CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority and benefit from U.S. Provisional Patent Application No. 62/182,651 , filed June 22, 2015, for "Gun Position and Near field hydrophone composite calibration using single air-gun firing," the entire content of which is incorporated in its entirety herein by reference.

BACKGROUND TECHNICAL FIELD

[0002] Embodiments of the subject matter disclosed herein generally relate to methods and devices for calibrating an air gun position and/or near-field hydrophone associated with the air gun. DISCUSSION OF THE BACKGROUND

[0003] Reflection seismology is a method of geophysical exploration to determine the properties of a portion of a subsurface layer in the earth, which is information especially helpful in the oil and gas industry. Marine reflection seismology is based on the use of a controlled source (e.g., air gun, vibratory element, etc.) that sends energy waves into the earth. By measuring the time it takes for the reflections to come back to plural receivers, it is possible to estimate the depth and/or

composition of the features causing such reflections and thus, to generate an image of the subsurface. These features may be associated with subterranean hydrocarbon deposits and the generated image may indicate, to those skilled in the art, the location of these deposits. Thus, improving the functionality of any component (source or receiver or computer that generates the image) of the seismic acquisition system results in a better image of the subsurface, and consequently, a higher likelihood of finding the deposits.

[0004] For marine applications, commonly used seismic sources are essentially impulsive (e.g., air guns that hold compressed air that is suddenly allowed to expand). An air gun produces a high amount of acoustic energy over a short time. Such a source is towed by a vessel at a certain depth along direction X. The acoustic waves from the air gun propagate in all directions. The air gun instantaneously releases large peak acoustic pressures and energy. Such a source array is illustrated in Figure 1. Note that the source array includes plural source elements. A source element is, for example, the above noted air gun. The source elements are grouped, typically, in sub- arrays. A typical source array includes three sub-arrays. Each sub-array may include a float and plural air guns suspended from the float.

[0005] Figure 1 shows a generic source array 104 (note that the full

configuration of the source array is not shown for simplicity) being towed behind a vessel 101. When the source array is activated, acoustic energy is coupled into the water and transmitted into the earth, where part of the energy is partially reflected back from the ocean bottom 1 13 and from rock formation interfaces 1 12 (rock layer that has a change in acoustic impedance). Sensors or receivers 106 used to record the reflected energy include hydrophones, geophones and/or accelerometers. The receivers can be encapsulated in either fluid filled or solid streamers 105 that are also towed by vessels at shallow depth.

[0006] Returning to the air guns, an air gun stores compressed air and releases it suddenly underwater when fired. The released air forms a bubble (which may be considered spherical), with air pressure inside the bubble initially greatly exceeding the hydrostatic pressure in the surrounding water. The bubble expands, displacing the water and causing a pressure disturbance that travels through the water. As the bubble expands, the pressure decreases, eventually becoming lower than the hydrostatic pressure. When the pressure becomes lower than the hydrostatic pressure, the bubble begins to contract until the pressure inside again becomes larger than the hydrostatic pressure. The process of expansion and contraction may continue through many cycles, thereby generating a pressure (i.e., seismic) wave. The pressure variation generated in the water by a single air gun (which can be measured using a hydrophone or geophone located near the air gun) as a function of time is called the near-field signature and is illustrated in Figure 2.

[0007] A first pressure increase due to the released air is called primary pulse. The primary pulse is followed by a pressure drop known as a ghost. Between highest primary pressure and lowest ghost pressure there is a peak pressure variation (P-P). The pulses following the primary and the ghost are known as a bubble pulse train. The pressure difference between the second pair of high and low pressures is a bubble pressure variation P _b -P _b - The time T between pulses is the bubble period.

[0008] Single air guns are not practical because they do not produce enough energy to penetrate at desired depths under the seafloor, and plural weak oscillations (i.e., the bubble pulse train) following the primary (first) pulse complicates seismic data processing. These problems are overcome by using arrays of air guns (i.e., the source array), which generate a larger amplitude primary pulse and canceling secondary individual pulses by destructive interference.

