Methods for reducing the effects of free surface multiple reflections and for seismic surveying, and a memory storage medium

Abstract

A method for reducing the effects of multiple free-surface reflections from seismic signal measurements resulting from seismic energy transmitted to the Earth's subsurface is developed using colocalized pressure and vertical motion component measurements in response to the transmitted seismic energy. The method involves inputting the pressure and vertical motion component measurements into a computer. A downward component of the measurements is then determined in the computer. A response to the Earth's impulse in the absence of a free surface is then determined from the downward component.

Description

/ 22 METHODS FOR REDUCING THE EFFECTS OF FREE SURFACE MULTIPLE REFLECTIONS AND FOR SEISMIC SURVEYING, AND A MEMORY STORAGE MEDIUM

[001] This description refers to the field of seismic reflection exploration. More specifically, the description refers to methods for interpreting seismic reflection signals obtained in marine environments, where the water surface reflects upward seismic energy. This reflected energy subsequently forms part of the excitation energy in the subbottom (formations below the waterbed), resulting in a total “wave field” of seismic energy detected having subbottom events induced both by energy propagating directly from a seismic energy source and by energy reflected from the water surface.

[002] Some types of reflection seismology record independent measurements of the total wavefield (all the energy detected by seismic sensors or receivers in response to seismic energy transmitted to the subsurface) that allow a linear decomposition into ascending and descending wavefield components, denoted by U and D, respectively. These wavefield components can be normalized to, for example, velocity, acceleration, or particle pressure. Without loss of generality, in the description that follows the wavefield components can be normalized by pressure.

[003] At any depth (e.g., below the water surface) of seismic sensor deployment, denoted by z, the incident seismic wave field from one or more seismic energy sources exciting the Earth's subsurface is composed of all downward waves. However, seismic energy reflected from acoustic impedance changes in the subsurface can be reflected again, in particular, for example, from a reflector near or on the surface, such as the water surface (free surface) in marine seismic surveying. As a result, the Petition 870230067699, dated 02 / 08 / 2023, p. 6 / 33 / 22 Effective excitation (the “effective” source) of the subsurface or subbottom is a combination not only of the energy emitted by the seismic energy source(s), but also of all reflections from the free surface. An expression describing the upward wave field in the frequency-wavenumber domain as the product of the Earth's response to a downward wave field can be written as: U = DP (a) where P0 is the impulse response of the Earth in the absence of a free surface, where the signals are measured at the sensor depth z.

[004] Sonneland & Berg (1987), followed later by substantial theoretical elaboration by Amundsen (2001), used the previous principle to demonstrate, in a marine environment, that Eq. (a) can be inverted to achieve free surface (water layer) multiple reflection attenuation and signature deconvolution, thus providing the deconvolved wavefield as represented in Eq. (b): P0=D (b)

[005] The so-called “up / down deconvolution” is widely used to process seismic surveys using seismic signals detected by the ocean floor node (OBN), where independent sensor nodes are placed on the waterbed, and using seismic signals detected by the ocean floor cable (OBC), where cables with seismic sensors at spaced locations are placed on the waterbed. This up / down deconvolution is useful because it effectively achieves the combination of true three-dimensional (3D) source signature deconvolution and free surface multiple attenuation. Furthermore, it generally performs the former better than more conventional modular processes that have been adapted for use with OBN / OBC acquired seismic data. Petition 870230067699, dated 02 / 08 / 2023, page 7 / 33 / 22

[006] A possible limitation of using the upslope wavefield is that specular reflections at, and just below, the sensor or receiver implantation depth (the terms “sensor” and “receiver” are used interchangeably throughout this description) z are limited in their extent to one immediately around each receiver. Since receivers are typically widely spaced, this can result in a substantially incomplete image of the shallow subbackground in OBC / OBN seismic surveys. A second aspect of this is that the reflection angles are large, leading to sometimes unacceptable levels of wave stretching during seismic imaging.

[007] In contrast, the descending wave field, which exploits mirror imagery, does not suffer from such limitations. Mirror imagery uses “virtual” receivers instead of physically embedded receivers. The virtual receivers are “located” as far above the free surface (e.g., the water surface) as the real receivers are located below the free surface. Consequently, the reflection angles are smaller, and specular reflections can be effectively detected over a wider area around each receiver. As a result, the descending wave field is often preferred in seismic interpretation because it produces better shallow images that have more complete specular reflection coverage.However, the descending wave field may suffer from the limitation that there is no deconvolution technique as powerful as there is for the ascending wave field; the use of the descending wave field depends on some combination of conventional methods used for OBN / OBC surveys. Summary

[008] One aspect of the present description relates to a method for reducing the effects of multiple free-surface reflections of seismic signal measurements resulting from seismic energy transmitted to the Earth's subsurface to Petition 870230067699, dated 02 / 08 / 2023, page 8 / 33 / 22 based on colocalized measurements of pressure and vertical component of motion in response to transmitted seismic energy. The method involves inputting the pressure and vertical component of motion measurements into a computer. In the computer, a downward component of the measurements is determined. A response to the Earth's impulse in the absence of a free surface of the downward component is determined.

