Patent Publication Number: US-9429669-B2

Title: Seismic source and method for single sweep intermodulation mitigation

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application claims the benefit of priority under 35 U.S.C. §119(e) to U.S. Provisional Application 61/716,150 filed on Oct. 19, 2012, the entire contents of which is hereby incorporated by reference. 
    
    
     BACKGROUND 
     1. Technical Field 
     Embodiments of the subject matter disclosed herein generally relate to methods and systems for mitigating seismic noise artifacts due to intermodulation distortion (IMD) that may be present in the recorded seismic data. 
     2. Discussion of the Background 
     Land seismic data acquisition and processing may be used to generate a profile (image) of the geophysical structure under the ground (subsurface). While this profile does not provide an accurate location for oil and gas reservoirs, it suggests, to those trained in the field, the presence or absence of such reservoirs. Thus, providing a high-resolution image of the subsurface is important, for example, to those who need to determine whether the oil and gas reservoirs are located. 
     Geophysical prospectors generate seismic waves in order to probe the subsurface (e.g., for imaging the earth). These acoustic waves may be generated from an explosive, implosive, impulsive, or a vibratory source executing swept-frequency (chirp) or random sequence. A recording of the acoustic reflection and refraction wavefronts that travel from the source to a receiver are used to produce a seismic field record. Variations in the travel times of the reflection events in these field records indicate the position of reflection and/or refraction surfaces within the earth. 
     IMD noise (intermodulation distortion noise) results from the modulation of signals containing two or more different frequencies in a non-linear system. The non-linear system of particular concern is the earth coupling and the two or more different frequencies may be (i) the frequency emitted by the source and (ii) harmonics of the same frequency. The intermodulation between each frequency component will form additional signals at frequencies that are not just at harmonic frequencies (integer multiples) of either, but also at the sum and difference frequencies of the original frequencies. There are other nonlinear mechanisms in the vibrator itself that produce IMD distortion products, but since these effects are included in the measured ground force signal, they are incorporated into the source signature signal so that their distortion artifacts can be mitigated directly by performing a source signature deconvolution as a data processing step. 
     A swept-frequency or chirp type seismic source may use a long pilot signal such as 2 to 64 seconds to ensure sufficient energy is imparted to the earth. With a swept frequency type source, the energy is emitted in the form of a sweep of regularly increasing (upsweep) or decreasing (downsweep) frequency in the seismic frequency range. The vibrations of the source are controlled by a control system, which can control the frequency and phase of the seismic signals. These sources are low energy and, thus, this causes noise problems that may affect the recorded seismic data. For example, the source generated harmonic energy may be an additional source of energy manifesting as noise, distortion or interference with recorded data. Generally for chirps, the source emits only one frequency at a time and its harmonics, so nonlinear coupling effects in the earth will result in noise that is indistinguishable from harmonic noise. With vibrator rocking, usually front to back or side to side, sub-harmonic energy can also be produced and any IMD products between sub-harmonics, fundamental or harmonics are also indistinguishable from sub-harmonic noise and its multiples. One exception is due to amplitude tapers that are generally applied at the start and end of a chirp. The taper intervals are usually between 100 to 1000 ms in duration. During the amplitude taper at the beginning or end of a chirp, the reference contains more than one frequency due to the amplitude modulation of the chirp signal. Thus, there is some potential for IMD production during taper intervals since more than two frequencies, which are not harmonics or sub-harmonics of one another, are simultaneously generated and when the vibrator output signal enters the nonlinear coupling, IMD seismic waves are emitted in addition to fundamental, harmonic and sub-harmonic waves. 
     A bigger problem is in the case when pseudorandom sequences are employed. The temporal frequency content of random signals is rich in spectral diversity, i.e., many frequencies are generated simultaneously. Thus, the potential for IMD noise interference in seismic records is much greater when pseudorandom sequences are used. In correlated shot records, the IMD noise is most evident on near offset traces (these correspond to receivers close to a vibrator). The IMD noise that is seen in correlated shot gathers is primarily linked to strong arrival events like first break events and surface waves. 
     Therefore, there are instances when vibratory sources may generate harmonics, sub-harmonics and IMD noise which can cross-feed with signals from other sources, giving misleading results when the signals are processed to separate the signals from each source. In addition, the harmonics are a source of noise that can mask weak reflection signals from deeper layers. 
     Currently, for reducing the seismic survey time, multiple sources are deployed at close locations and are actuated simultaneously, thus, reducing the time necessary to complete the survey. However, using multiple sources at the same time only increase the IMD noise. Multiple sources may be used if some means for distinguishing between signals emanating from the different sources can be provided. There are various methods for reducing the harmonic noise and cross-feed but none is capable of addressing related noises, e.g., subharmonic and/or IMD noise. 
