Seismic data filtering based on vibrator-coupled ground model

A vibrator-coupled ground filter improves seismic data recorded during a seismic operation. This filter is based on a ground model that takes into consideration the vibrator system, the coupling system between the baseplate and captured ground, and the coupled ground system. Using acceleration data from the baseplate and the reaction mass, the ground model can be used to derive particular variables for the ground model to help characterize the system. Using the derived variables in a ground filter, the recorded seismic data can be corrected to remove errors in the trace data produced by typical assumptions.

BACKGROUND OF THE DISCLOSURE

The oil and gas exploration industry employ geophysical tools and techniques to identify a subterranean structure having potential hydrocarbon deposits. Commonly referred to as seismic exploration, these techniques and tools generate an image of subsurface structures by recording energy in the form of vibrations reflected or refracted from geologic formations. In seismic exploration, for example, seismic waves generated by a source and imparted into the ground reflect off rocks in the subsurface. Boundaries between different rocks often reflect seismic waves, and information relating to these waves is collected and processed to generate a representation or images of the subsurface.

When seismic waves generated by the source reach a bedding plane separating rocks of different acoustic density, then a portion of the waves reflects back to the surface, causing the ground surface to rise or fall depending on whether the expansion or compression phase of the wave is being recorded. The remaining portion of the waves is refracted and diffracted. A two-dimensional image, which is called a seismic line, is essentially a cross-sectional view of the earth oriented parallel to the line of geophones. The information may also be collected as an intersecting grid of seismic lines referred to as a 3-D seismic volume.

Any number of exploration systems can gather the desired information for processing. Dynamite explosions, vibrator trucks, air guns or the like can create the seismic waves. Sensors such as velocity geophones, accelerometers, and/or hydrophones can be laid out in lines, or towed in the case of hydrophones, to measure how long it takes the waves to leave the seismic source, reflect off a rock boundary, and return to the sensors used.

An example seismic system10inFIG. 1can generate geophysical information to image earth subsurface structures. The system10has a central controller/recorder90in communication with a seismic acquisition array12known as a spread. The array12has spaced sensor stations20, which can each have one or more sensors22. The sensors22measure geophysical information and can include 3-component sensors for obtaining 3-dimensional energy known as 3D seismic. The sensors22can include accelerometers, velocity geophones, microphones, or the like, and the array12can be deployed on land or a seabed location.

A seismic source30imparts acoustic energy into the ground, and the sensors22receive energy after reflection and refraction at boundaries in subsurface structures. The array12then communicates sensor data with the central controller or recorder90using wireless technology or other communication technique.

To impart the acoustic energy, the seismic source30can be a vibrator, such as shown inFIG. 2, although other types of sources can be used. The vibrator30transmits force to the ground using a baseplate70and a reaction mass50. As is typical for land seismic, the vibrator30is mounted on a carrier vehicle (not shown) that uses bars32/34to lower the vibrator30to the ground. With the vibrator30lowered, the weight of the vehicle holds the baseplate70engaged with the ground so seismic source signals can be transmitted into the earth.

The reaction mass50positions directly above baseplate70and stilts52extend from the baseplate70and through the mass50to stabilize it. Internally, the reaction mass50has a cylinder56formed therein. A vertically extending piston60extends through this cylinder56, and a head62on the piston60divides the cylinder56into chambers. The ends of the piston60connect to cross-pieces54U-L that connect to the stilts52.

Feet36with isolators40isolate the baseplate70from the bars34, and tension members42interconnect between the feet36and the baseplate70. The tension members42hold the baseplate70when the vibrator30is raised and lowered to the ground. Finally, shock absorbers44are also mounted between the bottom of the feet36and the baseplate70to isolate vibrations therebetween.

During operation, a controller80receives signals from a first sensor85that measures acceleration of the baseplate70and receives signals from a second sensor87that measure acceleration of the reaction mass50. Based on feedback from these sensors85/87and a desired sweep signal for operating the vibrator30, the controller80generates a pilot signal to control a servo valve assembly82. Driven by the drive signal, the servo valve assembly82alternatingly routes hydraulic fluid between a hydraulic fluid supply84and the piston60. The reaction mass50reciprocally vibrates on the piston60. In turn, the force generated by the vibrating mass50transfers to the baseplate70via the stilts52and the piston60so that the baseplate70vibrates at a desired amplitude and frequency or sweep to generate a seismic source signal into the ground.