[009] A method for seismic surveying according to another aspect of this description includes triggering a seismic energy source to transmit seismic energy into subsurface formations. Colocalized measurements of pressure and vertical component of motion are made in response to the transmitted seismic energy. The measurements are entered as input to a computer. In the computer, a downward component of the measurements is determined. An impulse response from the Earth in the absence of a free surface of the downward component is determined. The determined impulse response is stored and / or displayed.

[0010] In some embodiments, pressure measurements comprise measurements of a time derivative of pressure.

[0011] In some embodiments, measurements of a time derivative comprise hydrophone measurements.

[0012] In some embodiments, measurements of the vertical component of motion include measurements of particle velocity.

[0013] In some applications, particle velocity measurements include geophone measurements.

[0014] Some methods additionally involve, on the computer, transforming the colocalized measurements of pressure and vertical component of motion in response to transmitted seismic energy into the frequency-wavenumber domain and transforming the determined impulse response into the space-time domain. Petition 870230067699, dated 02 / 08 / 2023, p. 9 / 33 / 22

[0015] Some embodiments further comprise filtering the determined impulse response from the Earth by a filter representing a band-limited monopole seismic energy source.

[0016] In some modes, seismic energy is transmitted by a source close to the surface of a body of water.

[0017] In some modes, pressure and vertical motion component measurements in response to transmitted seismic energy are made by sensors placed near the bottom of a body of water.

[0018] In some modalities, the descending component of the measurements is determined by linear decomposition.

[0019] A computer program stored on a non-transient computer-readable medium according to another aspect of the description has operable logic to cause a programmable computer to perform acts including accepting as input to the computer colocalized measurements of pressure and vertical component of motion resulting from seismic energy transmitted to the Earth's subsurface; determining a downward component of the measurements; determining an impulse response of the Earth in the absence of a free surface of the downward component; and at least one of storing and displaying the determined impulse response.

[0020] In some embodiments, pressure measurements comprise measurements of a time derivative of pressure.

[0021] In some embodiments, measurements of a time derivative comprise hydrophone measurements.

[0022] In some forms, measurements of the vertical component of motion include measurements of particle velocity.

[0023] In some applications, particle velocity measurements include geophone measurements.

[0024] Some program modes additionally include operable logic to make the computer execute the Petition 870230067699, dated 02 / 08 / 2023, page 10 / 33 / 22 transformation of colocalized pressure and vertical motion component measurements in response to seismic energy transmitted to the frequency-wavenumber domain and transforming the determined impulse response to the space-time domain.

[0025] Some program embodiments additionally comprise operable logic to enable the computer to perform filtering of the determined impulse response from the Earth by a filter representing a band-limited monopole seismic energy source.

[0026] In some modes, seismic energy is transmitted by a source close to the surface of a body of water.

[0027] In some modes, pressure and vertical motion component measurements in response to transmitted seismic energy are made by sensors placed near the bottom of a body of water.

[0028] In some modalities, the descending component of the measurements is determined by linear decomposition.

[0029] Other aspects and potential advantages will become apparent from the description and claims that follow. Brief Description of the Drawings

[0030] Figure 1 shows an example of seismic signal acquisition usable with methods according to the present description.

[0031] Figure 2 shows the components of the ascending and descending wave field at the water depth z=Zr.

[0032] Figure 3 shows a one-dimensional model of sparse reflectors below 300 m of seawater.

[0033] Figure 4 shows the result of applying up / down deconvolution to the data in Figure 2 compared to the actual reflectivity.

[0034] Figure 5 shows the result of applying down / down deconvolution according to the present description to the data Petition 870230067699, dated 02 / 08 / 2023, page 11 / 33 / 22 descendants shown in Figure 2. The bottom trace is the result of applying Eq. (7). The top trace applied the additional terms in Eq. (8) and the delay term in Eq. (9). This can be compared with the actual reflectivity in Figure 3 or Figure 4.

[0035] Figure 6 is a flowchart of an exemplary embodiment of a method according to the present description.

