、……、 N + i The dip angle of each stratigraphic interface; ε N+1 , ε N+2 , ε N+3 ... ε N+i The first N +1、 N +2、 N +3、……、 N + i The dip angle of the normal to each stratigraphic interface.

6. The method for tracing two-dimensional ray forward modeling seismic gathers according to claim 1, characterized in that, In step S2, the angle of emission of rays from the ground surface β Tracing downwards from 0, according to Snell's law of refraction, layer by layer, the incident point of the incident ray at the interface between the incident ray and the incident stratum is calculated, and the travel time of the incident ray in each layer is calculated, specifically including: (1) Incident rays at the first stratigraphic interface The dip angle of the incident ray at the first stratigraphic interface γ 1 and the coordinates of the ground starting point ( x 0, y 0) Determine the incident rays at the first stratigraphic interface; Normal dip angle of the first stratigraphic boundary The first incident angle at the stratigraphic interface ; Inclination angle corresponding to the incident ray When, the slope of the incident ray The equation of the incident ray at the first stratigraphic interface (1-19) By combining equations (1-1) and (1-19), the intersection point of the incident ray at the first stratigraphic interface and the first stratigraphic interface is obtained as ( x 1, y 1) (1-20) When the angle of inclination of the corresponding incident ray At that time, the intersection point of the incident ray from the first stratigraphic interface and the first stratigraphic interface is ( x 1, y 1) (1-21) point( x 1, y 1) and ( x 0, y The distance between 0) is S 1. Δ during travel t 1 (1-22) (2) Incident rays at the second stratigraphic interface The dip angle of the incident ray at the second stratigraphic interface γ The intersection of the incident ray from the 2nd and 1st stratigraphic interfaces with the 1st stratigraphic interface ( x 1, y 1) Determine the incident rays at the second stratigraphic interface; Normal dip angle of the second stratigraphic boundary The angle of refraction at the first stratigraphic interface The second stratigraphic interface incident angle ； Inclination angle corresponding to the incident ray The corresponding incident ray slope The equation of the incident ray at the second stratigraphic interface (1-23) By combining equations (1-2) and (1-23), the intersection point of the incident ray at the second stratigraphic interface and the second stratigraphic interface is obtained as ( ). x 2, y 2) (1-24) When the angle of inclination of the corresponding incident ray At that time, the intersection point of the incident ray from the second stratigraphic interface and the second stratigraphic interface is ( x 2, y 2) (1-25) point( x 2, y 2) and ( x 1, y 1) The distance between them is S 2. Δ during travel t 2 （1-26) (3) Incident rays at the third stratigraphic interface The dip angle of the incident ray at the third stratigraphic interface γ The intersection of the incident ray from the third and second stratigraphic interfaces with the second stratigraphic interface ( x 2, y 2) Determine the incident rays at the third stratigraphic interface; Normal dip angle of the third stratigraphic boundary The angle of refraction at the second stratigraphic interface The third stratigraphic interface incident angle ； Inclination angle corresponding to the incident ray The corresponding incident ray slope The equation of the incident ray at the third stratigraphic interface (1-27) By combining equations (1-3) and (1-27), the intersection point of the incident ray at the third stratigraphic interface and the third stratigraphic interface is obtained as ( x 3, y 3) (1-28) When the angle of inclination of the corresponding incident ray At that time, the intersection point of the incident ray from the third stratigraphic interface and the third stratigraphic interface is ( x 3, y 3) (1-29) point( x 2, y 2) and ( x 3, y 3) The distance between them is S 3. Δ during travel t 3 (1-30) …… ( N ) No. N Incident rays at each stratigraphic interface No. N The dip angle of the incident rays at each stratigraphic interface γ N and the N -1 incident rays at the stratigraphic interface and the first N -1 intersection of stratigraphic interfaces ( x N-1 , y N-1 Determine the first N Incident rays at each stratigraphic interface; No. N normal dip angle of each stratigraphic interface , No. N -1 angle of refraction at the stratigraphic interface , No. N Incident angle of each stratigraphic interface ; Inclination angle corresponding to the incident ray , corresponding to the slope of the incident ray , No. N Equations of incident rays at each stratigraphic interface (1-31) Solve equations (1-4) and (1-31) simultaneously to obtain the first... N The incident rays at the first stratigraphic interface and the first N The intersection of the stratigraphic interfaces is ( x N , y N ) (1-32) When the angle of inclination of the corresponding incident ray At that time, the N The incident rays at the first stratigraphic interface and the first N The intersection of the stratigraphic interfaces is ( x N , y N ) (1-33) point( x N-1 , y N-1 )and( x N , y N The distance between them is S N Δ during travel t N (1-34)。 