     Thus, there is a need to develop a method, a source and/or a seismic survey system that is capable of imparting energy to the earth in such a way that IMD noise may be mitigated. 
     SUMMARY 
     According to an exemplary embodiment, there is a method for calculating an intermodulation noise effect generated with one or more land seismic sources. The method includes receiving seismic data (g) generated by actuating the one or more land seismic source with a single sweep; selecting a number of detectors that detect a subset (ga-gf) of the seismic data (g); estimating earth responses (ha 1 -hf 1 ) based on (i) the subset seismic data (ga-gf) and (ii) a ground force (gf) of the one or more land seismic source; calculating plural intermodulation noises (noiseA 1 -noiseF 1 ) for the number of detectors (a-f) based on the earth responses (ha 1 -hf 1 ); and removing the plural intermodulation noises (noiseA 1 -noiseF 1 ) from corresponding detector signals (ga-gf) to mitigate the intermodulation noise effect. 
     According to another exemplary embodiment, there is a computing device for calculating an intermodulation noise effect generated with one or more land seismic sources. The device includes an interface for receiving seismic data (g) generated by actuating the one or more land seismic source with a single sweep; and a processor connected to the interface. The processor is configured to select a number of detectors that detect a subset (ga-gf) of the seismic data (g), estimate earth responses (ha 1 -hf 1 ) based on (i) the subset seismic data (ga-gf) and (ii) a ground force (gf) of the one or more land seismic source, calculate plural intermodulation noises (noiseA 1 -noiseF 1 ) for the number of detectors (a-f) based on the earth responses (ha 1 -hf 1 ), and remove the plural intermodulation noises (noiseA 1 -noiseF 1 ) from corresponding detector signals (ga-gf) to mitigate the intermodulation noise effect. 
     According to another exemplary embodiment, there is a non-transitory computer readable medium including computer executable instructions, wherein the instructions, when executed by a computer, implement the method discussed above. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present invention, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  illustrates a field seismic survey; 
         FIG. 2  illustrates an IMD noise model; 
         FIG. 3  is a flowchart of a method for calculating IMD noise; 
         FIG. 4  is a graph illustrating true earth responses; 
         FIG. 5  is a graph illustrating estimating earth responses according to an embodiment; 
         FIG. 6  is a graph illustrating windowing functions to be applied to data according to an embodiment; 
         FIG. 7  is a graph illustrating windowed first break wave and ground roll wave according to an embodiment; 
         FIG. 8  illustrates a comparison between estimated and actual IMD noise; 
         FIG. 9  illustrates IMD noise removal after a first pass according to an embodiment; 
         FIG. 10  illustrates IMD noise removal after a second pass according to an embodiment; 
         FIG. 11  is a flowchart of a method for mitigating IMD noise according to an embodiment; and 
         FIG. 12  is a schematic diagram of a computing device configured to run a method for mitigating IMD noise. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The following description of the exemplary embodiments refers to the accompanying drawings. The same reference numbers in different drawings identify the same or similar elements. The following detailed description does not limit the invention. Instead, the scope of the invention is defined by the appended claims. The following embodiments are discussed, for simplicity, with regard to the terminology and structure of a land seismic system having a single source. However, the embodiments to be discussed next are not limited to a system with a single source but they may be applied to systems having multiple sources. 
     Reference throughout the specification to “one embodiment” or “an embodiment” means that a particular feature, structure or characteristic described in connection with an embodiment is included in at least one embodiment of the subject matter disclosed. Thus, the appearance of the phrases “in one embodiment” or “in an embodiment” in various places throughout the specification is not necessarily referring to the same embodiment. Further, the particular features, structures or characteristics may be combined in any suitable manner in one or more embodiments. 
     A method for operating a vibratory source with two different pilot signals that are used alternately to drive the source is described in U.S. Provisional Patent Application Ser. No. 61/716,110 (herein &#39;110), filed on Oct. 19, 2012, the entire content of which is incorporated herein by reference. This application describes that the second pilot signal may be a time-reversed version of the first pilot signal. In this way, the IMD noise that occurs in negative time for one sweep can be used to predict IMD noise in the positive time for the other sweep and vice versa. The pilot signals may be a traditional sweep signal, e.g., a sine function, or a pseudo-random sweep, as discussed, for example, in U.S. Pat. No. 7,859,945 (herein &#39;945), the entire content of which is incorporated herein by reference. 
     Before discussing in more detail a novel method for IMD noise mitigation, a land seismic system  100  that generates and also collects seismic data is discussed with reference to  FIG. 1 . Consider the configuration of a system  100  for land generating and collecting seismic data. The exemplary survey system  100  includes four vibrators  110 ,  111 ,  112 , and  113  placed at the surface of the earth  101 . Vibrators  110 ,  111 ,  112 , and  113  may be conventional truck-mounted vertical P-wave vibrators; however, it is understood that other vibrators, such as horizontal shear-wave vibrators, may be utilized or even a mixture of both P-wave and shear wave vibrators. The deployment of the vibrators may vary widely depending upon the survey requirements. For example, for a 3-D survey the vibrators may be spaced far apart and not collinear with one another. 