[0036] Figure 7 shows an example processing system that can be used to implement methods according to this description. Detailed Description

[0037] The acquisition of usable seismic signals with methods according to the present description is described herein generally with reference to the acquisition of signals using ocean-floor cables (OBCs). It should be clearly understood that the methods according to this description are equally applicable to seismic signals acquired using ocean-floor nodes (OBNs), and the reference in the following description to OBC sensors or receivers is equally applicable to signals acquired with OBN sensors or receivers.

[0038] Figure 1 shows a vertical sectional view of an OBC seismic survey being conducted using, for example, two different “source” vessels to tow seismic energy sources. In some embodiments, only one source vessel may be used. According to the present description, any number of source vessels may be used and the following description is not intended to limit the scope of the present description. Source vessels move along the surface 16A of a body of water 16, such as a lake or the ocean. In the present example, a vessel referred to as a “primary source vessel” 10 may include equipment, generally shown in 14, comprising components or subsystems (none of which are shown separately) for navigation of the primary source vessel 10, to Petition 870230067699, dated 02 / 08 / 2023, page 12 / 33 / 22 operation of seismic energy sources and to recover and process seismic signal records. Primary source vessel 10 is shown towing two seismic energy sources spaced 18, 18A.

[0039] Equipment 14 on primary source vessel 10 may be in signal communication with corresponding equipment 13 (including components similar to the equipment on primary source vessel 10) located on a vessel referred to as a “secondary source vessel” 12. The secondary source vessel 12 in the present example also tows seismic energy sources spaced 20, 20A close to the water surface 16A. In the present example, equipment 14 on the primary source vessel 10 can, for example, send a control signal to the corresponding equipment 13 on the secondary source vessel 12, such as by radiotelemetry, to indicate the activation (triggering) time of each of the sources 18, 18A towed by the primary source vessel 10. The corresponding equipment 13 can, in response to such a signal, activate the seismic energy sources 20, 20A towed by the secondary source vessel 12.

[0040] The seismic power sources 18, 18A, 20, 20A may be air guns, water guns, marine vibrators, or arrays of such devices. The seismic power sources are shown as discrete devices in Figure 1 to illustrate the general principle of seismic signal acquisition. The type and number of seismic power sources that may be used in any example are not intended to limit the scope of the description.

[0041] In Figure 1, an OBC 22 is deployed on the bottom 16B of water 16 so that the spaced seismic receiver modules 24 are arranged on the bottom of water 16B in a pre-selected pattern. The receiver modules 24 may include a pressure or time gradient responsive seismic sensor and one or more seismic particle motion sensors, for example, one- or three-component geophones or Petition 870230067699, dated 02 / 08 / 2023, page 13 / 33 / 22 accelerometers of one or three components (none of the sensors are shown separately). The type and number of seismic sensors in each module 24 are not intended to limit the scope of the description. The seismic sensors in each module 24 generate electrical and / or optical signals (depending on the sensor type) in response, in particular, to the detected seismic energy resulting from actuations of seismic energy sources 18, 18A, 20, 20A. In some embodiments, the sensors may comprise pressure- or temporal-derived sensors, such as hydrophones, and one or more particle motion-responsive sensors, such as geophones or accelerometers. In some embodiments, such particle motion-responsive sensors can be oriented so as to be primarily sensitive (ignoring any cross-component coupling for explanatory purposes) to the vertical motion of particles.The signals generated by the various sensors can be conducted to a device near the water surface 16A, such as a recording buoy 23, which may include a data recorder (not shown separately) to store the signals for later retrieval and processing by equipment 14 on the primary source vessel 10, or other processing equipment to be described further below. The data storage functions performed by the recording buoy 23 can be carried out by different types of equipment, such as a data storage unit on a recording vessel (not shown) or a recording module (not shown) deployed on the water bottom 16B, for example, near each sensor module 24, or even on the primary or secondary source vessels. Consequently, the description is not limited in scope to use with a recording buoy or any other specific recording device.

[0042] Although the description of signal acquisition explained with reference to Figure 1 is for sensors deployed on the waterbed, it will be recognized that it is possible to obtain corresponding measurements in any Petition 870230067699, dated 02 / 08 / 2023, page 14 / 33 / 22 selected depth in the water, using, for example, seismic sensors arranged on a towed cable as described in U.S. Patent No. 7,239,577 granted to Tenghamn, et al.