7. The method for tracing two-dimensional ray forward modeling seismic gathers according to claim 1, characterized in that, Step S3: Based on the law of reflection and Snell's law of refraction, ray tracing is performed layer by layer towards the Earth's surface to calculate the intersection points of the reflected rays with the interfaces of each stratum, and the travel time of the reflected rays in each layer is calculated. Specifically, this includes: (1) No. N +1 incident rays from the stratigraphic interface No. N +1 angle of incidence of the stratigraphic boundary γ N+1 and the N The incident rays at the first stratigraphic interface and the first N The intersection of the stratigraphic interfaces ( x N , y N Determine the first N +1 incident rays from a stratigraphic interface; No. N +1 normal dip angle of the formation interface , No. N +1 incident angle at the formation interface ; Corresponding incident ray tilt angle , corresponding to the slope of the incident ray , No. N +1 incident ray equation at the stratigraphic interface (1-35) The combined equations (1-35) and the first N Equations (1-10) for +1 stratigraphic interfaces are used to obtain the... N +1 incident rays from the stratigraphic interface and the first N +1 intersection of stratigraphic interfaces is ( x N+1 , y N+1 ) (1-36) When the angle of inclination of the corresponding incident ray At that time, the first N +1 incident rays from the stratigraphic interface and the first N +1 intersection of stratigraphic interfaces is ( x N+1 , y N+1 ) (1-37) point( x N+1 , y N+1 )and( x N , y N The distance between them is S N+1 Δ during travel t N+1 (1-38) (2) No. N +2 incident rays from stratigraphic interfaces No. N + The dip angle of the incident rays at the two stratigraphic interfaces γ N+2 and the N +1 incident rays from the stratigraphic interface and the first N +1 intersection of stratigraphic interfaces ( x N+1 , y N+1 Determine the first N +2 incident rays from stratigraphic interfaces; No. N +2 normal dip angles of the formation interfaces , No. N +1 refraction angle of the formation interface , No. N +2 incident angles at formation interfaces ; Corresponding incident ray tilt angle The corresponding incident ray slope , No. N +2 incident ray equations at the stratigraphic interfaces (1-39) The combined equations (1-39) and the first N Equations (1-11) for +2 stratigraphic interfaces are used to obtain the... N +2 incident rays from stratigraphic interfaces and the first N The intersection of the two stratigraphic interfaces is ( x N+2 , y N+2 ) (1-40) When the angle of inclination of the corresponding incident ray , No. N +2 incident rays from stratigraphic interfaces and the first N The intersection of the two stratigraphic interfaces is ( x N+2 , y N+2 ) (1-41) point( x N+2 , y N+2 )and( x N+1 , y N+1 The distance between them is S N+2 Δ during travel t N+2 (1-42) (3) No. N +Incident rays from 3 stratigraphic interfaces No. N + The dip angle of the incident rays at the three stratigraphic interfaces γ N+3 and the N +2 incident rays from stratigraphic interfaces and the first N +2 intersections of stratigraphic interfaces ( x N+2 , y N+2 Determine the first N +Incident rays from 3 stratigraphic interfaces; No. N +3 stratigraphic interfaces normal dip angle , No. N +2 refraction angles at stratigraphic interfaces , No. N +3 incident angles at formation interfaces Corresponding incident ray tilt angle The corresponding incident ray slope , No. N +Incident ray equations for 3 stratigraphic interfaces (1-43) The combined equations (1-43) and the first N +3 equations for the stratigraphic interfaces (1-12), obtain the th... N +3 incident rays at stratigraphic interfaces and the first N + The intersection of the three stratigraphic interfaces is ( x N+3 , y N+3 ) (1-44) When the angle of inclination of the corresponding incident ray , No. N +3 incident rays at stratigraphic interfaces and the first N + The intersection