     Each vibrator may be equipped with a sweep generator module and control system electronics. For example,  FIG. 1  shows vibrator  113  having the sweep generator module  113   a  and the control system electronics  113   b . After receiving a start command, for example, initiated via a telemetry link with the recording system or by the operator of the vibrator, each vibrator begins sweeping. As discussed above, the vibrators are not coordinated to sweep simultaneously, which is different from many existing methods. However, in one application, the vibrators are coordinated to sweep simultaneously. Each vibrator sweep generator may be loaded with a unique pilot signal. In one application, the vibrator sweep generator receives its corresponding pilot signal from a central controller  129 . Thus, the pilot signal may be generated locally or centrally. 
     Sensors (not shown) attached to vibrators  110 ,  111 ,  112 , and  113  are connected to a vibrator separation system  126 . The sensors can be motion sensors, such as accelerometers mounted to the reaction mass, the base plate of the vibrator, or the earth immediately adjacent to the vibrator, a transducer or combination of transducers configured to measure the differential pressure in the actuation chamber of the vibrator, a load cell attached to the bottom of the base plate for measurement of the ground force (contact force), or a weighted sum of the base plate and the reaction mass accelerometers useful for estimating the ground force. Additionally, the sensor could comprise strain gauges mounted on the driven structure of the vibrator to provide an estimate of the ground force. Thus, these sensors provide the ground force signals to the vibrator separation system  126 . 
     Alternatively, (i) the pilot or reference signal generated by the vibrator controller that the vibrator output follows or (ii) a Kalman filter estimate of the ground force provided by the vibrator controller (e.g., available from Sercel, Inc., Houston, Tex.) can be utilized for the sensor movement or (iii) another signal that is representative of the signal imparted into the earth, for example the base plate accelerometer signal. The sensor measurement, or some filtered version of the sensor measurement, is the measured signal and represents the actual source vibration imparted to the earth by the vibrator. In this respect, it is noted that while the vibrator follows a pilot signal, the output of the vibrator (the sweep) may be different from the pilot signal. The measured signals may be transmitted to a recording system  128  by hardwired link, a radio telemetry link, or by a separate acquisition system that records and stores the measured signals so that the measured signals can be integrated with the acquired seismic data set at a later time. The recording system  128  may be implemented in the same hardware as the central controller  129 . 
     Receiver sensors, geophones for example,  120 ,  121 ,  122 ,  123 , and  124  are positioned at the surface of the earth  101  in the survey region at locations displaced from the vibrator position. The receiver sensors may be conventional moving coil type geophones, Micro Electro-Mechanical System (MEMS) sensor elements, or hydrophones for transition zone areas like marshes. In some areas, a receiver sensor may include a group of receiver sensors arranged as a receiver array to help attenuate ground roll or other noise modes. Receiver sensors are not limited to vertical component type sensors; horizontal geophones and  3 -C geophones/accelerometers may also be used depending upon the nature of the survey to be conducted. For simplicity, receivers  120 ,  121 ,  122 ,  123 , and  124  will be considered single component vertical geophones configured to function as point receivers in this embodiment. 
     As shown in  FIG. 1 , vibratory energy radiated by each vibrator  110 ,  111 ,  112 , and  113  travels through the earth from each vibrator to the receiver sensors  120 ,  121 ,  122 ,  123 , and  124  in the survey area. The vibratory signal received by each receiver sensor will actually be a composite signal comprised of contributions from each vibratory source. Transfer functions  130 ,  131 ,  132 , and  133  represent the transmission path response from vibrator  110 ,  111 ,  112 , and  113  to receiver sensor  120  respectively. The transfer function will depend upon the vibratory signal radiated by each vibrator, the refraction and reflection by the subterranean formations of the vibratory source energy, and the response of the receiver sensor. Subsequent processing steps can be used to remove the embedded response due to the choice of source measured signal and receiver response. 
     The method for mitigating the IMD noise is now discussed. It is noted that this method may use a single sweep instead of two as discussed above with reference to &#39; 110 . Note that IMD noise is mainly associated with random sweeps. The method discussed next can also be applied to non-random sweeps, for example, traditional sine sweeps, by replacing the IMD noise term with a harmonic distortion noise term. Thus, the exemplary embodiments discussed next exemplify the IMD noise but the same embodiments can be applied to other distortion models. Considering in one embodiment that the IMD noise refers to an additive noise that corresponds to a difference between a measured ground force gf(t) and a real source s(t) representing the actual propagated signal, an equation describing a relation between the measured seismic data g(t) and the real source s(t) is as follows, where “ ” represents the convolution operator in the time domain:
 