[0043] An explanation of the methods according to this description can begin by describing the components of the scattered wave field due to a seismic source being used with OBN or OBC receivers as in Figure 1 (although the receivers can be placed at any other depth in the water layer). After a review of how up / down deconvolution works, a new idea is introduced in which an equally powerful deconvolution technique can be used on the descending wave field. The method can be referred to as down-down deconvolution. The description will conclude with a discussion of the source estimation methods that can be used with down / down deconvolution. 1. The components of the wave field

[0044] The phantom source wavefield (reflected at the surface) can be defined as a pair of monopoles with a time spectrum represented by b(ω): S = _^(ω) (^ik^zs +Re+i.)ikz (1)

[0045] The pair of monopoles represents the ghosting effect due to the depth of the source z and the reflectivity function of the free surface (water surface), R. The vertical wave number is given by kz, which obeys the dispersion relation of the scalar wave equation and the Fourier sign convention of Claerbout (1985) is used here.

[0046] The receiver (for example, as explained with reference to Figure 1) at the depth is indicated by zr and, for convenience, it is assumed that the receivers are implanted on the waterbed, as explained with reference to Figure 1, so that the depth of the receiver is the same Petition 870230067699, dated 02 / 08 / 2023, page 15 / 33 / 22, which states that the depth of the water layer at each location is received. The water layer covers an elastic or acoustic reflective half-space (e.g., all materials below the water bottom 16B in Figure 1). In the absence of a free surface (water surface 16A in Figure 1), 0 denotes the impulse response of the acoustic reflective half-space measured just above the water bottom (16B in Figure 1). A downward plane wave propagated down from the water surface to the water bottom undergoes a phase change of exp(+ikzzr). For convenience, one can define: Z - e+ikz2z (2)

[0047] With reference to Figure 2, it is possible to construct the components of the wave field one step at a time and conclude that the ascending U and descending D wave fields can be represented by their respective infinite series: D - S' + S 'ZP0 RU - S P0 + S Zp02r +S 'Z2P02R2... +S'Z2P03r2...(3) where the identities S' -SZ+1 / 2 are used. Each term of the ZPR series in Eq. (3) is the product of the previous term multiplied by 0, that is, a delay equivalent to the travel time through the water layer, reflection from the free surface and reflection from the underlying Earth materials, i.e., the materials below the water bottom.

[0048] The series in Eq. (3) are Taylor series expansions of the expressions:

[0049] called D - —S— 1- ZP0R u - —— p - ZPo r0(4) The denominator in both expressions of Eq. (6) is sometimes the “scattering operator” because it describes all scattering between the free surface and the Earth’s reflectivity. Eq. (4) represents takeoff points for a wide range of forecasting techniques. Petition 870230067699, dated 02 / 08 / 2023, page 16 / 33 / 22 multiple, including Backus filtering and surface-related multiple filtering (SRME) known in the art. 2. Upward / downward deconvolution

[0050] The reason for the expressions in Eq. (4), namely: It is known to be low. This deconvolution = P - ZpR 7 1 - ZpR0(5) in the technique as up / down deconvolution performs 3D signature deconvolution and multiple free surface attenuation in a single step. P0 is the impulse response of the dipole just above the water bottom in the absence of a free surface. It is common to replace the dipole source just above the water bottom with a band-limited monopole at the water surface. Therefore, full up / down deconvolution is generally considered: a (ω)UZ+1 / 2 ikz D a(ω)p y+1 / 2P0Zik(6) where a (ω) is a desired time spectrum and the term converts the dipole source into a monopole source. 3. Downward / downward deconvolution -1 / ik^

[0051] Taking the inverse of the first expression in Eq. (4) and multiplying by S, it can be observed that:

[0052] 5' - ZPR = —0 D(7) Eq. (7) indicates that it is possible to deconvolve the descending wave field from the source wave field in z zr and find that it has substantially isolated P, the desired impulse response,0. This can be called “downward / downward deconvolution”. However, a new rearrangement P can complete the solution for 0 as: Petition 870230067699, dated 02 / 08 / 2023, p. 17 / 33 / 22

[0053] Therefore, in one embodiment of a method according to this description, first perform the deconvolution of Eq. (7), then remove the additive effect of δ(x, y, t), and finally remove the data correction implied by Z. The free surface reflectivity function R can be treated as a scalar or as a more elaborate operator. As noted for the up / down deconvolution case, because 0 is the plane wave impulse response at receiver depth z — Zr, the further adjustment to convert the impulse response into a monopole band-limited response on the free surface can use the following expression: a (ω) P Z+1 / 2 ikz ° a (ω) 1 C ikz ZR L S Ί 7+1 / 2 _ a(ω) 1( S । Ί 7-1 / 2 Z 1 Z D) ikzR LDJ (9) which formulates the complete deconvolution. However, in some circumstances, some terms may be optionally omitted in the same way as in the up / down deconvolution. Experience in evaluating a method according to this description shows that subject to careful regularization, Eqs. (7), (8) and (9) are computed easily and reliably. The components required to perform the complete deconvolution, Eq. (9), are described in more detail below. 4. Downward / downward deconvolution requirements

[0054] a (ω)- is the desired time spectrum of the monopole source, and can be chosen to determine the bandwidth of the deconvolution output and help regularize the deconvolution process.