[0009] Figure 2 represents a situation in which the bubble generated by a single air gun drifts slowly toward the surface, surrounded by water having the hydrostatic pressure constant or slowly varying as the bubble slowly drifts upward. However, when another air gun is fired simultaneously in proximity to the first air gun, the hydrostatic pressure is no longer constant or slowly varying. The bubbles of neighboring guns affect each other.

[0010] A source array includes plural individual source elements (e.g., air guns). An individual source element may be a single air gun or a cluster of air guns. Since the dimensions of the source array, including plural individual source elements, are comparable with the generated wave's wavelength, the overall wave generated by the source array is directional, i.e., the shape of the wave, or its signature varies with the direction until, at a great enough distance, the wave starts having a stable shape. After the shape become stable, the amplitude of the wave decreases inversely proportional to the distance. The region where the signature shape no longer changes significantly with distance is known as the "far-field," (or where the wavelength of the wave is much smaller than a distance d from the gun to the observation point) in contrast to the "near-field" region (where the wavelength is larger than distance d) where the shape varies. Knowledge of the wave source's far-field signature is desirable in order to extract information about the geological structure generating the detected wave upon receiving the far-field input wave.

[0011] In order to estimate the source array's far-field signature, an equivalent notional signature for each individual source may be calculated for each of the guns using near-field measurements (see e.g., U.S. Patent No. 4,476,553 incorporated herewith by reference). The equivalent notional signature is a representation of an amplitude due to an individual wave source as a function of time, the source array's far-field signature being a superposition of the notional signatures corresponding to each of the individual sources. In other words, the equivalent notional signature is a tool for representing the contribution of an individual source to the far-field signature, such that the individual source contribution is decoupled from contributions of other individual wave sources in the source array.

[0012] However, the stability and reliability of the far-field signature depends on the stability of each of the individual source elements and of the source array's geometry. During a seismic survey, the individual source elements' behavior may change (e.g., they change their positions due to water currents or other reasons) and thus affect both the near-field and the far-field source signature.

[0013] U.S. Patent Publication 2013/0325427 (Hegna) discloses a method for computing notional source signatures from near-field measurements and modeled notional signatures. However, this method is affected by the environmental changes that are present in the field and also by the constant movement of the air guns relative to their expected position when deployed under water.

[0014] It would be desirable to have methods and apparatuses capable of calibrating the air guns' positions and/or the near-field hydrophones' responses that avoid the above mentioned limitations.

SUMMARY

[0015] According to an embodiment, there is a method for calibrating marine equipment. The method includes firing, during a calibration phase, a source element, wherein the source element is part of a source sub-array and a geometry of the sub- array during the calibration phase is substantially the same as a geometry during a seismic data acquiring phase; recording with plural near-field sensors direct waves incoming from the source element; selecting a cost function C; calculating distances L, between an actual firing position of the fired source element and the plural near-field sensors, based on the recorded direct waves; and calculating the actual firing position of the fired source element based on the distances L, and the cost function C. [0016] According to another embodiment, there is a method for calibrating marine equipment. The method includes firing, during a calibration phase, a source element G _j ; recording with plural near-field sensors (NFH _a -NFH _c ), during the calibration phase, direct waves incoming from the fired source element G _j ; calculating distances L _aj between the fired source element (G _j ) and near-field sensors NFH _a , based on the recorded direct waves; and calculating sensitivities c _a or sensitivity ratios c _a /Cb of the near-field sensors NFH _a for calibrating their responses.

[0017] According to still another embodiment, there is a computing device for calibrating marine equipment. The device includes an interface for sending firing instructions, during a calibration phase, to a source element Gj. The interface receives recordings of plural near-field sensors (NFH _a -NFH _c ), during the calibration phase, wherein the recordings include direct waves incoming from the fired source element G _j . The device also includes a processor connected to the interface and configured to calculate distances L _aj between the fired source element (G _j ) and the near-field sensors NFH _a , based on the recorded direct waves, and calculate sensitivities c _a or sensitivity ratios Cg/Cb of the near-field sensors NFH _a for calibrating their responses.

[0018] According to another exemplary embodiment, there is a computer readable media non-transitorily storing executable codes which when executed on a computer make the computer perform a method as noted above.

BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate one or more embodiments and, together with the description, explain these embodiments. In the drawings:

[0020] Figure 1 illustrates a conventional marine seismic survey system;

[0021] Figure 2 is a graph illustrating a time variation of a pressure when a gun is fired underwater;

[0022] Figure 3 illustrates a marine source sub-array and a seismic data processing unit;

[0023] Figure 4 schematically illustrates a source sub-array and corresponding source elements that are moving relative to a supporting float; [0024] Figure 5 is a flowchart of a method for calibrating an actual firing position of a source element;

[0025] Figure 6 schematically illustrates how a source element dangles relative to a supporting float;

[0026] Figure 7 schematically illustrates three source elements and

corresponding near-field sensors belonging to a source sub-array;

[0027] Figure 8 is a flowchart of a method for calibrating near-field sensors associated with source elements of a same source sub-array;

[0028] Figure 9 illustrates various time point parameters recorded by a near- field sensor; and

[0029] Figure 10 illustrates a computing device for calibrating a firing position of a source array and/or a near-field sensor.

DETAILED DESCRIPTION

[0030] The following description of the embodiments refers to the accompanying drawings. The same reference numbers (except for the first digit) 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 seismic marine source array having plural air guns. However, the embodiments to be discussed next are not limited to air guns, but may be applied to other types of similar seismic sources. Further, the source array may be used in any aquatic environment, i.e., in a river, lake, pond or other body of water, i.e., any body of water that does not have salt water.

[0031] 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. [0032] Before discussing details of the embodiments, a partial marine source array is discussed with regard to Figure 3. This figure illustrates a single sub-array 301 of a marine source array 300. Sub-array 301 (the source array may include any number of sub-arrays) includes air guns (guns herein) 310, 31 1 , 312, 313, 314, and 315 and near-field sensors 320, 321 , 322, 323, 324, and 325, which may be located near (e.g., above) the individual sources 310-315, respectively. Near-field sensors 320-325 may be hydrophones or geophones. The number and arrangement of the individual sources are merely exemplary and are not intended to be limiting. Each of the guns 310-315 may be a single air gun or a cluster of air guns. Near-field sensors 320-325 may be located at about 0.5 to 1 m above the corresponding air guns 310- 315. The distance in-between neighboring air guns may be about 3 m. The marine source sub-array 301 may include a float 330 for supporting the guns to a desired depth.

[0033] Near-field sensors 320-325 are connected to a seismic data processing unit 340 (e.g., located on the towing vessel), including an interface 342, a processor 344 and a memory 346. The seismic data processing unit 340 may also include a monitoring unit 348 and a display 350. In one application, processing unit 340 is the gun controller. In another application, each gun has its own gun controller 360-365, mounted next to the gun. The gun controllers 360-365, if installed next to their corresponding guns, may be configured to communicate via interface 342 with the seismic data processing unit 340, e.g., for receiving instructions from the processing unit 340 and/or for providing information to the processing unit. Each air gun may include an internal sensor called time break (TB) that provides an approximate time of when the air gun is fired. For illustration purposes, TB sensors 370 to 375 are shown in Figure 3 being located inside corresponding guns.

[0034] As the sub-array 301 is towed under water by a survey vessel 101 as illustrated in Figure 4, air guns 310-315 interact with the water current and thus, they are not staying at their designated (or expected or predetermined) positions 31 OA to 315A, but rather deviate to real firing gun positions 310B to 315B. This happens for any survey system taking place in a sea or ocean as the underwater currents are always present and also because the air guns are not fixedly connected to the float. In this regard, note that each air gun is connected to float 301 with a corresponding linkage 31 OC to 315C. The linkage includes one or more chains. In one application, the linkage includes ropes or wires, instead or in addition to the chains. Because of these linkages, the air guns can dangle in water relative to the float. In addition, the movement of the vessel and implicitly the movement of the sub-array relative to the Earth, makes the air guns to deviate from their expected positions 31 OA to 315A.