 g ( t )= s ( t )   h ( t )= gf ( t )   h ( t )+ imd ( t )   h ( t )  (1).
 
     The ground force gf(t) is measured, for example, with a sensor located at the vibrator, the IMD noise is generated at the vibrator baseplate/earth interface or in close proximity to it primarily due to nonlinearities in the medium (for example soil) beneath the baseplate, and the real source s(t) is the real seismic signal radiated into the earth by the vibrator in response to the applied force. h(t) is the real transfer function (response) of the earth (it cannot be measured exactly because noise is always present), and g(t) is the seismic data recorded with the seismic detectors shown in  FIG. 1 . Although  FIG. 1  shows plural sources, the method now discussed is applied to a single seismic source for simplicity. However, the method may also be applied to plural sources. It is noted that for an ideal case, the ground force gf(t) may be considered to be identical to the pilot signal applied to the source. For this reason, this document refers interchangeably to the (measured) force and the pilot signal as gf(t). Further, it is assumed that a change in the IMD noise from receiver to receiver undergoes the same spectral absorption effect as the first break or inline ground roll signals. 
     An IMD noise model is illustrated in  FIG. 2 . The model  200  takes into account the ground force gf generated by the vibrator  202 , and the IMD noise generated by soil/coupling nonlinearities  204 . The addition of these two quantities at block  206  produces the actual radiated signal s. The transfer functions ha to hf represent each wave path from the vibrator to a corresponding receiver  220   a  to  220   f . For completeness,  FIG. 2  also shows summing blocks  210   a  to  210   f  with some additive noise signals Va to Vf that are labeled respectively  215   a  to  215   f . The signals  215   a  to  215   f  represent noise present near the receiver due to the local environment, noise that is not coherent with the source signal s(t), for example, wind noise, thermal noise or even traffic noise. The detector signals ga(t) to gf(t) are found to be a combination of source produced energy and environmental noise. If the additive environmental noise is ignored, the following equations are generated by model  200 :
 