[0055] 1 ikz - is an operator that converts the dipole source into a monopole source (Aki and Richards, 1980).

[0056] R- is the free surface reflectivity, and is often considered a scale counter close to -1. However, it is easy to use other reflectivities, such as frequency-dependent reflectivity (Orji et al., 2013). Since R has, at worst, a slight band limitation, it is easy and robustly deconvolved. Petition 870230067699, dated 02 / 08 / 2023, p. 18 / 33 / 22

[0057] Z=e+'kl2zr- is an operator that extrapolates the wave field through the water layer twice. Knowing Z depends on knowing the propagation speed and the water depth. For the OBN or OBC case, these parameters are usually known with precision.

[0058] 5' =SZ+1 / 2- is a term that there are several ways to determine. In the case of sufficiently deep water,S can be derived by isolating 5(t, x,y) as the initial part of d(t, x,y) using windows: D = S'+S' ZP0 R + S' Z2P02R2.

[0059] S can also be derived from a linear combination of U and Du using the expression S=D-RZU. It can be shown that this is closely related to the cross-ghosting method described in Soubaras (1996).

[0060] S can be derived from near-field pressure signal recordings or time-derived pressure (hydrophone) using the notional source technique of Ziolkowski et al. (1982) together with Z+1 / 2 of the knowledge of Z (see above).S can also be calculated using source modeling software together with Z+1 / 2 of the knowledge of Z (see above).

[0061] Dé the descending wave field, which can be derived as a linear combination, D=(P+ρωK² / k) / 2 of the pressure and vertical component of the particle motion (velocity) fields. This is based on good quality particle pressure and velocity field measurements with minimal noise. 5. An Example

[0062] The following example uses a synthetic set of simulated reflections below a 300 m layer of water. The source is a simulation of the acoustic or seismic signature of a real air gun (or array). The reflectivity consists of a sparse number of isolated reflectors that are Petition 870230067699, dated 02 / 08 / 2023, page 19 / 33 / 22 shown in the lower trace of Figure 3, which was delayed by zr / v, where v+1 / 2 denotes the water velocity. In current notation, it is 0. The two upper traces in Figure 3 show the ascending and descending seismic receiver traces (signal representations) that would result from using the air gun source and the sensor placed just above the water bottom.

[0063] For illustration, the total pressure and vertical velocity of the particle (P&Vz) are also shown as the 2nd and 3rd traces from the bottom. Normally U and D are derived from the recorded PeV. It is worth noting that the only descending information prior to =3zv is the signature of the seismic source.

[0064] The up / down deconvolution considers D as the effective seismic source. Deconvolving it from U, as in Eq. (5) and applying the displacement in Eq. (6) produces the deconvolved result, UDZ, which is shown in comparison with the actual reflectivity, P0Z, shown in Figure 4.

[0065] Using the descending trace of Figure 2, and the known source term, S, the initial division in Eq. (7) was performed. The result is shown as the lower trace in Figure 5. This substantially achieves the deconvolution, but requires the additional terms of Eq. (8) and the shift of Eq. (9) to complete the deconvolution. The result is shown as the upper trace in Figure 5, which can be compared with the actual reflectivity, +1 / 2 in Figure 3, or Figure 4. This example illustrates the principle and demonstrates that this new method should work as explained.

[0066] An example of an embodiment of a method according to the present description will now be explained with reference to Figure 6.

[0067] The seismic signals acquired as explained with reference to Figure 1 can be recorded. The recorded signals comprise time series of pressure and vertical particle motion with reference to the location of the source(s) and sensors from which the signals are obtained. Petition 870230067699, dated 02 / 08 / 2023, page 20 / 33 / 22 recorded, can be decomposed into ascending and descending wave field components, denoted by U and D, respectively. Typically, the recorded data consist of pressure and velocity readings of vertical particles (P and Vz, respectively).

[0068] For convenience, the D, U, P, and Vz fields are shown in the frequency wavenumber domain unless otherwise specified. The well-known decomposition of P,Vz to D,U is performed by subtracting and adding pressure-normalized versions of Vz to P as follows, P v cos θ (12)

[0069] Where ρ, ν and θ are, respectively, the apparent density of the medium, the propagation speed of the medium and the angle of the propagating wave ray.

