Abstract:
Embodiments related to a piezoelectric bender that comprises a spring and mass element to provide additional constructive resonance. An embodiment provides an apparatus comprising: a base plate; a piezoelectric body coupled to the base plate; a spring coupled to the base plate; and a mass element coupled to the spring, wherein the base plate, the piezoelectric body, the spring, and the mass element are operable to produce at least two resonance frequencies in the apparatus.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims the benefit of U.S. Provisional Application No. 61/873,106, filed Sep. 3, 2013, entitled “Piezoelectric Bender With Additional Constructive Resonance,” the entire disclosure of which is incorporated herein by reference. 
    
    
     BACKGROUND 
     Embodiments relate generally to marine vibrators for marine geophysical surveys. More particularly, embodiments relate to a piezoelectric bender that comprises a spring and mass element to provide additional constructive resonance. 
     Sound sources are generally devices that generate acoustic energy. One use of sound sources is in marine seismic surveying in which the sound sources may be employed to generate acoustic energy that travels downwardly through water and into subsurface rock. After interacting with the subsurface rock, e.g., at boundaries between different subsurface layers, some of the acoustic energy may be returned toward the water surface and detected by specialized sensors (e.g., hydrophones, geophones, etc.). The detected energy may be used to infer certain properties of the subsurface rock, such as structure, mineral composition and fluid content, thereby providing information useful in the recovery of hydrocarbons. 
     One example of a sound source includes a bender as the active part. This type of sound source is typically referred to as a “piezoelectric bender” because it uses the piezoelectric effect to generate acoustic energy. A piezoelectric bender may include a base plate of elastic material (e.g., aluminum) and a piezoelectric body attached to the base plate. When an electrical field is applied across the composite assembly of the base plate and the piezoelectric body, the composite assembly should bend and thus create vibrations from the composite assembly to a fluid (e.g., water). The piezoelectric bender may have a first resonance frequency as a result of the composite assembly functioning as a spring, together with the surrounding oscillating water mass. 
       FIG. 1  shows a finite-element analysis of an axial-symmetric model of a piezoelectric bender  100  working close to its first resonance. As illustrated, the piezoelectric bender  100  may comprise a base plate  105  and piezoelectric body  110 , which may bend from a first position to a second position shown at  105 ′ and  110 ′, respectively. The axial line of symmetry for the piezoelectric bender  100  is represented by reference number  102 .  FIG. 2  is a graph showing an example of far-field intensity as a function of frequency for the piezoelectric bender  100  of  FIG. 1 . As illustrated by  FIG. 2 , the piezoelectric bender  100  may have a sharp resonance peak, causing the bandwith of this design to be limited. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These drawings illustrate certain aspects of some of the embodiments of the present invention and should not be used to limit or define the invention. 
         FIG. 1  shows an axial-symmetric model of an example piezoelectric bender. 
         FIG. 2  shows a graph showing far-field intensity as a function of frequency for an example piezoelectric bender with one resonance frequency. 
         FIG. 3  shows a cross-sectional view of an embodiment of a piezoelectric bender that comprises a spring and mass element. 
         FIG. 4  shows a top view of the example piezoelectric bender of  FIG. 3 . 
         FIG. 5  shows a close-up of the cross-sectional view of  FIG. 3  showing the edge of the example piezoelectric bender. 
         FIG. 6  shows an axial-symmetric model of an embodiment of a piezoelectric bender that comprises a spring and mass element. 
         FIG. 7  shows a graph showing far-field intensity as a function of frequency for an example piezoelectric bender with a second resonance frequency. 
         FIG. 8  shows a side view of an embodiment of an assembly of piezoelectric benders arranged in a stack. 
         FIG. 9  shows an example embodiment of a marine seismic survey system using a piezoelectric bender. 