 Ga ( f )= S ( f ) Ha ( f )={ GF ( f )+ IMD ( f )} Ha ( f ),  (2a)
 
 Gb ( f )= S ( f ) Hb ( f )={ GF ( f )+ IMD ( f )} Hb ( f ),  (2b)
 
 Gf ( f )= S ( f ) Hf ( f )={ GF ( f )+ IMD ( f )} Hf ( f ),  (2f)
 
where equation (1) is written in the time domain and equations (2a-2f) are written in the frequency domain. For the frequency domain, it is noted that a Fourier transform (F{ }) for a real sequences x(t) is given by:
 
 F{x ( t )}= X ( f ),
 
where X is the Fourier transform of x.
 
     Assuming that a volume of data has been acquired that includes measurements of the ground force signal and receiver signals, a novel method for mitigating IMD source generated noise artifacts in a seismic shot record is illustrated in  FIG. 3 .  FIG. 3  includes a step  300  of selecting a model as discussed above. Then, in step  302 , the measured ground force and receiver signals are converted to their frequency domain representations through means of FFT calculations. An initial frequency domain estimate of Ha(f) to Hf(f) that appear in equation (2a-2f) above is calculated in step  304 . These initial earth response estimates or earth transfer function estimates are called Ha 1 ( f ) to Hf 1 ( f ). Note that identifier “1” indicates a first pass. Later on, additional passes are introduced and they are identified by other identifiers, e.g., “2”. Thus, the estimated earth transfer function from the source to the first receiver in the frequency domain is given by:
 
 Ha 1( f )= Ga ( f )/ GF ( f )={1 +IMD ( f )/ GF ( f )} Ha ( f )= Ha ( f )+ Ha ( f ){ IMD ( f )/ GF ( f )}  (3)
 
Ha 1 ( f ) is shown in equation (3) to include two parts, a first part which is the actual earth response Ha(f) and a second part which is a noise artifact created by the IMD source noise that was not included in the ground force measurement, e.g., Ha(f){IMD(f)/GF(f)}. It is this extra source noise energy that was improperly mapped in the initial earth impulse response calculation that is desired to be estimated to form a new source signal estimate, so that both the ground force signal and the extra IMD source generated noise are all mapped properly and thereby remove the IMD source noise artifacts that are present in, for example, ha 1 ( t ), which is the initial time domain estimate of the earth impulse response ha(t).
 
     Considering that A(f) is defined as:
 
 A ( f )= IMD ( f )/ GF ( f )  (4),
 
equation (3) becomes
 
 Ha 1( f )= Ha ( f )(1 +A ( f ))  (5a),
 
which is common for all receiver offsets, i.e.,
 
 Hb 1( f )= Hb ( f )(1 +A ( f ))  (5b)
 
. . .
 
 Hf 1( f )= Hf ( f )(1 +A ( f ))  (5f).
 
     Because response functions ha to hf are different with shifting arrival events, it is possible to combine receiver estimates to determine A(f) and then remove it. One way to determine A(f) is now discussed. 
     For simplicity, assume that it is desired to remove the IMD noise artifacts from seismic data associated with six detectors (e.g., geophones) closest to the vibrator and these detectors record signals ga to gf. In one application, more or less detectors may be used. Thus, it is possible to compute in step  304  the earth responses Ha 1  to Hf 1  in the frequency domain by performing a source signature deconvolution using the ground force GF as the source signature in the frequency domain as follows:
 
 Ha 1( f )= Ga ( f ) GF ( f )^/{ GF ( f ) GF ( f )^+ e 1}  (6a)
 
 Hb 1( f )= Gb ( f ) GF ( f )^/{ GF ( f ) GF ( f )^+ e 1}  (6b)
 
. . .
 
 Hf 1( f )= Gf ( f ) GF ( f )^/{ GF ( f ) GF ( f )^+ e 1},  (6f)
 
where symbol “^” denotes the complex conjugate and e 1  is a small quantity used to stabilize spectral division to handle the case where GF(f) may have spectral zeroes.
 