[0070] A solution can be calculated for a band-limited monopole source located on the water surface in the absence of free surface reflectivity, that is, what is expressed on the right-hand side of the following expression: a (ω) ikz P0Z+1 / 2a (ω) Γ £ \ S_ ikz LR l D ,(13)

[0071] The new concept is contained in the brackets in Eq. (13). The components required for the solution are: Give the descending wave field.

[0072] Zé the wave extrapolator to extrapolate a descending wave field to a depth equal to twice the thickness of the water layer.

[0073] S =SZ+1 / 2 is the wave field of the surface source that would be observed at a depth equal to the thickness of the water layer. Petition 870230067699, dated 02 / 08 / 2023, p. 21 / 33 / 22

[0074] R is the free surface reflectivity (ω) is the spectrum of a desired band-limited monopole source i is the square root of -1 kz is the vertical spatial frequency consistent with the dispersion relation of the scalar wave equation at the time frequency ω: In Figure 6, the pressure and velocity of the particles, p(t,x,y), vz(t,x,y) are entered into a computer or processor (Figure 7).

[0075] In 61, on the computer, the input signals can be transformed by Fourier, p (t,x,y), v(t,x,y)^ P(ω, kx, k), Vz(ω, kx, ky), in the frequency-wavenumber domain (f - k).

[0076] In step 62, on the computer, derive the descending wave field, D, from the input data (Fourier transforms), P eVz.

[0077] In 63, on the computer, calculate the Earth's impulse response. At each temporal / spatial frequency, evaluate the bracketed part of Eq. (13) using the following: a. form the ratio S / D b. subtract one from the results of 0) c. divide the result of 0) by the reflectivity of the free surface, R d. extrapolate from depth to push the apparent seismic source depth down by an amount equal to the thickness of the water layer ^F

[0078] In 64, which is optional, for each frequency / number of waves apply the terms outside the brackets in Eq. (13): a. Apply the band-limiting filter a (ω) to the results of 63, element 0 above Petition 870230067699, dated 02 / 08 / 2023, p. 22 / 33 / 22 b. Divide the result by i times the number of vertical waves, kz^F

[0079] In 65, on the computer, the inverse transformation from the frequency / wavenumber domain to the time / space domain,F(ω,kx,ky )^f(t, x, y)

[0080] In 66, produce the results f(t, x, y) for recording and / or display and possible use as input for other seismic data processes.

[0081] All the above calculations can be performed on any general-purpose or specific-purpose computer or processor. Figure 7 shows an example of a computing system 100 according to some embodiments. The computing system 100 can be an individual computer system 101A or an arrangement of distributed computer systems. The individual computer system 101A may include one or more analysis modules 102 that can be configured to perform various tasks according to some embodiments, such as the tasks explained with reference to Figures 2-6. To perform these various tasks, the analysis module 102 can operate independently or in coordination with one or more processors 104, which can be connected to one or more storage media 106.A display device, such as a graphical user interface of any known type, may be in signal communication with the processor 104 to allow user input of commands and / or data and to display results of the execution of a set of instructions according to the present description.

[0082] The processor(s) 104 may also be connected to a network interface 108 to allow the individual computer system 101A to communicate via a data network 110 with one or more additional individual computer systems and / or computing systems, such as 101B, 101C and / or 101D (note that the systems of Petition 870230067699, dated 02 / 08 / 2023, page 23 / 33 / 22 Computer systems 101B, 101C, and / or 101D may or may not share the same architecture as computer system 101A and may be located in different physical locations, for example, computer systems 101A and 101B may be at a drilling well location while communicating with one or more computer systems, such as 101C and / or 101D, which may be located in one or more offshore data centers, on board ships, and / or located in various countries on different continents.

[0083] A processor may include, without limitation, a microprocessor, microcontroller, processor module or subsystem, programmable integrated circuit, programmable gate array, or other control or computing device.