of the three stratigraphic interfaces is ( x N+3 , y N+3 ) (1-45) point( x N+2 , y N+2 )and( x N+3 , y N+3 The distance between them is S N+3 Δ during travel t N+3 (1-46) …… ( N + i ) No. N + i Incident rays at each stratigraphic interface No. N + i The dip angle of the incident rays at each stratigraphic interface γ N+i and the N + i -1 incident rays at the stratigraphic interface and the first N + i -1 intersection of stratigraphic boundaries Determine the first N + i Incident rays at each stratigraphic interface; No. N + i normal dip angle of each stratigraphic interface , No. N + i -1 angle of refraction at the stratigraphic interface , No. N + i Incident angle of each stratigraphic interface ; Corresponding incident ray tilt angle The corresponding incident ray slope , No. N + i Equations of incident rays at each stratigraphic interface (1-47) The combined equations (1-47) and the first N + i Equation (1-13) for the first stratigraphic interface, to obtain the... N + i The incident rays at the first stratigraphic interface and the first N + i The intersection of the stratigraphic interfaces is (1-48) When the angle of inclination of the corresponding incident ray , No. N + i The incident rays at the first stratigraphic interface and the first N + i The intersection of the stratigraphic interfaces is (1-49) point and The distance between them is S N+i Δ during travel t N+i （1-50) For reflected rays, when a ray incident from the ground is reflected at a specific interface, the reflected ray exits towards the ground and is incident below each interface; for rays with N The strata at the first interface, in the first N The first interface reflects light, the second... N The inclination angle of the reflected ray from the first interface is also the first... N +1 incident ray dip angle at the stratigraphic interface , i =1,th N +1 incident angle at the formation interface , i =1,; when the reflected ray enters the first... N After +2 formation interfaces i ≥2, , Here i = 2, 3, … , N .

8. The method for tracing two-dimensional ray forward modeling seismic gathers according to claim 1, characterized in that, In step S4, tracing the normal rays of each layer corresponding to the common center point gather according to Snell's law of refraction specifically includes: Requires taking the first N The normal rays of the first stratigraphic interface, firstly... N The normal rays from each stratigraphic interface serve as the initial incident rays for reverse tracing. According to Snell's law of refraction, ray tracing is performed layer by layer towards the surface. The normal rays are traced back towards the surface, incident below the stratigraphic interface, and exit towards the surface at an angle of θ. β 0, with the exit angle of the emitted ray β 0. Determine the slope of the initial incident ray of the normal ray, and use the coordinates of the CMP point of the common center point CMP gather ( x m , y m Using the initial incident ray as the starting point, trace back to the first... N Each stratigraphic interface; According to step S3, from the... N The normal rays from each stratigraphic interface are traced back to the surface. Here, the incident angle of each layer is calculated based on the mathematical and physical model of reflected rays established in step S1. α and angle of refraction β Finally, find the first... N Normal ray emission angle at each stratigraphic interface β 0; in the N During the process of the normal rays from the first stratigraphic interface tracing back to the surface, the first... N The incident ray at the +1 stratigraphic interface is the initial ray that traces the normal ray back to the surface. N + i Emissions from strata interfaces, where 1≤ i ≤ N ; Therefore, the first N Normal ray emission angle at each stratigraphic interface β 0 （1-51) γ N+i It is the first in the ray reflection path N + i The dip angle of the incident rays at each stratigraphic interface. It is the first N + i The normal dip angle of each stratigraphic interface; The coordinates of the CMP point in the common center point CMP gather ( x m , y m Using this as the starting point of the initial incident ray, the result is obtained through the process described above. β Using 0 as the initial angle of inclination of the incident ray, and tracing it to the strata through which the incident ray passes and the mathematical and physical model of the incident ray, the trajectory is determined. N The first stratigraphic interface, to obtain the... N Normal rays of a stratigraphic interface.

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