     In step  306 , the calculated transfer functions Ha 1  to Hf 1  are transformed from the frequency domain to the time domain by applying an inverse Fourier transform (IFFT). Thus, the transfer functions ha 1  to hf 1  are obtained. The true earth responses ha to hf are illustrated in  FIG. 4 , which also shows the first break transfer function FB and the in line ground roll transfer function GR, that represent the earth impulse response for each of those wave modes. 
     The signature deconvolution results (obtained using only the ground force), i.e., the estimated earth responses ha 1  to hf 1  are illustrated in  FIG. 5 . Note the rich IMD noise content in  FIG. 5 . To estimate the IMD noise contribution, the strong arrival events are selected since the strongest IMD artifacts will tend to accompany these events, e.g., the direct p-wave arrival (first break) and the ground roll; and, in the first pass of IMD removal is it intended to extract the IMD noise associated with these events. In step  308 , the first break and the ground roll are windowed using window functions wa to wf as illustrated in  FIG. 6 . The windowed FB and GR transfer functions (wha to whf) are illustrated in  FIG. 7 . 
     Returning to  FIG. 3 , in step  310 , the FFT of wha to whf is calculated to obtain their frequency domain representations WHa 1  to WHf 1 . Transfer functions NA 1  to NF 1  that relate the initial earth response estimates to the windowed earth response estimates are computed at each receiver as discussed next. For each receiver, these transfer functions are calculated in step  312 , in the frequency domain, as follows:
 
 NA 1( f )= Ha 1( f ) WHa 1( f )^/{ WHa 1( f ) WHa 1( f )^+ e 2}  (7a)
 
 NB 1( f )= Hb 1( f ) WHb 1( f )^/{ WHb 1( f ) WHb 1( f )^+ e 2}  (7b)
 
. . .
 
 NF 1( f )= Hf 1( f ) WHf 1( f )^/{ WHf 1( f ) WHf 1( f )^+ e 2},  (7f)
 
where e 2  is another small parameter used to stabilize the spectral division process, NA 1  is the IMD noise transfer function estimate for receiver  220   a  in the frequency domain, and Wha 1 ( f ) is the frequency domain representation of the windowed transfer function wha for receiver  220   a.  
 
     The IMD noise transfer function estimates NA 1  to NF 1  in the frequency domain are each actual estimates of the quantity (1+A(f)) that is common to equations (5a-5f). NA 1  to NF 1  are then transformed in step  314  into their time domain representations to obtain na 1  to nf 1  through application of an IFFT. The time domain representations of NA 1  to NF 1  will each have a spike at or in close proximity to zero lag; this spike represents the portion of the signal in hfa 1  that is highly correlated with wha. In other words, for example, because FB and GB events are present in both the unwindowed transfer function ha 1 ( f ) and also in the windowed version wha 1  in the same positions, this will produce a spike at zero lag. Because the portion of the signal that is creating the IMD noise artifact is desired to be determined and not the contribution due to the measured signal GF, in step  314 , the near zero lag terms are removed from the IMD source noise estimates na 1  to nf 1  to obtain a 1  to f 1 . In step  316 , terms a 1  to f 1  are transformed in the frequency domain by applying a Fourier transform FFT to get A 1  to F 1 . The frequency domain transfer functions A 1  to F 1  and their corresponding time domain representations a 1  to f 1 , each represent an estimate of the relationship between the unmeasured IMD source generated noise and the measured ground force signal. In other words, A 1  to F 1  each provide an estimate of the transfer function “A(f)” that appears in equations (5a-5f) above. 
     In step  316 , an IMD source noise is calculated for each receiver using the following process. First the newly obtained terms A 1  to F 1  are convolved in step  316  with the GF to obtain an IMD source noise estimate for each receiver as follows:
 
Noise A 1( f )= A 1( f ) GF ( f ),  (8a)
 
Noise B 1( f )= B 1( f ) GF ( f ),  (8b)
 
. . .
 