[0084] Storage media 106 can be implemented as one or more computer-readable or machine-readable storage media. Note that while in the example embodiment of Figure 7 storage media 106 is shown as being disposed within the individual computer system 101A, in some embodiments, storage media 106 can be distributed within and / or across multiple internal and / or external compartments of the individual computing system 101A and / or computing systems, for example, 101B, 101C, 101D.Storage media 106 may include, without limitation, one or more different forms of memory, including semiconductor memory devices such as dynamic or static random access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), read-only memories (EEPROMs) and electrically erasable and programmable flash memories; magnetic disks such as hard disks, floppy disks and removable disks; other magnetic media including tapes; optical media such as compact discs (CDs) or digital video discs (DVDs); or other types of storage devices. Note that... Petition 870230067699, dated 02 / 08 / 2023, page 24 / 33 / 22. Computer instructions to cause any individual computer system or a computing system to perform the tasks described above may be provided on a computer-readable or machine-readable storage medium, or may be provided on multiple computer-readable or machine-readable storage media distributed across a multi-component computing system having one or more nodes. Such computer-readable or machine-readable storage medium may be considered part of an article (or article of manufacture). An article or article of manufacture may refer to any single manufactured component or multiple components. The storage medium may be located on the machine executing the machine-readable instructions or located at a remote location from where the machine-readable instructions may be downloaded over a network for execution.

[0085] It should be recognized that computing system 100 is only one example of a computing system and that any other embodiment of a computing system may have more or fewer components than those shown, may combine additional components not shown in the example embodiment of Figure 7, and / or computing system 100 may have a different configuration or arrangement of the components shown in Figure 7. The various components shown in Figure 7 may be implemented in hardware, software, or a combination of hardware and software, including one or more of the signal processing and / or application-specific integrated circuits.

[0086] In addition, the actions of the processing methods described above can be implemented by running one or more functional modules in information processing devices, such as general-purpose processors or application-specific chips like ASICs, FPGAs, PLDs, GPUs, coprocessors, or other appropriate devices. These modules, Petition 870230067699, dated 02 / 08 / 2023, page 25 / 33 / 22 combinations of these modules and / or their combination with general hardware are all included in the scope of this description.

[0087] A novel method is described here in which the descending wave field recorded just above the waterbed can be deconvolved to reveal the Earth's response to a monopole source in the absence of a free surface. This method removes free surface multiples and performs 3D signature deconvolution. It requires a good estimate of the seismic source signature, which can be derived from OBN or OBC measurements (among other approaches), and a good estimate of the descending wave field.

[0088] In light of the principles and example modalities described and illustrated in this document, it will be recognized that the example modalities may be modified in arrangement and detail without departing from such principles. The preceding discussion has focused on specific modalities, but other configurations are also contemplated. In particular, even though expressions such as “a modality” or similar are used in this document, these phrases are intended to refer generally to modality possibilities and are not intended to limit the description to particular modality configurations. As used in this document, these terms may refer to the same or different modalities that are combinable into other modalities.As a rule, any embodiment referenced herein is freely combinable with any one or more of the other embodiments referenced herein, and any number of features from different embodiments are combinable with each other, unless otherwise indicated. Although only a few examples have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible within the scope of the examples described. Consequently, all such modifications should be included within the scope of this description, as defined in the following claims.

[0089] References cited in this description include: Petition 870230067699, dated 02 / 08 / 2023, p. 26 / 33 / 22 Aki, K., and Richards, PG, 1980, Theory and Methods of Quantitative Seismology, Volume 1, WH Freeman and Company, New York. Amundsen, L., 2001, Elimination of free surface-related multiples without the need for a source wavelet, Geophysics, 66, 1.

[0090] Claerbout, J.F., 1985, Imaging the Earth’s interior, Blackwell, Oxford.

[0091] Orji, O.C., Sollner, W.C., and Gelius, L.J., 2013, Sea Surface Reflection Coefficient Estimation, SEG Technical Program Expanded Abstracts : 51-55.

[0092] Sonneland, L., e Berg, L.E., 1987, Comparison of two approaches to water layer multiple attenuation by wave field extrapolation, SEG Technical Program Expanded Abstracts: 276-277.

[0093] Soubaras, R., 1986, Ocean bottom hydrophone and geophone processing, SEG Technical Program Expanded Abstracts 1996, 24-27

[0094] Ziolkowski, A., Parkes, G., Hatton, L. and Haugland, T., 1982, The signature of an air gun array: Computation from near-field measurements including interactions, Geophysics, 47(10). Petição 870230067699, de 02 / 08 / 2023, pág. 27 / 33

Claims

1 / 5 CLAIMS 1. A method for reducing the effects of multiple free-surface reflections from seismic signal measurements, the resulting measurements of seismic energy transmitted to the Earth's subsurface from colocalized measurements of pressure and vertical component of motion in response to the transmitted seismic energy, characterized in that the method comprises: inputting as input to a computer the measurements related to pressure and vertical component of motion; in the computer, determining a descending component of the measurements without using an ascending component of the measurements; in the computer, determining an impulse response of the Earth to the transmitted seismic energy in the absence of a free surface from the descending component; and at least one of storing and displaying the determined impulse response.