As the moving reaction mass50acts upon the baseplate70to impart a seismic source signal into the earth, the signal travels through the ground, reflects at discontinuities and formations, and then travels toward the earth's surface. At the surface, the array12ofFIG. 1having the geophone receivers or other sensors22coupled to the ground detect the reflected signals, and the recorder90ofFIG. 1records the seismic data92received from the geophone receivers22.

At some point, a data processing system98receives the seismic data92from the seismic recorder90. (The seismic data92can also include recorded data from the seismic vibrator30if information such as pilot signal, acceleration data, and weighted sum ground force are stored separately.) The data processing system98can use a correlation processor to correlate the computed ground force supplied by the vibrator30to the seismic data92received by the geophone receivers22. Ultimately, the correlated information can be used to create an image or representation of the earth's subsurface structures.

When operating such a prior art vibrator30, operators experience problems in accurately determining the ground force that the vibrator30is applying to the ground and in accurately correlating the vibrator's operation with the generated source signal. Ideally, operators would like to know the actual ground force applied by the baseplate70to the ground when imparting the seismic energy. As shown inFIG. 2, a local sensor85(e.g., accelerometer or geophone) is typically positioned on the upper cross piece54U of the vibrator50, which positions above the reaction mass50.

In operation, the controller80shown inFIG. 2measures the signal imparted into the ground using the local sensor85located on the upper cross-piece54U and using the sensor87located on the reaction mass50. When the data processing system98ofFIG. 1receives the seismic data92making up the seismic spread, it also receives the acceleration signals from these sensors85/87on the source30. The system98's correlation processor then uses various algorithms to distinguish wave signal data from distortions and other spurious signals.

A problem with this method is that original source signal distortion may vary and make correlation difficult. When calculated ground force signals at the vibrator30are cross-correlated with far-field signals measured in the field, the results may be corrupted by unrealistic assumptions used in modeling the system10. In particular, the vibrator30works on the surface of the ground, which can vary dramatically from location to location due to the presence of sand, rock, vegetation, etc. Thus, the baseplate70is often not evenly supported when deployed against the ground at a given location. In addition, the baseplate70will flex and directly affect the control system during operation. As a result, the radiated energy produced can vary from location to location depending on where the vibrator30is deployed. Therefore, the vibrator's source signature is not the same (or nearly the same) from location to location and is not characteristically repeatable, which is desirable when performing seismic analysis. Thus, a more accurate knowledge of the source signal imparted into the ground by the source30can make the correlation easier at the data processing stage.

SUMMARY OF THE DISCLOSURE

A vibrator-coupled ground filter improves seismic data recorded during a seismic operation. This filter is based on a ground model that takes into consideration the vibrator system, the coupling system between the baseplate and captured ground, and the coupled ground system. Using acceleration data from the baseplate and the reaction mass, the ground model can be used to derive particular variables for the ground model to help characterize the system. Using the derived variables in the ground filter, the recorded seismic data can be corrected to remove errors in the trace data produced by typical assumptions.

In a seismic data processing method, for example, acceleration data of a reaction mass and a baseplate of a source of seismic energy is obtained as well as seismic data of one or more seismic sensors responsive to the seismic energy of the source. Variables for a ground model are derived by analyzing a frequency response relating the reaction mass acceleration data and the baseplate acceleration data as input and output relative to one another. Using the ground model with the derived variables, a source signal indicative of operation of the source is filtered. This source signal can be a pilot signal or a weighted ground force sum. The filtered source signal is available for processing with the seismic data of the one or more seismic sensors so the seismic data can be correlated with the filtered source signal.

In a seismic data processing apparatus, for example, memory stores a ground model, a source signal indicative of operation of a source of seismic energy, acceleration data of a reaction mass and baseplate of the source, and seismic data of one or more seismic sensors responsive to the seismic energy of the source. One or more processing units are operatively coupled to the memory. The one or more processing units analyze a frequency response relating the reaction mass acceleration data and the baseplate acceleration data as input and output relative to one another and derive variables for the ground model based on the analyzed frequency response. The one or more processing units filter the source using the ground model with the derived variables and make the filtered source signal available for processing with the seismic data so the seismic data can be correlated with the filtered source signal.

DETAILED DESCRIPTION OF THE DISCLOSURE

A. Seismic System

An example seismic system10inFIG. 3can generate geophysical information to image earth subsurface structures. The system10has a central controller/recorder90in communication with a seismic acquisition array12known as a spread. As before, the array12has spaced sensor stations20, which can each have one or more sensors22. The sensors22measure geophysical information and can include 3-component sensors for obtaining 3-dimensional energy known as 3D seismic. The sensors22can include accelerometers, velocity geophones, microphones, or the like, and the array12can be deployed on land or a seabed location.