     
    
    
     DETAILED DESCRIPTION 
     It is to be understood that the present disclosure is not limited to particular devices or methods, which may, of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting. All numbers and ranges disclosed herein may vary by some amount. Whenever a numerical range with a lower limit and an upper limit is disclosed, any number and any included range falling within the range are specifically disclosed. Although individual embodiments are discussed, the invention covers all combinations of all those embodiments. As used herein, the singular forms “a”, “an”, and “the” include singular and plural referents unless the content clearly dictates otherwise. Furthermore, the word “may” is used throughout this application in a permissive sense (i.e., having the potential to, being able to), not in a mandatory sense (i.e., must). The term “include,” and derivations thereof, mean “including, but not limited to.” The term “coupled” means directly or indirectly connected. If there is any conflict in the usages of a word or term in this specification and one or more patent or other documents that may be incorporated herein by reference, the definitions that are consistent with this specification should be adopted for the purposes of understanding this invention. 
       FIGS. 3 and 4  illustrate an embodiment of a piezoelectric bender  300 . As illustrated, the piezoelectric bender  300  comprises base plates  305  and piezoelectric bodies  310  attached to the base plates  305 . Each of the base plates and piezoelectric bodies  310  may form a corresponding composite assembly  302 . To provide the additional constructive resonance, the piezoelectric bender  300  further comprises springs  315  with mass elements  320  attached to the springs  315 , as seen in  FIG. 3 . In particular, the springs  315  and mass elements  320  may be included in the piezoelectric bender  300  to provide a second resonance frequency within the frequency range of interest. 
     The base plates  305  may each comprise an outer surface  325  and an inner surface  330 . In the illustrated embodiment, the base plates  305  are spaced to provide a gap  335  between the respective inner surfaces  330 . The gap  335  may be filled with air in some embodiments. In alternative embodiments, the gap  335  may be a vacuum. The gap  335  may be sized to permit flexing and bending of the base plates  305  and springs  315  without interference with one another. As illustrated, the base plates  305  may be generally planar. In some embodiments, the base plates  305  may be in the form of a flexible disk, as best seem on  FIG. 4 . In embodiments, the base plates  305  may each be a flat, circular disk having substantially uniform thickness. However, other configurations, including both axially-symmetric and not, of the base plates  305  may be suitable for particular applications. By way of example, the base plates  305  may be rectangular, square, elliptical, or other suitable shape for providing the desired acoustic energy. The base plates  305  may comprise spring steel, aluminum, a copper alloy, glass-fiber reinforced plastic (e.g., glass-fiber reinforced epoxy), carbon fiber reinforced or other suitable flexible spring material. Examples of suitable copper alloys may include glass-fiber reinforced epoxy, brass, beryllium, copper, phosphor bronze, or other suitable copper alloy. In some embodiments, the base plates  305  may comprise spring steel. In particular embodiments, the base plates  305  may have a thickness from about 1 millimeters to about 8 millimeters. In general, the base plates  305  should have a thickness that allows sufficient deformation but withstand expected pressures. 
     With additional reference to  FIG. 5 , the base plates  305  may be secured to another in a manner that allows the base plates  305  to bend and create the desired acoustic energy. In particular embodiments, the base plates  305  may be coupled to one another at their outer edges  340 . In the illustrated embodiment, the outer edges  340  may include an area of reduced thickness referenced on  FIGS. 3 and 5  by numeral  342 , which functions to facilitate bending and flexing of the base plates  305 . As illustrated, the piezoelectric bender  300  may further comprise a ring  345 , for example, that couples the base plates  305  to one another at their outer edges  340  In the illustrated embodiment, the ring  345  may include an inner extension  350  that extends from ring body  355  between the outer edges  345  of the base plates  305 . The ring  345  may be coupled to the base plates  305  by soldering or other suitable coupling technique, such as use of an adhesive or fasteners (e.g., screws). While the ring  345  is shown for securing the base plates  305  to one another, other suitable techniques may be used to secure the base plates  305 . For example, the base plates  305  may be configured so that the outer edges  345  overlap without the need for the ring  345 . 