Noise F 1( f )= F 1( f ) GF ( f ),  (8f)
 
and then an inverse Fourier transform is applied to NoiseA 1 ( f ) to NoiseF 1 ( f ) in step  316  to obtain IMD noise estimates noiseA 1  to noiseF 1  in the time domain. Finally, in step  316 , any noise that falls outside the source sweep length is removed, because it is assumed that no IMD source noise energy should be produced when the source is inactive.
 
     In the noise model depicted in  FIG. 2  it was assumed the same IMD source noise (i.e., a single IMD noise source) propagates to each receiver filtered only by corresponding earth transmission paths. In other words, noiseA 1  to noiseF 1  are each estimates of the term labeled IMD in  FIG. 2  and in theory, these terms are very close to the same estimate, but in practice they may not be identical either due to artifacts introduced by processing steps like windowing, truncation effects or due to environmental noise. For this reason, the calculated noises noiseA 1  to noiseF 1  may be combined as shown in step  318  to form the signal nAve 1 . For simplicity, it is assumed nAve 1  to be the mean of the noise estimates; that is, nAve 1 =(noiseA 1 + . . . +noiseF 1 )/6; however, the combination of the noise estimates is not limited to a simple mean calculation, for example, a weighted average might be used instead if, for example, one receiver had more environmental noise than another or calculation of a trimmed mean could be another option. Referring to  FIG. 8 , the combined or average noise estimate nAve 1  is illustrated as curve  800  while the true noise is illustrated as curve  802 . By averaging the individual estimates of the IMD source noise together, an estimate of the actual IMD source noise is improved because the averaging process rejects some of the noncoherent noise that might be present in the record due to environmental noise, like Va . . . Vf ( 215   a - 215   f ) shown in  FIG. 2 . 
     To implement the noise mitigation process, a second signature deconvolution of the data is performed in step  320  in the frequency domain. However, during this second signature deconvolution, it is desired to add to the ground force all or a portion of the IMD noise average estimate (nAve 1 ) calculated in the previous steps. Thus, a term k, larger than zero and smaller than or equal to one is added to estimate the amount of correction to be applied. By default, the value of k is one. After frequency transforming nAve 1  to form NAve 1  through application of an FFT transform, a new estimate S 1  of the source signal, which is the original ground force signal augmented by the averaged IMD source noise estimate Nave 1 , can be written as shown in equation (9):
 
 S 1( f )= GF 1( f )+ kN AVe1( f )  (9)
 
     The equations for the revised earth responses (or transfer functions) in the frequency domain become:
 
 Ha 2( f )= Ga ( f )[ S 1( f )^]/{ S 1( f )[ S 1( f )^]+ e 3}  (10a)
 
 Hb 2( f )= Gb ( f )[ S 1( f )^]/{ S 1( f )[ S 1( f )^]+ e 3}  (10b)
 
. . .
 
 Hf 2( f )= Gf ( f )[ S 1( f )^]/{ S 1( f )[ S 1( f )^]+ e 3}.  (10c)
 