As before, a seismic source30imparts acoustic energy into the ground, and the sensors22receive energy after reflection and refraction at boundaries in earth subsurface structures. The seismic source30can be similar to the vibrator disclosed previously with reference toFIG. 2. For the benefit of the present discussion, reference is made to the components of the vibrator30ofFIG. 2, including a reaction mass50, a baseplate70, and a controller80as diagramed inFIG. 3. However, the seismic source30according to the present disclosure need not necessarily be a hydraulically operated vibrator. Instead, the seismic source30can be a seismic vibrator have an electric motor, can have an internal or external drive, and can generate seismic shear waves (S-waves) or seismic compression waves (P-waves). In general, the vibrator30can be any type of vibrator having a controller80and having a reaction mass50and a baseplate70for imparting energy into the ground.

As before, the moving reaction mass50acts upon the baseplate70of the vibrator30to impart seismic source signals into the ground. The signals travel through the ground, reflect at discontinuities and formations, and then travel toward the earth's surface. At the surface, the array12having the geophone receivers22coupled to the earth detects the reflected signals, and the array12communicates seismic data with the central controller or recorder90using wireless technology or other communication technique.

The recorder90records the seismic data92from the geophone receivers22. At some point, a data processing system98is employed to process the seismic data92. (The seismic data92can also include recorded data from the seismic vibrator30if information such as pilot signal, acceleration data, and weighted sum ground force are stored separately.) To improve the subsequent imaging produced by the data processing system98, a vibrator-coupled ground filter system94according to the present disclosure is used to refine or improve the original seismic data92so that the improved data96can be provided to the data processing system98. When this is done, the data processing system98can use its correlation processor (not shown) to correlate a computed ground force from the information supplied by the vibrator30to the seismic data96and can ultimately provide more clear data for seismic imaging.

As noted previously, the vibrator's controller80measures the acceleration data from local sensors. Part of the seismic data92received at the recorder90includes the acceleration data for both the baseplate70and reaction mass50of the vibrator30from such local sensors. The dynamic motions related to the coupling conditions of the vibrator30are recorded and embedded in the baseplate acceleration data. In addition, the motion of the vibrator's actuator (e.g., hydraulic system) is recorded and embedded in the reaction mass acceleration data. These measurements are recorded during data acquisition using the recorder90and are used by the filter system94to process the data. In particular, the ground filter system94uses this acceleration data and a model of the coupling between the vibrator30and the ground to filter or correct the seismic data92before processing with the data processing system98.

Before turning to particular details of the filter system94, discussion first focuses on a vibrator-coupled ground model used for the filter system94.

As noted above, the vibrator30works on the earth surface where the surface medium can change dramatically from location to location. When the vibrator's baseplate70is coupled with the ground by applying the hold-down weight force to the baseplate70, the baseplate70and the coupled ground join together and become one system. Due to the low rigidity of the baseplate70and variant surface conditions, the vibrator-coupled ground model can be a complex system.

FIG. 4diagrammatically depicts a vibrator-coupled ground model100according to the present disclosure. In addition to the vibrator system30, the ground model100has three subsystems, which include a coupling system110, an inhomogeneous and elastic coupled ground system120, and a homogenous elastic deep ground130. These subsystems express the complicated transmission of the Vibroseis wavelet from the vibrator system (30) to the ground (130).

The vibrator-coupled ground model100expresses the rigidity of the baseplate70as part of non-ideal contact stiffness present at the boundary interaction of the baseplate70and the ground. This model100can serve as a more realistic representation of the vibrator-ground interaction and can describe a wide range of non-linear contact behavior (such as a partial contact and a full contact).

InFIG. 4, the ground system120is described as a linear second-order system that consists of a ground mass Mg, a ground stiffness Kg, and a ground viscosity Dg. The vibrator system30is also treated as a linear and rigid body. In this model100, the baseplate70is only considered to have a mass MBPand its stiffness is distributed to become a part of the contact stiffness. Therefore, the contact stiffness in this model100is located in between the vibrator baseplate70and the ground. The contact stiffness here is defined as a group of “springs” (kc1, kc2, etc.) connecting the vibrator baseplate70and the ground130, and the value depends on the number of “springs” (kc1, kc2, etc.) that physically connect the baseplate70and the ground during vibrator operation. Therefore, the contact stiffness is a variable stiffness.

As is known, partial decoupling often occurs as the vibrator30shakes at high frequencies due to the low rigidity of the vibrator baseplate70. Such decoupling becomes even worse on uneven ground. When the vibrator30is in a compressing mode, there are more contact areas between the vibrator baseplate70and the ground. More contact areas mean more “springs” and more stiffness in the model100.

As the vibrator30goes to a releasing mode, however, partial decoupling may happen. This means that the baseplate70loses some contact with the ground so that the contact stiffness is reduced. The contact stiffness is reduced halfway through the compression cycle until halfway through the release cycle, and its value decreases as the sweep frequency increases. When the vibrator30is located on uneven ground, the vibrator baseplate70is subject to many motions such as bending, flexing, and twisting so that the contact stiffness becomes more unpredictable, and harmonic distortion becomes more severe.

In the model100ofFIG. 4, the coupling system110attempts to describe the coupling conditions at the interface between the baseplate70and the coupled ground system120. The coupling system110can be modeled by a group of springs kc1, kc2, . . . , kcnand a damper Dc. In this system120, the springs kc1, kc2, . . . , kcnconnect the vibrator's baseplate70and the coupled ground system120and are used to represent the variant contact stiffness in between the baseplate70and the coupled ground system120during operation of the vibrator30. Notably, the baseplate's stiffness is separated as a number of small local stiffness coefficients distributed to join with these springs kc1, kc2, . . . , kcndepending on the contact area between the baseplate70and the coupled ground. The damper Dcrepresents the viscosity of the surface medium (e.g., thin layer of vegetation or grass on the ground).

For its part, the coupled ground system120inFIG. 4is described as an inhomogeneous and elastic system and can be represented by a mass-spring-damper model. This system120is inhomogeneous because the values of the captured ground mass Mg, the ground stiffness Kg, and the ground viscosity Dgvary from location to location. When loaded to the vibrator's baseplate70during vibration, this system120(and especially the captured ground mass Mg) joins with the baseplate70and becomes a part of the vibration source.

At each vibrator shaking spot, the vibrator's baseplate70feels this coupled ground system120, and the motion of this system120is embedded and detected in the baseplate acceleration data being recorded, as noted previously. The three parameters Mg, Kg, and Dgof this ground coupled system120can be estimated using vibrator field measurements as described in more detail later. Fortunately, this system120can be treated as an elastic linear system because the total effect of its nonlinearities may be small and may be ignored, especially when compared to the nonlinearities existing in the vibrator hydraulic system and the nonlinearities due to low rigidity of the baseplate70.

The deep ground body130inFIG. 4is described as a homogeneous and elastic system. In this deep ground body130, the traveled wavelet remains practically invariant. In particular, experimental testing can show that far-field wavelets remain invariant in deep ground and that the deep ground can be treated homogenously and elastically.

All of the systems30,110,120combined together make up the vibrator-coupled ground model100. Additional details of the ground model100can be found in Zhouhong Wei, “Modeling and modal analysis of seismic vibrator baseplate,”Geophysical Prospecting,58, 19-31 (2010), which is incorporated herein by reference in its entirety.

Given the vibrator-coupled ground model100ofFIG. 4, the block diagram ofFIG. 5shows particular details to be quantified in the vibrator-coupled ground model100for creating a vibrator-coupled ground filter150for use in the purposes disclosed herein. Essentially, the vibrator-coupled ground filter150ofFIG. 5contains the vibrator's baseplate system105, the coupling system110, and the inhomogeneous elastic coupled ground system120expressed in formulas. This vibrator-coupled ground filter150is minimum phase.

In the ground filter150, the vibrator's baseplate system105can be represented by the following transfer function:

In this baseplate system105, Mbpis the mass of the vibrator baseplate (70), Dcis the contact viscosity of the coupling system110, and Kcis the contact stiffness of the coupling system110, which consists of many small springs.

For its part, the coupling system110in the ground filter150can be represented by the following transfer function:

Finally, the coupled ground system120in the ground filter150can be represented by the following transfer function:

In the coupled ground system120, Mgis the mass of the captured ground mass, Dgis the contact viscosity, and Kgis the contact stiffness for the captured ground.

Thus, the vibrator-coupled ground filter150is based on the transfer functions of these systems G1(s), G2(s), and G3(s), as well as the variables for Mbp, Dc, Kc, Mg, Dg, Kg, etc.