     As illustrated in  FIGS. 3-5 , the piezoelectric bodies  310  may each be coupled to the outer surfaces  325  of the base plates  305 . The piezoelectric bodies  310  may include a piezoelectric ceramic material. Examples of suitable piezoelectric ceramic materials include barium titanate, lead zirconate, lead titanate, and combinations thereof. Piezoelectric crystals may also be used, in some embodiments, which may include gallium phosphate, quartz, tourmaline, and combinations thereof As illustrated, the piezoelectric bodies  310  may be generally planar. In some embodiments, the piezoelectric bodies  310  may be in the form of a disk, as best seem on  FIG. 4 . In embodiments, the piezoelectric bodies  310  may each be a flat, circular disk having substantially uniform thickness. However, other configurations of the piezoelectric bodies  310  may be suitable for particular applications. By way of example, the piezoelectric bodies  310  may be rectangular, square, elliptical, or other suitable shape for providing the desired acoustic energy. In particular embodiments, the piezoelectric bodies  310  may have a thickness from about 2 millimeters to about 5 millimeters. In general, the piezoelectric bodies  310  should have a thickness that allows sufficient deformation but withstand expected pressures. In particular embodiments, the piezoelectric bodies  310  may be coupled to the base plates  305  by use of an adhesive material, such as an electrically conductive epoxy. 
     While not illustrated, electrical connections may be made to the base plates  305  and piezoelectric bodies  310 . For example, an electrical connection may be made to each of the base plates  305 , and another electrical connection may be made to each of the piezoelectric bodies  310 . Voltage may be applied across the electrical connections so that the applied electrical field results in a mechanical strain in the piezoelectric bodies  310  with resultant blending and flexing of the composite assemblies  302  to generate acoustic energy. 
     Referring to  FIG. 3 , the piezoelectric bender  300  may comprise springs  315  with mass elements  320  attached to the springs  315 . As previously mentioned, the springs  315  and mass elements  320  may be included in the piezoelectric bender  300  to provide a second resonance frequency within the frequency range of interest. The properties of the springs  315  and the mass elements  320  (e.g., stiffness, size, position, mass, etc.) can be chosen to achieve a specific and desired second resonance frequency. As illustrated, the springs  315  and the mass elements  320 , in some embodiments, may be disposed in the interior of the piezoelectric bender  300 . For example, the springs  315  and mass elements  320  may be located in the gap  335  between the base plates  305 . In other embodiments, the springs  315  and the mass elements  325  may be located elsewhere, for example, they may be located external to the piezoelectric bender  300 . 
     The springs  315  may be generally planar and comprise spring steel, aluminum, a copper alloy, glass-fiber reinforced plastic (e.g., glass-fiber reinforced epoxy), carbon fiber reinforced or other suitable flexible spring material. Examples of suitable copper alloys may include glass-fiber reinforced epoxy, brass, beryllium, copper, phosphor bronze, or other suitable copper alloy Suitable flexible spring materials may have a high yield strength and not permanently deform when caused to deform and flex by action of the piezoelectric bodies  310 . In some embodiments, the springs  315  may each be a class V flextensional transducer. In some embodiments, the springs  315  may each be in the form of a disk. In particular embodiments, the springs  315  may each be a flat, circular disk having substantially uniform thickness. However, other configurations of the springs  315  may be suitable for particular applications. By way of example, the springs  315  may be rectangular, square, elliptical, or other suitable shape for providing the desired acoustic energy. In particular embodiments, the springs  315  may have a thickness from about 0.1 millimeters to about 3 millimeters. In general, the springs  315  should have a thickness that allows sufficient deformation but withstand expected pressures. 
     The springs  315  may be coupled to the inner surfaces  330  of the base plates  305 . In the illustrated embodiment, the springs  315  may be indirectly coupled to the base plates  305  with a spacer  360  disposed between each of the springs  315  and the corresponding one of the base plates  305 . The spacers  360  may be sized to provide sufficient space between the base plates  305  and springs  315  for clearance when flexing and bending occurs. In some embodiments, the spacers  360  may each be in the form of a disk. In other embodiments, the spacers  360  may be rectangular, square, circular, elliptical, or other suitable shape. In some embodiments, each spacer  360  may be integrally formed with the corresponding one of the base plates  305 . 
     The mass elements  320  may be attached to the springs  315 . In the illustrated embodiments, the mass elements  320  may be attached at the perimeter of the springs  315 . In particular embodiment, the mass elements  320  may be in the form of an annular-plate that adds weight to the perimeters of the springs  315 . However, other configurations of the mass elements  320  may be suitable for particular applications. For example, the mass elements  320  may be in the form of blocks, bars, or other suitable shapes. In embodiments, the piezoelectric bender  300  may comprise a pair of mass elements  320  wherein a single one of the mass elements  320  may be added to each of the springs  315 . In other embodiments, two or more mass elements  320  may be added to each of the springs. 
     Accordingly, because the springs  315  and mass elements  320  may provide additional constructive resonance, the piezoelectric bender  300  may display at least two resonance frequencies when submerged in water. One of the resonance frequencies may result from interaction of the composite assemblies  302  of the base plates  305  and piezoelectric bodies  310  functioning as springs, together with the surrounding oscillating water mass. Another of the resonance frequencies may result from vibration of the springs  315  due to interaction with the base plates  305 . For example, the piezoelectric bender  300  may display two or more resonance frequencies within a seismic frequency band, typically a range between about 1 Hz and about 300 Hz. In some embodiments, the piezoelectric bender  300  may display two more resonance frequencies between about 1 Hz to about 200 Hz. In alternative embodiments, the piezoelectric bender  300  may display two or more resonance frequencies between about 0.1 Hz and about 100 Hz, alternatively, between about 0.1 Hz and about 10 Hz, and alternatively, between about 0.1 Hz and about 5 Hz. In particular embodiments, piezoelectric bender  300  may display a first resonance frequency between about 3 Hz to about 8 Hz and one or more additional resonance frequencies from about 8 Hz to about 24 Hz and, alternatively, from about 24 Hz to about 72 Hz. 
     Referring to  FIG. 6 , a finite-element analysis of an axial-symmetric model of the piezoelectric bender  300  of  FIG. 3  is shown with additional constructive resonance. As illustrated, the piezoelectric bender  300  may comprise a base plate  305  and piezoelectric body  310 , which may bend from a first position to a second position. As further illustrated, a spring  315  with mass element  320  may be coupled to the base plate  305  via spacer  360 . The spring  315  with mass element  320  may bend from a first position to a second position shown at  315 ′ and  320 ′, respectively. The axial line of symmetry for the piezoelectric bender  300  is represented by reference number  302 . 
       FIG. 7  is a graph showing the results of a finite-element simulation for a piezoelectric bender having additional constructive resonance. The simulation was performed for a piezoelectric bender similar to the piezoelectric bender  300  shown on  FIG. 3 . On  FIG. 7 , far-field intensity is shown as a function of frequency. As illustrated, the piezoelectric bender exhibits a first resonance frequency  700  at 40 Hz and a second resonance frequency  705  at 60 Hz. The second resonance frequency  705  may be due to the additional constructive resonance provided by the inclusion of springs and mass elements (such as springs  315  and mass elements  320  shown on  FIG. 3 ). The additional constructive resonance can increase the bandwith of the piezoelectric bender. 
       FIG. 8  illustrates a bender assembly  800  in accordance with particular embodiments. As illustrated, the bender assembly  800  may comprise a plurality of piezoelectric benders  300  arranged in a stack  805 . The piezoelectric benders  300  in the stack  805  may be similar in construction to the embodiment illustrated in  FIGS. 3-5 . In  FIG. 8 , twelve piezoelectric benders  300  are shown arranged in a single stack  805 . It should be noted that, in some embodiments, the stack  805  may include more (or less) piezoelectric benders  300  than shown. Moreover, while not shown, the bender assembly  800  may include two or more stacks  805  of piezoelectric benders  300  in some embodiments. 
     The bender assembly  800  may further comprise a plurality of rods  810  which may have their axes aligned with the axis of the stack  805 . Spacers  815  may be disposed on the rods  810  to maintain a desired axial separation of the piezoelectric benders  300  in the stack  805 . The illustrated embodiment contains eight rods  810 ; however, particular embodiments may comprise more (or less) than eight rods  810  as desired for a particular application. The number, size, and spacing of the rods  810  and spacers  815  may depend on a number of factors, including the size and number of the piezoelectric benders  300 . A pair of plates  820  may be disposed on either end of the rods  810 . The plates  820  may hold the rods at pre-determined intervals. Nuts  825  or other suitable fastening means may be used to secure the rods  810  to the plates  820 . Springs  830  may be disposed on the ends of the rods  810 . The bender assembly  800  may further comprise a manifold  835  for a pressure-compensating system, which may be coupled to each of the benders  300  with a short pipe. The pressure-compensating system may function to protect the benders  300  from the hydrostatic pressure. While not illustrated, the manifold  835  may be coupled to a vessel which as the same pressure as the surrounding water. 
       FIG. 9  illustrates an example technique for acquiring marine seismic data that can be used with embodiments of the present techniques. In the illustrated embodiment, a survey vessel  900  moves along the surface of a body of water  902 , such as a lake or ocean. The survey vessel  900  may include thereon equipment, shown generally at  904  and collectively referred to herein as a “recording system.” The recording system  904  may include devices (none shown separately) for detecting and making a time indexed record of signals generated by each of seismic sensors  906  (explained further below), and for actuating a marine vibrator  908  comprising a piezoelectric bender  300  (e.g., shown on  FIGS. 2-5 ) at selected times. The recording system  904  may also include devices (none shown separately) for determining the geodetic position of the survey vessel  904  and the various seismic sensors  906 . 
     As illustrated, the survey vessel  900  (or a different vessel) may tow the marine vibrator  908  in the body of water  902 . A source cable  910  may couple the marine vibrator  908  to the survey vessel  900 . The marine vibrator  908  may be towed in the body of water  902  at a depth ranging from 0 meters to about 120 meters, for example. While not shown separately on  FIG. 9 , it is contemplated that embodiments of the marine vibrator  908  may include more than one piezoelectric bender  300  towed by the survey vessel  900  or a different vessel. In some embodiments, one or more arrays of piezoelectric benders  300  may be used. For example, at least one bender assembly  800  shown on  FIG. 8  may be towed by the survey vessel  900 . At selected times, the marine vibrator  908  may be triggered, for example, by the recording system  904 , to generate acoustic energy. 
     The survey vessel  900  (or a different vessel) may further tow at least one sensor streamer  912  to detect the acoustic energy that originated from the marine vibrator  908  after it has interacted, for example, with rock formations  914  below the water bottom  916 . As illustrated, both the marine vibrator  908  and the sensor streamer  912  may be towed above the water bottom  916 . The seismic streamer  912  may contain seismic sensors  906  thereon at spaced apart locations. In some embodiments, more than one sensor streamer  912  may be towed by the survey vessel  900 , which may be spaced apart laterally, vertically, or both laterally and vertically. While not shown, some seismic surveys locate seismic sensors  906  on ocean bottom cables or nodes in addition to, or instead of, a sensor streamer  912 . The seismic sensors  906  may be any type of seismic sensors known in the art, including hydrophones, geophones, particle velocity sensors, particle displacement sensors, particle acceleration sensors, or pressure gradient sensors, for example. By way of example, the seismic sensors  906  may generate response signals, such as electrical or optical signals, in response to detected acoustic energy. Signals generated by the seismic sensors  906  may be communicated to the recording system  904 . The detected energy may be used to infer certain properties of the subsurface rock, such as structure, mineral composition and fluid content, thereby providing information useful in the recovery of hydrocarbons. 
     In accordance with an embodiment of the invention, a geophysical data product indicative of certain properties of the subsurface rock may be produced from the detected energy. The geophysical data product may include processed seismic geophysical data and may be stored on a non-transitory, tangible computer-readable medium. The geophysical data product may be produced offshore (i.e. by equipment on a vessel) or onshore (i.e. at a facility on land) either within the United States or in another country. If the geophysical data product is produced offshore or in another country, it may be imported onshore to a facility in the United States. Once onshore in the United States, geophysical analysis may be performed on the data product. 
     The foregoing figures and discussion are not intended to include all features of the present techniques to accommodate a buyer or seller, or to describe the system, nor is such figures and discussion limiting but exemplary and in the spirit of the present techniques.