[0035] Thus, according to the method to be discussed next, a calibration test is made to re-estimate (or calculate or determine) the real firing gun positions 310B to 315B. According to the method illustrated in Figure 5, at least one air gun (j) is fired in step 500 while the source array configuration (e.g., geometry of the source array, which include inline and cross-line distances between the source elements) used during this calibration phase is substantially the same as the configuration used during the actual seismic survey (seismic data acquisition phase). Note that if more than one gun is fired, the guns are fired one at a time, so that there is no overlap of the recorded data. More specifically, the calibration phase is performed before and/or during and/or after the actual marine seismic survey. The calibration phase preserves the source array configuration of the actual marine seismic survey, with one or more of the sub- arrays being deployed. The same survey speed may be used when towing the sub- array during the calibration phase. Step 500 may also fire several times the at least one air gun for generating data appropriate for statistical processing. In one application, each air gun of the source sub-array is fired during step 500. If this is the case, the air guns are fired one by one. In still another application, all the air guns of the source array are fired, one by one, several times.

[0036] In step 502, the responses of all the NFH sensors are recorded. The NFH sensors record direct waves incoming from the fired gun, i.e., the direct waves are not reflected from the water-air interface. Waves from the water-air interface are also recorded, later in time. However, for this method, only the direct waves are used as discussed later. While all the guns of the source array may be fired during step 500, for calculating the real position of a given gun 312, only the measurements from the NFH sensors 320-325 in the same sub-array 301 are used as now discussed.

[0037] Considering (as illustrated in Figure 6) that G represents the real firing positon of the firing gun 312 (note that this quantity is a vector and indicates the location of the firing gun relative to a fixed reference XYZ), _t is the position (as a vector) of the i ^th NFH sensor, and L _t is the distance between the real firing position of the firing gun 312 and the i ^th NFH sensor's position, a cost function C is selected in step 504. The cost function C is related to the real firing position G of the firing gun, the actual positions ^~ P _t of the NFH sensors, and the distances L _t between the real firing position of the firing gun and the NFH sensors. In one embodiment, the cost function C is given by:

where the sum is over all NFH sensors in the sub-array including the fired gun 312. The norm can be an Euclidian or another L2 norm.

[0038] In another embodiment, it is possible to have another cost function C, as follows:

Those skilled in the art would know to modify equations (1 ) and (2) to obtain another cost function that depends on the same quantities as discussed above.

[0039] Considering that the cost function C of equation (1 ) is selected, one notes that the position ^~ P _t of the i ^th NFH sensor is known from the geometry of the source array. In this respect, note that the NFH sensors are substantially fixed to a rigid structure as illustrated in Figure 3. This ridig structure may be a plate. However, the real firing position G of the fired air gun is not known.

[0040] The distance L _t between the real firing position of the firing gun 312 and the i ^th NFH sensor's position may be calculated in step 506 as follows. For the firing gun 312, consider that the distance between firing gun 312 and the corresponding

NFH sensor 322 does not change, i.e., it is the length of the link 312C, L _g herein. This distance is the same irrespective if the air gun 312 is at position 312A or 312B.

[0041] A difference between (1 ) the distance L _g between air gun 312 and its NFH sensor 323 and (2) a distance L _t between air gun 312 and the i ^th NFH is considered to be Diff _t . Then, based on the above observation, it follows that:

Lt = L _g + Difft (3). [0042] The difference Diff _{ can be calculated as follows: by analyzing the recordings of the NFH, sensors, the time of the rising edge captured by NFH 322 (i.e., the peak corresponding to the incoming direct wave) and the time of the rising edge captured by the i ^th NFH sensor are selected. Based on these times, it is possible to calculate the time delay of the signal emitted by gun 312 and recorded by NFH sensor 322 and the i ^th NFH sensor. If this time delay is multiplied by the speed of sound in water, the difference Diff _t is obtained. Because l _g is known (the length of the linkage, which does not change when the gun dangles), based on equation (3), each distance L _t can be calculated.

[0043] At this point, both the ^~ P _t and the L _t are known. Thus, in step 508, by applying an inversion algorithm (e.g., least square optimization) to the cost function C, it is possible to calculate the real firing position G of gun 312 (j). The method then advances to step 510 where a decision is made if other guns' real firing positions need to be calculated. If the gun j is not the last one, the algorithm returns to step 500 and selects a next gun. If gun j is the last one, the algorithm advances to step 512. Note that the steps presented until now apply to a sub-array. The method may stop after calculating the real positions of a single sub-array. However, in another embodiment, the method may advance to calculate the real firing positions of the guns for a second sub-array.

[0044] In step 512, a difference between the real firing position G of a gun "i" relative to its expected position (or nominal position NM) is calculated as Drifted) = G - ^~ NM, where the difference Drift, is a function of the water speed v. It is possible that the calibration test includes shots of a given gun at different water speeds. In this case, it is possible to estimate the difference Drift, at any water speed by using interpolation or extrapolation.

[0045] The difference Drift, is used in step 514 to calibrate the air gun drift and then, in step 516, the seismic data collected during a seismic survey (with calibrated guns) may be processed with known techniques and methods for generating the image of the subsurface. One will note that the drift function Drift, calculated above improves the accuracy of the surveyed subsurface's image by correcting the collected seismic data with the actual shooting positions of the air guns. [0046] While the drift function Drift, may be used to improve the accuracy of the collected seismic data as discussed above, one skilled in the art would understand that this function can be used for other purposes.

[0047] Steps of the method discussed above that fire a single NFH sensor during a calibration phase may be used to also calibrate the NFH sensors themselves. In other words, the NFH sensors need to be calibrated as there are many factors during a seismic survey that can make these sensors to not accurately measure the source signature.

[0048] In this respect, a typical NFH sensor, i.e., a hydrophone, is subject to many influences that affect the stability of its sensitivity. Hydrostatic pressure, temperature, rough handling, marine fouling, corrosion, and water leakage are some of the more obvious influences. Other influences are more subtle. For example, many hydrophones have small piezoelectric elements with high electrical impedances. The leakage resistance of such generators needs to stay very high for operating reasons. The usual materials that protect the generator elements from the water medium are not completely waterproof. Over a period of time, small amounts of water will enter the generator's housing, lower the leakage resistance, and cause a drop in sensitivity at low frequencies. Some chemical changes among the metals, oil, crystals, rubbers, plastics, and so forth that form the NFH sensor also tend to pollute the generator environment and affect the hydrophone sensitivity. Thus, a hydrophone should be recalibrated from time to time.

[0049] Such a calibration method is now discussed with regard to Figures 7 and 8. Figure 7 schematically illustrates a sub-array 701 having a float 730 from which three guns G, are suspended. For simplicity, the figure shows only three guns. Along the linkages that hold the guns suspended from the float 730, there is a NFH sensor NFH, for each gun. In this specific example, the NFH sensors dangle with the corresponding gun, if the case.

[0050] Suppose that a distance between gun G _j and NFH _a sensor is L _aj , and a maximum value (i.e., amplitude) of a signal recorded by NFH _a sensor is v _aj , which has the unit of volt. Note that a signal recorded by NFH _a sensor looks like a wiggly line, depending on the noise and events recorded. A NFH _a sensor is characterized by its sensitivity c _a , which is defined as the voltage generated when the sensor experiences a given ambient pressure, and it has the unit of volt/bar. This means that sensor NFH _a has a sensitivity c _a = 1 if it records a voltage of 1 V for a pressure of 1 bar. The NFH's sensor sensitivity takes into account not only the sensitivity of the sensor itself, but also the influence of the any cable and/or conductor and/or circuit in its analog-to- digital converter (ADC), which include but is not limited to electrical gains.

[0051] The maximum value v _aj of a recording (or response) of a sensor NFH _a takes place during the peak period, i.e., around 5 to 10 ms after the firing of the gun (note that the primary pulse of the source signature in Figure 2 needs some time to propagate from the air gun to the sensor). This maximum value is independent of the surface reflection, i.e., the ghost also illustrated in Figure 2. This is so because the maximum value corresponds to an incoming direct wave that did not reflect from the water-air interface.

[0052] Following the propagation of a shock wave SW from gun G _j (see Figure 7), the intensity M _j of this wave at NFH _a sensor and NFH _b sensor is given by: ca ^c b

where the intensity M _j has the unit of bar times m.

[0053] Distance L _bj between gun G _j and sensor NFH _b is reliable (it does not change as there is a direct link, e.g., the chains, between the gun and sensor) while distances L _aj or L _Cj are not, because gun G _j can and will move relative to either sensor NFH _a and NFH _C . Thus, according to the method of Figure 8, in step 800, gun G _j is fired. Similar to the method discussed with regard to Figure 5, gun G _j may be fired a couple of times for providing statistically meaningful data. The firing of the gun occurs during a calibration phase. This means that the calibration phase may take place prior, during and/or after the phase of collecting seismic data.

[0054] In step 802, the NFH sensors record the data (incoming direct waves from the fired source element), which may be stored in a storing device 346. Distances L _aj are calculated in step 804, where a is different from j. Note that distances L _aa (i.e., the distance between the NFH sensor and the corresponding air gun) are known from the geometry of the source array. Distance L _aj may be the distance between sensor NFH _a and (i) the actual firing position of the source element (calculated with the method discussed in Figure 5) or (ii) the nominal position of the source element (the expected firing position of the source element, which is not the true position).

[0055] From the recordings of the NFH sensors, e.g., peak arrival times t _aj , t _bj , and tq from gun G _j to each of the sensor NFH _a , NFH _b , and NFH _C (those skilled in the art would understand that other quantities may be used for calculating arrival times differences, for example, compare dt from the take-off point TO or the half-height point T1 (the time for which the amplitude is half of its maximum value; in practice this point is the most stable point) as illustrated in Figure 9, where curve 900 indicates the response recorded by an NFH sensor; Point T2 is the peak arrival time), it is possible to calculate any of distances Laj as follows:

Laj = Lbj + (t _aj - t _bj ) ^■ v (5)

where v is the sound velocity in water. If the take-off point TO or the half-height point T1 are used instead of the peak arrival times, formula (5) above should be corrected to replace the peak arrival times with the corresponding choice. The take-off point, half- height point or peak arrival time are generically called herein "time point parameter." The sound velocity in water may depend with the water temperature (near the surface) and salinity. The sound velocity in water can be measured with a local sensor, can be inferred from existing marine data, or it can be calculated based on various known models.

[0056] In step 806, the gun intensity M _j (defined in equation 4) is received, e.g., from field test data interpolation, as a function of the gun type, volume, charging pressure, depth and pressure. Then, it is possible to calculate in step 808 the absolute values of the sensitivities c _a , c _b , and c _c .

[0057] However, it is possible that the gun intensities M _j values are not known. In this case, it is possible to calculate in step 812 the ratios of the sensitivities of any two guns Ca/Cb. In this case, at least two guns G, and G _j are fired, sequentially. From the NFH responses, distances L _aj and L _bj are calculated as discussed above with regard to step 804. Note that indices "a" and "b" in this discussion refer to any two guns and indices "i" and "j" refer to any two NFH sensors from a given sub-array.

[0058] From the definition of the wave intensity, it is possible to write the following equations in step 812: ^v ai ' L _a i ^v b \ ' Lbj V _a ^; · L _a ^; Vfrj ¹ L _b ^;

= ; = ; ... (6)

^b ^b

[0059] Based on equations (5) and (6), it is possible to formulate the ratios Ca/c _b as follows:

[0060] Note that the error in the sensitivity c _a is amplified by the error in distances l_aj. Based on this observation and the existing data measurements, the error in the difference between two distances L _aj and L _bj (see equation (5)) is about 3%. Then, the error in the ratio cJCb may be brought to about 3%, given that the method discussed in Figure 5 has been used to calculate the real firing positions of the guns. If distances L _aj are not calibrated with the method of Figure 5, then the error in the sensitivity ratio may get up to about 17%, which is about 1.4 dB.

[0061] If equation (7) is used for calculating the sensitivity ratio, and there is some systematic error in calculating lengths L _a j and Ui, then this error will cancel out, bringing the error in sensitivity to about 1 %, which is less than 0.1 dB of error.

[0062] The method discussed in Figure 8 may then advance to step 814 in which the NFH sensor response NFHj for all "j" is calculated. Note that the reading of a NFH sensor is called herein a signature (measured in volt) and the ratio between the signature and the sensitivity c _a of the sensor is the pressure reading (measured in barr). If the sensitivity ratios cJCb and Ca/c _c for three sensors are known, then the pressure readings (i.e., the ratio of the signature reading and the corresponding sensitivity) can be corrected to have their relative values correct (e.g., consider that sensitivity c _a = 1 ), while their absolute values are still a constant away from the actual values. With these NFH sensor calibrations, the source signatures and measured pressures may be more accurately evaluated, which positively impacts the processing of seismic data in step 816. As a result of the improved processing data in step 816, an image of the subsurface generated in step 818 is more accurate, which helps the oil company drill the well faster and cheaper.

[0063] To improve the above discussed method, it is possible in step 800, instead of firing each gun once, to fire it many times (e.g., 10 times) to create statistically meaningful data. In this way, the calibration of the sensors and/or lengths may benefit from statistical methods to remove the random error.

[0064] The above discussed calibration methods are surface independent, thus not related to the weather or sea conditions. Therefore, these new methods are advantageous over the existing methods discussed in the Background, as those methods depend on the surface conditions.

[0065] The above discussed method of distance calibration (Figure 5) of the real gun positions gives a more accurate source array geometry, which is the first step before the calibration of the hydrophone response. The gun position geometry allows a better estimation of notional and the source directivity, which are some of the ingredients of the far-field reconstruction method, and they can be an added value for the directional designature method.

[0066] The method of Figure 8 can obtain a better calibration of the hydrophone responses and can bring the incertitude to 0.5% of the incertitude of a traditional method that does not calibrate the geometry of the source array.

[0067] The novel methods calculate the hydrophone response to include the hydrophone sensitivity and the ADC impacts, so it is useful in cases with calibrated hydrophones or non-calibrated hydrophones. A reliable hydrophone response is the base of all the NFH related works, so to bring its incertitude to a negligible level (0.1 dB versus 1.4dB before) is a notable achievement.

[0068] As discussed above, the two methods discussed with regard to Figures 5 and 8 are weather independent, because they use only the peak values from the recordings, which correspond to direct waves that propagate in water without reflection on the surface. Other methods, such as that described in Hegna, bring the incertitude of the surface reflection into the calculations, thus being weather dependent. Therefore, the calibrated result in Hegna is not reliable when the surface layer of water changes.

[0069] An exemplary computing device that can implement the above methods is illustrated in Figure 10. The computing device 1000, which can be controller 340, includes a processor 1002 that is connected through a bus 1004 to a storage device 1006. Computing device 1000 may also include an input/output interface 1008 through which data can be exchanged with the processor and/or storage device. For example, a keyboard, mouse or other device may be connected to the input/output interface 1008 to send commands to the processor and/or to collect data stored in storage device or to provide data necessary to the processor. In one application, the processor calculates based on functional block 1003, which includes the steps from Figures 5 and/or 8, the distances L _aj between each gun and the NFH sensors using the above defined time point parameters (e.g., maximum peaks) recorded by the NFH sensors. Also, the processor may be used to process, for example, seismic data collected during the seismic survey. Results of this or another algorithm may be visualized on a screen 1010.

[0070] The disclosed exemplary embodiments provide a method and system for calibrating air gun positions and/or NFH sensors. 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.

[0071] As also will be appreciated by one skilled in the art, the exemplary embodiments may combine hardware and software aspects. The exemplary

embodiments may take the form of a computer-readable storage medium non-transitorily storing executable codes (i.e., a computer program) which when executed on a computer perform the above-described methods. Any suitable computer-readable medium may be utilized, including hard disks, CD-ROMs, digital versatile disc (DVD), optical storage devices, or magnetic storage devices such a floppy disk or magnetic tape. Other non- limiting examples of computer-readable media include flash-type memories or other known memories.

[0072] 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.

[0073] 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.