Input102to the ground filter150includes either a pilot sweep (Tref) or a weighted-sum ground force (Ws-gf), which are supplied by the vibrator (30). The weighted-sum ground force (Ws-gf) is characterized by the equation:
Ws-gf=Mrm×Accrm+Mbp×Accbp

Therefore, the weighted-sum ground force (Ws-gf) is determined by the masses Mrmand Mbpof the reaction mass (50) and baseplate (70), which are known, and the acceleration data Accrmand Accbpof the reaction mass (50) and baseplate (70) recorded at the vibrator (30).

Output104of the ground filter150includes a filtered pilot signal (filtered Tref) or a filtered weighted-sum ground force (filtered Ws-gf). This output104is used by the ground filter system (94) ofFIG. 3to filter the seismic data (92) of the recorder (90) before processing by the data processing system (98) so that the seismic data is processed with the more accurate vibrator-captured ground model100of the present disclosure. In turn, for example, the filtered weighted-sum ground force (filtered Ws-gf) can give better cross-correlated results between the vibrator's seismic energy and the seismic sensor responses and can reduce noise.

As discussed earlier, the dynamic motions related to the coupling condition and the inhomogeneous and elastic coupled ground system120are recorded and embedded in the baseplate acceleration data Accbpsupplied by the vibrator (30) to the recorder (90). In addition, the motion of the vibrator's actuator (e.g., hydraulic system) is recorded and embedded in the reaction mass acceleration data Accrmsupplied by the vibrator (30) to the recorder (90). As noted above, the vibrator measurements Accbpand Accrmare often recorded during data acquisition as the weighted-sum ground force (Ws-gf) using the recorder (90). To obtain the required variables for the vibrator-coupled ground filter150, the dynamic motions of the coupling system110and the coupled ground system120are extracted from the baseplate and reaction mass acceleration data Accbpand Accrmas described below.

D. Derivation of Filter Values

FIG. 6Ashows an example frequency response for a vibrator. In this frequency response, the reaction mass acceleration AccRMis used as an input signal, and baseplate acceleration AccBPis used as output responding to the input signal based on the ground model's transfer functions described previously. Thus, the frequency response inFIG. 6Ais based on the following:

In other words, the frequency response of the vibrator is analyzed with the reaction mass acceleration data as input and with the baseplate acceleration as output. The inverse could also be done so that a frequency response can be analyzed with the baseplate acceleration data as input and with the reaction mass acceleration as output. Although the frequency responses would appear different, it is understood that the frequency response analysis can generally relate the reaction mass acceleration data and the baseplate acceleration data as input and output relative to one another.

The magnitude plot200A shows the magnitude ratio (dB) of AccBPto AccRMrelative to frequency, and the phase plot250A shows the phase (degrees) relative to frequency. As shown in the magnitude plot200A, the magnitude ratio increases at a sloped section202of about 40 dB/dec as frequency increases. The magnitude ratio then reaches a turning point204at a resonant frequency between the baseplate (70) and the ground. Beyond this turning point204, the magnitude ratio flattens out to a sloped section206of 0 dB/dec. The phase in the phase plot250A shifts from 0 degrees to −180 degrees. At the resonant frequency254, the phase is expected to be −90 degrees.

In the frequency response, the turning point204is defined by the values of Mg, Kg, and Dgin the coupled ground system (120;FIGS. 3-4). The subsequent plateau section206is defined by the values of kc1, kc2, Dc1, and Dc2of the coupling system (110;FIGS. 3-4). Knowing this theoretical nature of the frequency response having reaction mass acceleration AccRMas input and baseplate acceleration AccBPas output, an actual measured frequency response from measured data can be compared to the disclosed ground model100to derive values for Mg, Kg, Dg, kc1-2, Dc1-2for the vibrator-coupled ground filter150.

To that end,FIG. 6Bshows a measured frequency response using example vibrator measurement data214compared to model data212using the disclosed ground model100. In these frequency responses, reaction mass acceleration data Accrmis again used as an input signal, and baseplate acceleration data Accbpis used as output responding to the input signal.

For the measured frequency response curves214/254, the baseplate and reaction mass accelerations Accbpand Accrmhave been measured and recorded on a standard vibrator (30) using a recorder (90). The measured frequency response curves214/254inFIG. 6Bare then compared to model frequency response curves212/252generated by the model data using the disclosed ground model100.

The values for the variables (Mg, Kg, Dg) in the ground model filter150are then obtained by successively modeling the measured frequency response seen in the measured data214. In the magnitude plot200B, the magnitude ratio spectra of the measured and model data curves212/214are shown. In the phase plot250B, the corresponding phase spectra curves262/264are shown. The plots200B/250B show that the model data curves212/262track the measured curves214/264. Based on this, it can be seen that the main dynamic motions have been captured by the disclosed ground model100, although some discrepancies are visible in these plots.

In both magnitude-ratio and phase spectra plots200B/250B, first regions204/254show the main resonance produced by the baseplate (30) and the coupled ground system110, which corresponds to flexure of the baseplate (30). In both magnitude-ratio and phase spectra plots200B/250B, the second regions206/256illustrate the dynamic modes resulting from the coupling system110.

Based on this understanding of the frequency responses, values for the vibrator-coupled ground filter150can be derived.FIG. 7shows a process300for deriving the vibrator-coupled ground filter150of the present disclosure.

Initially, recorded data from a survey is obtained (Block302). As noted above, this data includes the seismic signals obtained with the sensors (22) in the array (12) as inFIG. 3. Likewise, this data includes the pilot signal (Tref) and the weighted-sum ground force (Ws-gf), which includes the reaction mass and baseplate accelerations Accbpand Accrm.

The acceleration data Accbpand Accrmfor the reaction mass (50) and baseplate (70) are input into the transfer functions of the systems (i.e., G1(s), G2(s), and G3(s)) in the ground force model100(Block304). (As noted previously, the dynamic motions related to the coupling conditions are recorded and embedded in the baseplate acceleration data AccBP. In addition, the motion of the vibrator's actuator system is recorded and embedded in the reaction mass acceleration data AccRM.)

Useful information for the variables of the ground model100is then obtained from knowledge of the frequency response (as inFIGS. 6A-6B) and the transfer functions G1(s), G2(s), and G3(s) for the system100. In particular, variables that describe the captured ground force system120are extracted from the transfer functions G1(s), G2(s), and G3(s) (Block306). These variables include Mg, Kg, and Dg. For a given vibrator, the values for these variables are generally known and would be expected to lie within some target range. Yet, given the dynamic nature of the vibrator's operation, the values vary dynamically. Using the transfer functions G1(s), G2(s), and G3(s) and numerical analysis, the appropriate values for the variables Mg, Kg, and Dgcan be derived. In particular, these variables Mg, Kg, and Dggovern the first turning point204/254in the frequency response ofFIG. 6B. Using polynomial fitting, the values for these variables Mg, Kg, and Dgcan then be derived from the first region of the frequency response.

Additionally, variables that describe the coupling system110are extracted from the transfer functions of the system (Block308). These variables include kc1-2and Dc1-2. For a given vibrator, the values for these variables kc1-2and Dc1-2are generally known and would be expected to lie within some target range. Yet, given the dynamic nature of the vibrator's operation, the values vary dynamically. Using the transfer functions G1(s), G2(s), and G3(s) and numerical analysis, the appropriate values for the variables kc1-2and Dc1-2can be derived. In particular, these variables kc1-2and Dc1-2govern the second region206/256in the frequency response ofFIG. 6Bpast the turning point204/254. Using polynomial fitting, the values for these variables kc1-2and Dc1-2can then be derived from the second region of the frequency response for the ground model100.

At this point, the derived values for the variables Mg, Kg, Dg, kc1-2, and Dc1-2as well as the mass of the baseplate MBPare input into transform functions to convert the transfer functions G1(s), G2(s), and G3(s) into the frequency domain. Using standard mathematical techniques, the ground model with extracted variables is then converted into the frequency domain (Block310) so the desired vibrator-coupled ground model filter150can be calculated (Block312).

E. Data Processing Using Filter

FIG. 8shows a process350for using the vibrator-coupled ground filter150of the present disclosure. As is typically, the array (12) and recorder (90) ofFIG. 3obtain recorded data from a survey as discussed previously (Block352). At some point, the seismic data (92) is to be handled by the data processing system (98). To improve the subsequent imaging produced by the data processing system (98), the system filters the original seismic data (92) with the ground filter system (94) using the vibrator-coupled ground filter150of the present disclosure (Block354).

The improved data (96) can then be provided to the data processing system (98). In turn, the data processing system (98) can use its correlation processor to cross-correlate survey data using the filtered pilot reference signal (filtered Tref) or filtered weighted sum ground force (filtered Ws-gf) (Block356). The system (98) can then output the cross-correlated results, which can then be used for imaging purposes (Block358).

F. Analyses and Results

As depicted inFIG. 5, when the input102(either the pilot sweep Trefor the weighted-sum ground force Ws-gf) is injected into the vibrator-coupled ground filter150, it is passed through transfer functions corresponding to the vibrator's baseplate system105, the coupling system110, and the elastic coupled ground system120. This means that the input102(the pilot sweep or the weighted-sum ground force) will be sequentially filtered by these systems (105,110,120). The output104from the vibrator-coupled ground filter150becomes the filtered pilot sweep (filtered Tref) or the filtered weighted-sum ground force (filtered Ws-gf), which is the expected input to the deep ground (130) by the vibrator30. In other words, the wavelet produced by the cross-correlation function between the input102(pilot sweep or the weighted-sum ground force) and the output104(the filtered pilot sweep or the filtered weighted-sum ground force) will be indicative of an accurate wavelet that travels through the deep ground130. It should be in phase with the downhole wavelets except for a time shift.

To test the results, the graph400inFIG. 9plots amplitude spectra402from six downhole geophones and the amplitude spectrum404from a filtered pilot sweep (filtered Tref). The downhole geophone spectra402have been recorded using a standard vibrator driven by a linear sweep from 2 Hz to 160 Hz in 20 seconds. This linear sweep (pilot sweep) has been recorded as well. The downhole geophone spectra402plotted inFIG. 9are selected in 200 ft (60.96 m) intervals from 200 ft (60.96 m) to 1000 ft (304.8 m).

The filtered pilot sweep spectrum404is obtained by passing the pilot sweep through the vibrator-coupled ground filter150. It is observed that the amplitude spectrum404of the filtered pilot sweep (filtered Tref) matches very well with the amplitude spectra402from six downhole geophones. This indicates that the filtered pilot sweep (filtered Tref) is in the downgoing wavelet. Furthermore, the vibrator-coupled ground filter150does appear to accurately describe the filtering effects caused by the vibrator (30), the coupling condition between the baseplate (70) and the coupled ground, and the coupled ground system (120).

The plot410inFIG. 10provides another example and shows a comparison of two wavelets412/414. One wavelet414is produced by the cross-correlation between an original pilot sweep and the 1000 ft (304.8 m) downhole geophone data. Compensation for time delay of this wavelet414is made to provide a better comparison. The other wavelet412is the result of the cross-correlation function between the pilot sweep (Tref) and the filtered pilot sweep (filtered Tref), which is labeled as the Vibrator-Coupled Ground Model data412inFIG. 10. The two wavelets412/414match very well. The similarity of two wavelets412/414further confirms that the vibrator-coupled ground model100of the present disclosure is a reasonable model and each sub-model110,120, etc. can be used to represent its own system.

Standard Vibroseis theory indicates that far-field particle velocity is proportional to a time differential of a true ground force. Again, this theory is built on an assumption that the ground can be treated as an isotropic homogeneous elastic body. As demonstrated above, the deep ground can be assumed to be a relatively homogeneous and elastic body130, at least in the P-wave direction. However, the coupled ground system120ofFIGS. 4-5is definitely not a homogeneous body. Therefore, standard Vibroseis theory should be modified slightly to allow for the more realistic situation. The far-field particle velocity is proportional to the input of the deep ground130, which is the output104of the pilot sweep (Tref) or the weighted-sum ground force (We-gf) after it has passed through the vibrator-coupled ground model filter150.

FIGS. 11A-11Bdepict comparisons of wavelets generated by using the derivative of the pilot sweep (Tref) as well as the filtered pilot sweep (filtered Tref). In plot420ofFIG. 11A, wavelets422/424were obtained using the standard vibrator modeling. In plot430ofFIG. 11B, wavelets432/434were obtained from the modified vibrator modeling of the present disclosure. Curves422/432are produced by cross-correlating the derivatives of the pilot sweeps (Tref) with the 1000-ft (304.8 m) downhole geophone traces. The curves424/434are results of the cross-correlation function between the filtered pilot sweeps (filtered Tref) and the 1000-ft (304.8 m) downhole geophone traces.FIGS. 11A-11Bclearly demonstrates that the zero-phase wavelets can be obtained when the filtered pilot sweep (filtered Tref) was cross-correlated to the downhole geophone data.

FIGS. 12A-12Bdepict another representative example to show that the Vibrator-Coupled Ground Model 100 can describe the filtering effects seen in a Vibroseis wavelet caused by the vibrator-coupled ground system. These plots440/450depict the wavelets obtained by using the derivative of the weighted-sum ground force (Ws-gf) as well as the filtered weighted-sum ground force (filtered Ws-gf). In the plot440ofFIG. 12A, the wavelets442/444are generated using the standard vibrator modeling. In the plot450ofFIG. 12B, the wavelets452/454are produced by using the modified vibrator modeling. Once again, the wavelets442/452are produced when the derivatives of the weighted-sum ground force (Ws-gf) was cross-correlated with the 1000-ft (304.8 m) downhole geophone traces. The other wavelets444/454are resulted from the cross-correlation of the filtered weighted-sum ground force (filtered Ws-gf) with the 1000-ft (304.8 m) downhole geophone traces.

FIGS. 12A-12Bshow that the zero-phase wavelets can be obtained when the filtered weighted-sum ground force (filtered Ws-gf) was used to cross-correlate to the downhole geophone data. It can be observed that the wavelets inFIGS. 12A-12Bdelay slightly comparing to the wavelets inFIGS. 11A-11B. This tiny time-delay is due to the phase error between the pilot sweep (Tref) and the weighted-sum ground force (Ws-gf).

To prove the validity of the vibrator-coupled ground model100shown inFIG. 4and determine the robustness of the vibrator-coupled ground filter150shown inFIG. 5, another experimental test was performed in a completely different area from the downhole geophone site.FIG. 13shows an amplitude spectrum460comparing data recorded in an experimental test using a standard vibrator modeling. The curve462is produced from a surface geophone that was placed 1-m apart from the vibrator baseplate (70). The curve462represents the velocity power spectrum of particles where the surface geophone is located. The spectrum460was computed after geophone response removal.

Because the baseplate accelerometer is mounted on the top cross of the baseplate stilt structure, the signal recorded by the baseplate accelerometer needs to physically pass through the baseplate (70), the coupling system (110), and the coupled ground system (120) in order to connect with any nodes in the coupled ground system (120). Additionally, because the surface geophone records the particle velocity, it makes more sense to convert the baseplate acceleration into the baseplate velocity. Therefore, the other curve464is calculated from the data output from the vibrator-coupled ground filter150where the input to the filter150is the baseplate velocity, which is obtained by integrating the baseplate acceleration.

As can be seen, the curve464in the amplitude spectrum460obtained by utilizing the baseplate acceleration matches closely with the amplitude spectrum produced by using the surface geophone trace.FIG. 13indicates that the vibrator-coupled ground model100can simulate the filtering effects caused by the baseplate (70) and its vicinity. Moreover, it demonstrates that the coupled ground is a part of the source.

Portions of the present disclosure may be implemented in terms of logic, software, or code typically encoded on a variety of media including, but not limited to, computer-readable media, machine-readable media, program storage media, or computer program product. Such media may be handled, read, sensed, and/or interpreted by a computing device having a processor. Those skilled in the art will appreciate that such media may take various forms such as cards, tapes, magnetic disks (e.g., floppy disk or hard drive) and optical disks (e.g., compact disk read only memory (“CD-ROM”) or digital versatile disc (“DVD”)). It should be understood that the given implementations are illustrative only and shall not limit the present disclosure.

For example,FIG. 14shows a geophysical information processing system500that can be used in accordance with the present disclosure. Geophysical information may be received by the geophysical information processing system500after being gathered by a geophysical information collector such as the collector or recorder90as described above and shown inFIG. 3. The information collector90can include one or more or any combination of the components shown inFIG. 14. In one example, the geophysical information processing system500may include one or more processing devices, such as a computer520with a storage device510. The computer500can be, but is not limited to, a laptop computer, a desktop computer, a mainframe, or the like. The computer520may be in communication with the storage device510via any known interface and an interface for entering information into the computer520may be any acceptable interface. For example, the interface may include the use of a network interface530.

The storage device510can be any useful storage device having a computer-readable media. Instructions for carrying out methods described herein may be stored on computer-readable media in the computer520or may be stored on an external storage device.

Imaging, as used herein includes any representation of a subsurface structure including, but not limited to, graphical representations, mathematical or numerical representation, strip charts or any other process output representative of the subsurface structure. Geophysical information as used herein means information relating to the location, shape, extent, depth, content, type, properties, and/or number of geologic bodies. Geophysical information includes, but is not necessarily limited to marine and land seismic information. Seismic information includes, but is not limited to, one or more or any combination of the following, analog signals, digital signals, recorded data, data structures, database information, parameters relating to surface geology, source type, source location, receiver location, receiver type, time of source activation, source duration, source frequency, energy amplitude, energy phase, energy frequency, wave acceleration, wave velocity and/or wave direction.

Seismic information may be gathered using sensors monitoring seismic activities using, for example, a system as described above and shown inFIG. 3. The seismic activities result from active energy sources, including vibrator devices. The sensors can include geophones, accelerometers, pressure sensors, single component sensors, and/or multi-component sensors.