2. Method according to claim 1, characterized in that the pressure-related measurements comprise measurements of a time derivative of the pressure, preferably wherein the measurements of a time derivative comprise hydrophone measurements.

3. Method according to claim 1, characterized in that the measurements related to the vertical component of motion comprise particle velocity measurements, preferably wherein the particle velocity measurements comprise geophone measurements.

4. Method according to claim 1, characterized in that it further comprises, on the computer, transforming the colocalized measurements related to pressure and the vertical component of motion in response to seismic energy transmitted to the frequency-wavenumber domain and transforming the impulse response determined in the time-space domain.

5. Method according to claim 1, characterized in that it further comprises filtering the determined impulse response from the Earth by a filter representing a band-limited monopole seismic energy source, wherein the seismic energy is transmitted by a source near the surface of a body of water.

6. Method according to claim 1, characterized in that the measurements related to pressure and the vertical component of movement in response to transmitted seismic energy are made by sensors placed near the bottom of a body of water.

7. Method according to claim 1, characterized in that the descending component of the measurements is determined by linear decomposition.

8. A method for seismic surveying, characterized in that it comprises: activating a seismic energy source to transmit seismic energy into subsurface formations; making colocalized measurements related to pressure and the vertical component of motion in response to the transmitted seismic energy; inputting as input to a computer the measurements related to pressure or the time derivative of pressure, and the vertical component of motion; in the computer, determining a descending component of the measurements without using an ascending component of the measurements; in the computer, determining an impulse response of the Earth to the transmitted seismic energy in the absence of a free surface from the descending component; and at least one of the following: storing and displaying the determined impulse response.

9. Method according to claim 8, characterized in that the pressure-related measurements comprise measurements of a time derivative of pressure, preferably wherein the measurements of a time derivative comprise hydrophone measurements.

10. Method according to claim 8, characterized in that the measurements related to the vertical component of motion comprise particle velocity measurements, preferably wherein the particle velocity measurements comprise geophone measurements.

11. Method according to claim 8, characterized in that it further comprises, on the computer, transforming the colocalized measurements related to pressure and the vertical component of motion in response to seismic energy transmitted to the frequency-wavenumber domain and transforming the impulse response determined in the time-space domain.

12. Method according to claim 8, characterized in that it further comprises filtering the determined impulse response from the Earth by a filter representing a limited-band monopole seismic energy source wherein the seismic energy is transmitted by a source near the surface of a body of water.

13. Method according to claim 8, characterized in that the measurements related to pressure and the vertical component of movement in response to transmitted seismic energy are made by sensors placed near the bottom of a body of water.

14. Method according to claim 8, characterized in that the descending component of the measurements is determined by linear decomposition. Petition 870260033147, dated 09 / 04 / 2026, page 14 / 38 4 / 5 15. Memory storage medium, characterized in that it has instructions recorded within it which, when executed by a processor, cause the processor to execute the method as defined in claim 1, comprising: accepting as input to the computer colocalized measurements related to the pressure and vertical component of motion resulting from seismic energy transmitted to the Earth's subsurface; determining a descending component of the measurements without using an ascending component of the measurements; determining an impulse response of the Earth to the transmitted seismic energy in the absence of a free surface from the descending component; and at least one of storing and displaying the determined impulse response.

16. Memory storage medium according to claim 15, characterized in that the pressure-related measurements comprise measurements of a time derivative of the pressure, preferably wherein the measurements of a time derivative comprise hydrophone measurements.

17. Memory storage medium according to claim 15, characterized in that the measurements relating to the vertical component of motion comprise particle velocity measurements, preferably wherein the particle velocity measurements comprise geophone measurements.

18. Memory storage medium according to claim 15, characterized in that it further comprises operable logic to enable the computer to perform the transformation of colocalized measurements related to pressure and the vertical component of motion in response to seismic energy transmitted to the frequency-number wave domain and transforming the determined impulse response to the time-space domain.

19. Memory storage medium according to claim 15, characterized in that it further comprises operable logic for enabling the computer to perform filtering of the determined impulse response from the Earth by a filter representing a limited-band monopole seismic energy source, wherein the seismic energy is transmitted by a source near the surface of a body of water.

20. Memory storage medium according to claim 15, characterized in that measurements relating to pressure and the vertical component of motion in response to transmitted seismic energy are made by sensors located near the bottom of a body of water.

21. Memory storage medium according to claim 15, characterized in that the descending component of the measurements is determined by linear decomposition. Petition 870260033147, dated 09 / 04 / 2026, p. 16 / 38

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