     After calculating the transfer functions Ha 2  to Hf 2  in the frequency domain, an inverse Fourier transform IFFT may be applied to calculate the earth responses ha 2  to hf 2 . Thus, ha 2  to hf 2  represent the new estimate of the earth impulse response between the unmeasured source signal “s(t)” and the various received signals “ga(t) to gf(t)”.  FIG. 9  illustrates the IMD noise mitigation after this first pass of IMD noise mitigation. 
     A second pass of IMD noise estimation and IMD noise removal can be performed. The process is much the same as has been explained above. For a second pass, the new estimate of the signal that went into the ground S 1  is used in place of the ground force GF. Thus, signal S 1  replaces the ground force signal GF in the algorithm; and, a new estimate is made of the residual IMD noise not included in the previous estimate. During a second pass, it is possible to use a window extending from the beginning of the first break arrival FB to the end of the listen time; thereby the window covers all arrivals of interest, rather than just the first break and ground roll transfer functions.  FIG. 10  illustrates the IMD noise mitigation after a second pass of IMD noise removal. If needed successive passes of IMD noise removal can be applied following the same sequence as has already been explained. 
     For simplicity, in the above embodiments, it was assumed that there is one IMD non-linear mechanism. However, if two or more such mechanisms are considered, for example, the ground roll IMD is different than the first break ground roll, the model may be partitioned to accommodate these mechanisms. Also, the above model has been discussed with regard to a single vibrator and a single sweep. However, the method may be extended to multiple vibrators. 
     According to an embodiment, a method for calculating an intermodulation noise effect generated with one or more land seismic sources is discussed with regard to  FIG. 11 . The method includes a step  1100  of receiving seismic data (g) generated by actuating the one or more land seismic source with a single sweep; a step  1102  of selecting a number of detectors (a-f) that detect a subset (ga-gf) of the seismic data (g); a step  1104  of estimating earth responses (ha 1 -hf 1 ) based on (i) the subset seismic data (ga-gf) and (ii) a ground force (gf) of the one or more land seismic source; a step  1106  of calculating plural intermodulation noises (noiseA 1 -noiseF 1 ) for the number of detectors (a-f) based on the earth responses (ha 1 -hf 1 ); and a step  1108  of removing the plural intermodulation noises (noiseA 1 -noiseF 1 ) from corresponding detector signals (ga-gf) to mitigate the intermodulation noise effect. 
     One or more of the steps of the above methods may be implemented in a computing system specifically configured to calculate the IMD noise. An example of a representative computing system capable of carrying out operations in accordance with the exemplary embodiments is illustrated in  FIG. 12 . Hardware, firmware, software or a combination thereof may be used to perform the various steps and operations described herein. The computing system may be one of elements  126 ,  128  and  129  or may be implemented in one or more of these elements. 
     The exemplary computing system  1200  suitable for performing the activities described in the exemplary embodiments may include server  1201 . Such a server  1201  may include a central processor (CPU)  1202  coupled to a random access memory (RAM)  1204  and to a read-only memory (ROM)  1206 . The ROM  1206  may also be other types of storage media to store programs, such as programmable ROM (PROM), erasable PROM (EPROM), etc. The processor  1202  may communicate with other internal and external components through input/output (I/O) circuitry  1208  and bussing  1210 , to provide control signals and the like. The processor  1202  carries out a variety of functions as is known in the art, as dictated by software and/or firmware instructions. 
     The server  1201  may also include one or more data storage devices, including a hard drive  1212 , CD-ROM drives  1214 , and other hardware capable of reading and/or storing information such as DVD, etc. In one embodiment, software for carrying out the above discussed steps may be stored and distributed on a CD-ROM  1216 , removable memory device  1218  or other form of media capable of portably storing information. These storage media may be inserted into, and read by, devices such as the CD-ROM drive  1214 , the disk drive  1212 , etc. The server  1201  may be coupled to a display  1220 , which may be any type of known display or presentation screen, such as LCD displays, LED displays, plasma display, cathode ray tubes (CRT), etc. A user input interface  1222  is provided, including one or more user interface mechanisms such as a mouse, keyboard, microphone, touch pad, touch screen, voice-recognition system, etc. 
     The server  1201  may be coupled to other computing devices, such as the landline and/or wireless terminals via a network. The server may be part of a larger network configuration as in a global area network (GAN) such as the Internet  1228 , which allows ultimate connection to the various landline and/or mobile client devices. The computing device may be implemented on a vehicle that performs a land seismic survey. 
     The disclosed exemplary embodiments provide a system and a method for actuating sources asynchronously. It should be understood that this description is not intended to limit the invention. On the contrary, the exemplary embodiments are intended to cover alternatives, modifications and equivalents, which are included in the spirit and scope of the invention as defined by the appended claims. Further, in the detailed description of the exemplary embodiments, numerous specific details are set forth in order to provide a comprehensive understanding of the claimed invention. However, one skilled in the art would understand that various embodiments may be practiced without such specific details. 
     Although the features and elements of the present exemplary embodiments are described in the embodiments in particular combinations, each feature or element can be used alone without the other features and elements of the embodiments or in various combinations with or without other features and elements disclosed herein. 
     This written description uses examples of the subject matter disclosed to enable any person skilled in the art to practice the same, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the subject matter is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims.