EP0109341A2 — Diffraction tomography systems and methods

Claim 1

Independent Claim 236 words

A method for the reconstruction of a three-dimensional object which has diffracted waves of energy propagating through it at at least one view angle on a plane and for at least one planar orientation, comprising the steps of: a) obtaining signals which are a function of at least one of the phase and amplitude of each propagating wave after said wave has interacted with said object; and characterized by b) preprocessing and separating said obtained signals to obtain sets of preprocessed signals, each set representing the signals obtained from the propagation of an energy wave at a separate view angle wherein said preprocessing and separating step comprises additionally separating said obtained signals into second sets of signals, each second set of signals representing the signals obtained from the propagation of an energy wave at a separate planar orientation, wherein by said converting step, the two-dimensional planar projected reconstruction obtained is for each planar orientation, and a three-dimensional reconstruction of the object can be obtained from a plurality of two-dimensional planar projection reconstructions; c) converting said sets of preprocessed signals by means of a filtered cackpropagation technique into arrays representing the partial reconstruction of the object; d) interpolating each partial reconstruction onto a master array to obtain the two-dimensional reconstruction of a planar projection of the object; and e) displaying a reconstruction of a planar section of said object which was reconstructed from said two-dimensional planar projections.

Claim 2

Independent Claim 236 words

A method for the reconstruction of a three-dimensional object which has diffracted waves of energy propagating through it at at least one view angle on a plane and for at least one planar orientation, comprising the steps of: a) obtaining signals which are a function of at least one of the phase and amplitude of each propagating wave after said wave has interacted with said object; and characterized by b) preprocessing and separating said obtained signals to obtain sets of preprocessed signals, each set representing the signals obtained from the propagation of an energy wave at a separate view angle wherein said preprocessing and separating step comprises additionally separating said obtained signals into second sets of signals, each second set of signals representing the signals obtained from the propagation of an energy wave at a separate planar orientation, wherein by said converting step, the two-dimensional planar projected reconstruction obtained is for each planar orientation, and a three-dimensional reconstruction of the object can be obtained from a plurality of two-dimensional planar projection reconstructions; c) converting said sets of preprocessed signals by means of a filtered cackpropagation technique into arrays representing the partial reconstruction of the object; d) interpolating each partial reconstruction onto a master array to obtain the two-dimensional reconstruction of a planar projection of the object; and e) displaying a reconstruction of a planar section of said object which was reconstructed from said two-dimensional planar projections.

Claim 3

Independent Claim 252 words

A system for the reconstruction of a three-dimensional object which has diffracted waves of energy propagating through it at at least on view angle on a plane for at at least one planar orientation, comprising: a) means for obtaining signals which are a function of at least one of the phase and amplitude of each propagating wave after said wave has interacted with said object; and characterized by b) preprocessing and separating means for separating and preprocessing said obtained signals to obtain sets of preprocessed signals, each set representing the signals obtained from the propagation of an energy wave at a separate view angle wherein said preprocessing and separating means comprise means for separating said sets of preprocessed signals into second sets of signals, each second set of signals representing the signals obtained from the propagation of an energy wave at a separate planar orientation, wherein the two-dimensional planar projected reconstructions obtained are for each planar orientation, and by said filtering a three-dimensional reconstruction of the object can be obtained from a plurality of two-dimensional planar projected reconstructions; c) filter means for converting said sets of preprocessed signals into arrays representing the partial reconstruction of the object by means of a filtered backpropagation technique; d) interpolation means for interpolating each partial reconstruction array onto a master array to obtain the two-dimensional reconstruction of a planar projection of the object; and g) display means for displaying a reconstruction of a planar section of said object which was reconstructed from said two-dimensional planar projections.

Claim 4

Independent Claim 252 words

A system for the reconstruction of a three-dimensional object which has diffracted waves of energy propagating through it at at least on view angle on a plane for at at least one planar orientation, comprising: a) means for obtaining signals which are a function of at least one of the phase and amplitude of each propagating wave after said wave has interacted with said object; and characterized by b) preprocessing and separating means for separating and preprocessing said obtained signals to obtain sets of preprocessed signals, each set representing the signals obtained from the propagation of an energy wave at a separate view angle wherein said preprocessing and separating means comprise means for separating said sets of preprocessed signals into second sets of signals, each second set of signals representing the signals obtained from the propagation of an energy wave at a separate planar orientation, wherein the two-dimensional planar projected reconstructions obtained are for each planar orientation, and by said filtering a three-dimensional reconstruction of the object can be obtained from a plurality of two-dimensional planar projected reconstructions; c) filter means for converting said sets of preprocessed signals into arrays representing the partial reconstruction of the object by means of a filtered backpropagation technique; d) interpolation means for interpolating each partial reconstruction array onto a master array to obtain the two-dimensional reconstruction of a planar projection of the object; and g) display means for displaying a reconstruction of a planar section of said object which was reconstructed from said two-dimensional planar projections.

Claim 5

Independent Claim 78 words

A method for reconstruction of a subsurface geological formation which has diffracted at least one wave of energy propagating through it characterized by the steps of: a) obtaining signals which are a function of at least one of the phase and amplitude of the diffracted propagating wave after said wave has interacted with said formation; and b) converting said signals by means of a filtered backpropagation technique into an array representing the partial reconstruction profile of the formation.

Claim 6

Independent Claim 78 words

A method for reconstruction of a subsurface geological formation which has diffracted at least one wave of energy propagating through it characterized by the steps of: a) obtaining signals which are a function of at least one of the phase and amplitude of the diffracted propagating wave after said wave has interacted with said formation; and b) converting said signals by means of a filtered backpropagation technique into an array representing the partial reconstruction profile of the formation.

Claim 7

Dependent Claim 96 words

A method according to claim 3 wherein said at least one wave of energy approximates a cylindrical wave at at least one phase tilt, and characterized by: c) separating said obtained signals into sets of signals, each set of signals representing the signals obtained from the propagation of an energy wave at a separate phase tilt, wherein by said converting step each set of signals is converted into a separate array representing phase tilt; and d) interpolating said partial reconstruction array onto a master array, wherein the master array represents the two-dimensional reconstruction of said formation..

Claim 8

Dependent Claim 45 words

A method according to claim 4 characterized by: preprocessing signals after said obtaining step and before said converting step, wherein said signals or said converting step are obtained to provide signals which have been both preprocessed and separated according to said separating and preprocessing steps.

Claim 9

Dependent Claim 18 words

A method according to claim 4 or 5 characterized by: displaying said two-dimensional reconstruction of said subsurface formation.

Claim 10

Independent Claim 79 words

A system for reconstruction of a subsurface geological formation which has diffracted at least one wave of energy propagating through it characterized by: a) means for obtaining signals which are a function of at least one of the phase and amplitude of the diffracted propagating wave after said wave has interacted with said formation; and b) filter means for converting said signals by means of a filtered backpropagation technique into an array representing a partial reconstruction of the formation.

Claim 11

Independent Claim 79 words

A system for reconstruction of a subsurface geological formation which has diffracted at least one wave of energy propagating through it characterized by: a) means for obtaining signals which are a function of at least one of the phase and amplitude of the diffracted propagating wave after said wave has interacted with said formation; and b) filter means for converting said signals by means of a filtered backpropagation technique into an array representing a partial reconstruction of the formation.

Claim 12

Dependent Claim 112 words

A system according to claim 7 wherein said at least one wave of energy approximates at least one cylindrical wave at at least one phase tilt, and characterize by: c) means for separating said obtained signals into sets of signals, each set of signals representing the signals obtained from the propagation of an energy wave at a separate phase tilt, wherein said filter means filter and converts each set of signals into a separate array repreenting the partial reconstruction of the formation at the separate phase tilt; and d) interpolation means for interpolating said partial reconstruction array onto a master array, wherein the master array represents the two-dimensional reconstruction of said formation.

Claim 13

Dependent Claim 58 words

A system according to claim 8 characterized by: preprocessing means for preprocessing signals which have been obtained by said obtaining means but have not yet been converted by said filter means wherein said signals converted by said filter means are obtained signals which have been both preprocessed and separated by said means for separating and means for preprocessing.

Claim 14

Dependent Claim 20 words

A system according to claim 8 or 9 characterized by: display means for displaying said two-dimensional reconstruction of said formation.

Claim 15

Dependent Claim 196 words

ll. A method for tomographic reconstruction of a two-dijnensional object comprising: a) directing at a view angle one or more waves of energy toward an object being examined; b) detecting as a function of time the one or more fields produced by said one or more waves; c) producing one or more signals which are functions of said one or more detected fields; d) filtering said produced signals according to a filtered backpropagaation technique to generate a two-dimensional array representing the partial rconstruction of the object; e) interpolating said partial reconstruction onto a master array; f) changing said view angle; g) repeating steps a-f at different view angles to obtain a two-dimensional reconstruction of the object; and characterized by h) preprocessing said produced signals before said filtering step, wherein said produced signals filtered by said backpropagation filter are preprocessed signals; i) converting said one or more produced signals from analog to digital form; j) transforming said digital signals over time with a Fourier transform; k) normalizing said transformed signals; 1) complex phase converting said normalized signals; and m) phase unwrapping said complex phase converted signals to produce a one-dimensional array for input into said filtering step.

Claim 16

Dependent Claim 196 words

ll. A method for tomographic reconstruction of a two-dijnensional object comprising: a) directing at a view angle one or more waves of energy toward an object being examined; b) detecting as a function of time the one or more fields produced by said one or more waves; c) producing one or more signals which are functions of said one or more detected fields; d) filtering said produced signals according to a filtered backpropagaation technique to generate a two-dimensional array representing the partial rconstruction of the object; e) interpolating said partial reconstruction onto a master array; f) changing said view angle; g) repeating steps a-f at different view angles to obtain a two-dimensional reconstruction of the object; and characterized by h) preprocessing said produced signals before said filtering step, wherein said produced signals filtered by said backpropagation filter are preprocessed signals; i) converting said one or more produced signals from analog to digital form; j) transforming said digital signals over time with a Fourier transform; k) normalizing said transformed signals; 1) complex phase converting said normalized signals; and m) phase unwrapping said complex phase converted signals to produce a one-dimensional array for input into said filtering step.

Claim 17

Dependent Claim 80 words

A method according to claim 11 wherein said detected wave of energy is a very short pulse and said preprocessing step is characterized by: converting said produced signal from analog to digital form; timing the delay between the directing and detecting of said pulse; measuring the peak amplitude of said detected fields; and providing said time delay and measured peak amplitude for unwrapped complex phase converting said converted signals to produce a one-dlmensioanl array for input into said filtering step.

Claim 18

Independent Claim 207 words

A method for tomographic reconstruction of a three-dimensional object characterized by: a) directing at a view angle on a plane one or mre waves of energy toward an object being examined; b) detecting as a function or time the one or more fields produced by said one or more waves; c) producing one or more signals which are functions of said one or more detected fields; d) preprocessing said produced signals; e) filtering said preprocessed signals according to a filtered backpropagation technique to generate a two-dimensional array representing the partial reconstruction of the object; f) interpolating said partial reconstruction array onto a master array; g) changing said view angle on said plane; h) repeating steps a-g at different view angles on said plane to obtain a two-dimensional reconstruction of a planar projection of the object; i) changing said plane on which said waves of energy are directed at a view angle; j) repeating steps a-i at a sufficient number of different planes to obtain a plurality of planar projectins of the three-dimensional object profile from which a full three-dimensional reconstruction of the object profile can be obtained; and k) displaying a reconstruction of a planar section of said object profile which is obtained from said planar projections.

Claim 19

Independent Claim 207 words

A method for tomographic reconstruction of a three-dimensional object characterized by: a) directing at a view angle on a plane one or mre waves of energy toward an object being examined; b) detecting as a function or time the one or more fields produced by said one or more waves; c) producing one or more signals which are functions of said one or more detected fields; d) preprocessing said produced signals; e) filtering said preprocessed signals according to a filtered backpropagation technique to generate a two-dimensional array representing the partial reconstruction of the object; f) interpolating said partial reconstruction array onto a master array; g) changing said view angle on said plane; h) repeating steps a-g at different view angles on said plane to obtain a two-dimensional reconstruction of a planar projection of the object; i) changing said plane on which said waves of energy are directed at a view angle; j) repeating steps a-i at a sufficient number of different planes to obtain a plurality of planar projectins of the three-dimensional object profile from which a full three-dimensional reconstruction of the object profile can be obtained; and k) displaying a reconstruction of a planar section of said object profile which is obtained from said planar projections.

Claim 20

Dependent Claim 52 words

A method according to claim 13 characterized in that said preprocessing step comprises: projecting a two-dimensional array of said produced 'signals onto the line formed by the intersection of the detecting plane with the plane of rotation of the directing-detecting system to produce a one-dimensional array for input into said filtering steps.

Claim 21

Dependent Claim 64 words

. 15. A method according to claim 14 characterized in that said preprocessing step further comprises: converting said produced signal from analog to digital form; transforming said digital signals over time with a Fourier transform; normalizing said transformed signals; complex phase converting said normalized signals; and phase unwrapping said complex phase converted signals to produce a one-dimensional array for input into said filtering step.

Claim 22

Dependent Claim 76 words

A method according to claim 13 wherein said directed wave of energy is a very short pulse and said preprocessing step is characterized by: converting said produced signal from analog to digital form; timing the delay between the directing and detecting of said pulse; measuring the peak amplitude of said detected fields; and unwrapped complex phase converting said delay time and peak aplitude measured signals to produce a one-dimensional array for input into said filtering step.

Claim 23

Independent Claim 184 words

A system for tomographic reconstruction of a two-dimensional object comprising: a) one or more sources of waves of energy directed at a view angle at an object; b) one or more detecting means for detecting as a function of time the one or more fields produced by the waves interacting with said object; c) signal producing means for producing signals which are functions of said fields; d) filter means for filtering said produced signals according to a backpropagation technique to generate a two-dimensional array representing the partial reconstruction of the object; and e) interpolation means for interpolating said partial reconstruction array onto a master array; f) view angle changing means for chaning said view angle; and characterized by g) preprocessing means for preprocessing said signals produced by said signal producing means; h) an analog to digital converter for converting said detected signals; i) a Fourier transformer for transforming said converted signals; j) a normalizer for normalizing said transformed signals; k) complex phase converting means for complex phase converting said normalized signals; and 1) phase unwrapping mean for phase unwrapping said complex phase converted signals.

Claim 24

Independent Claim 184 words

A system for tomographic reconstruction of a two-dimensional object comprising: a) one or more sources of waves of energy directed at a view angle at an object; b) one or more detecting means for detecting as a function of time the one or more fields produced by the waves interacting with said object; c) signal producing means for producing signals which are functions of said fields; d) filter means for filtering said produced signals according to a backpropagation technique to generate a two-dimensional array representing the partial reconstruction of the object; and e) interpolation means for interpolating said partial reconstruction array onto a master array; f) view angle changing means for chaning said view angle; and characterized by g) preprocessing means for preprocessing said signals produced by said signal producing means; h) an analog to digital converter for converting said detected signals; i) a Fourier transformer for transforming said converted signals; j) a normalizer for normalizing said transformed signals; k) complex phase converting means for complex phase converting said normalized signals; and 1) phase unwrapping mean for phase unwrapping said complex phase converted signals.

Claim 25

Dependent Claim 91 words

A system according to claim 17 wherein said detected wave of energy comprises a very short pulse and said preprocessing means is characterized by: ' an analog to digital converter; delay timing means for timing the delay time between the directing and detecting of said pulse; amplitude measuring means for measuring the peak amplitude of said detected fields; and means for receiving the outputs of said delay timing means and amplitude measuring means and for converting said timed and measured signals into a two-dimensional array for input into said filter means.

Claim 26

Independent Claim 187 words

A system for tomographic reconstruction of a three-dimensional object characterized by: a) one or more source of waves of energy directed at a view angle on a plane at an object; b) one or more detecting means for detecting as a function of time the one or more fields produced by the waves interacting with said object; c) signal producing means for producing signals which are functions of said one or more fields; d) preprocessing means for preprocessing said produced signals; e) filter means for filtering said preprocessed signals according to a filtered backpropagation technique to generate a two-dimensional array representing the partial reconstruction of the object; f) interpolation means for interpolating said partial reconstruction array onto a master array; g) view angle changing means for changing said view angle, wherein a two-dimensional planar projection reconstruction maybe obtained; h) plane changing means for changing said plane on which said energy waves are directed at said view angles, wherein a three-dimensional reconstruction may be obtained; and i) display means for displaying a reconstruction of a planar section of said object which is obtained from said planar projection reconstructions.

Claim 27

Independent Claim 187 words

A system for tomographic reconstruction of a three-dimensional object characterized by: a) one or more source of waves of energy directed at a view angle on a plane at an object; b) one or more detecting means for detecting as a function of time the one or more fields produced by the waves interacting with said object; c) signal producing means for producing signals which are functions of said one or more fields; d) preprocessing means for preprocessing said produced signals; e) filter means for filtering said preprocessed signals according to a filtered backpropagation technique to generate a two-dimensional array representing the partial reconstruction of the object; f) interpolation means for interpolating said partial reconstruction array onto a master array; g) view angle changing means for changing said view angle, wherein a two-dimensional planar projection reconstruction maybe obtained; h) plane changing means for changing said plane on which said energy waves are directed at said view angles, wherein a three-dimensional reconstruction may be obtained; and i) display means for displaying a reconstruction of a planar section of said object which is obtained from said planar projection reconstructions.

Claim 28

Dependent Claim 55 words

A system according to claim 19 characterized in that said preprocessing means comprises: projection calculating means for projecting the two-dimensional array produced by said signal producing means onto a line formed by the intersection of the plane of said detecting means and the plane of rotation of said object of said source and detecting means.

Claim 29

Dependent Claim 62 words

A system according to claim 19 characterized in that said preprocessing means further comprises: an analog to digital converter for converting said detected signals; a Fourier transformer for transforming said converted signals; a normalizer for normalizing said transformed signals; complex phase converting means for complex phase converting said normalized signals; and phase unwrapping mean for phase unwrapping said complex phase converted signals.

Claim 30

Dependent Claim 89 words

A system according to claim 19 wherein said directed wave of energy comprises a very short pulse and said preprocessing means is characterized by: an analog to digital converter; delay timing means for timing the delay between the directing and detecting of said pulse; amplitude measuring means for measuring the peak amplitude of said detected fields; and means for receiving the outputs of said delay timing means and amplitude measuring means and for converting said timed and measured signals into a two-dimensional array for input into said filter means.

Claim 31

Independent Claim 98 words

A method for tomographic reconstruction of a subsurface formation characterized by: a) directing one or more waves of energy into said formation, the totality of said waves approximating one or more cylindrical waves of a given phase tilt; b) detecting as a function of time the one or more fields produced by said one or more waves; c) producing one or more signals which are functions of said one or more detected fields; and d) filtering said produced signals according to a filtered backpropagation technique to generate a two-dimensional array representing the partial reconstruction of the subsurface formation.

Claim 32

Independent Claim 98 words

A method for tomographic reconstruction of a subsurface formation characterized by: a) directing one or more waves of energy into said formation, the totality of said waves approximating one or more cylindrical waves of a given phase tilt; b) detecting as a function of time the one or more fields produced by said one or more waves; c) producing one or more signals which are functions of said one or more detected fields; and d) filtering said produced signals according to a filtered backpropagation technique to generate a two-dimensional array representing the partial reconstruction of the subsurface formation.

Claim 33

Dependent Claim 52 words

A method for tomographic reconstruction of a subsurface formation according to claim 23 characterized by: e) interpolating said partial reconstruction onto a master array: f) changing the phase tilt of said directed waves; and g) repeating steps a-f at different phase tilts to obtain a partial two-dimensional reconstruction of the subsurface formation.

Claim 34

Dependent Claim 16 words

A method according to claim 24 characterized by: displaying said partial reconstruction of said subsurface formation.

Claim 35

Dependent Claim 40 words

A method according to claim 24 characterized in that: said one or more directed waves are directed from the surface of said formation towards at least one borehole in said formation, said detecting occurring in said at least one borehole.

Claim 36

Dependent Claim 38 words

A method according to claim 24 characterized in that: said one or more directed waves are directed from at least one borehole in said formation towards the surface of said earth formation, said detecting occurring on said surface.

Claim 37

Dependent Claim 44 words

A method according to claim 24 characterized in that: said one or more directed waves are directed from at least one borehole in said formation toward at least one other borehole in said formation, said detecting occurring in said at least one other borehole

Claim 38

Dependent Claim 57 words

A method according to claim 24 characterized in that: said directed waves are directed from at least one borehole in said formation toward at least one other borehole in said formation and toward the surface of said formation, said detecting occurring in said at least one other borehole in said formation and on or above said surface.

Claim 39

Dependent Claim 23 words

A method according to claim 24 characterized by: preprocessing said produced signals wherein said produced signals of said filtering step are preprocessed signals.

Claim 40

Dependent Claim 35 words

A method according to claim 24 characterized in that: said directed waves are produced by spherical wave point source emitters which approximate a cylindrical wave by pulsing with a variable phase delay between each emitter.

Claim 41

Dependent Claim 41 words

A method according to claim 30 characterized in that: said directed waves are produced by spherical wave point source emitters which in conjunction with said preprocessing approximate a cylindrical wave by sequentially pulsing, wherein said preprocessing comprises stacking the detected signals.

Claim 42

Dependent Claim 60 words

A method according to claim 30 characterized in that said preprocessing step comprises: converting said produced signals from analog to digital form: transforming said analog signals over time with a Fourier transform; normalizing said transformed signals; complex phase converting said normalized signals; and phase unwrapping said complex phase converted signals.to produce a one-dimensional array for input into said filtering step.

Claim 43

Dependent Claim 94 words

A method according to claim 30 characterized in that said directed wave of energy comprises a very short pulse and said preprocessing step comprises: an analog to digital converter; delay timing means for timing the delay time between the directing and detecting of said one or more energy waves; amplitude measuring means for measuring the peak amplitude of said one or more detected fields; and providing said timed delay and measured peak amplitude for unwrapped complex phase converting said timed and measured signals to produce a two-dimensional array for input into said filter means.

Claim 44

Dependent Claim 47 words

A method according to claim 30 characterized in that said preprocessing step comprises: converting said produced signals from analog to digital form; transforming said analog signals over time with a Fourier transformer; normalizing said to transform signals; and processing said normalized signals according to the Born approximation.

Claim 45

Dependent Claim 35 words

A method according to claim 24 characterized in that said filtering step comprises: filtering said preprocessed signals with a convolutional phase-tilt dependent deblurring filter; and backpropagating the filtered preprocessed signals according to a backpropagation filter.

Claim 46

Dependent Claim 139 words

A method according to claim 36 characterized in that: said preprocessed signals are filtered and backpropagated according to a filtered backpropagation technique wherein q,m is a filtered backpropagation technique for object depth x q , and m indexes sample values of preprocessed signals; m is a convolutional, phase-tilt dependent deblurring filter; γ m = k , where M is the number of detectors detecting said fields; k is the wavenumber associated with the frequency of said directed waves; x is the distance of the investigated object depth q from the axis of rotation of said object; is the x axis unit vector; 1 o is the distance between the axis of rotation of said object and the detector array; and s o .r is a scalar product between the unit propation vector s o and the position vector r.

Claim 47

Independent Claim 121 words

A system for tomographic reconstruction of a subsurface earth formation characterized by: a) one or more sources of waves of energy directed at said earth formation, wherein the totality of the waves of said one or more sources approximate one or more cylindrical waves of a given phase tilt; b) one or more detecting means for detecting as a function of time the one or more fields produced by the waves interacting with said earth formation; c) signal producing means for producing signals which are a function of said one or more fields; and d) filter means for filtering said produced signals according to a filtered backpropagation technique to generate a two-dimenstional array representing the partial reconstruction of the subsurface formation.

Claim 48

Independent Claim 121 words

A system for tomographic reconstruction of a subsurface earth formation characterized by: a) one or more sources of waves of energy directed at said earth formation, wherein the totality of the waves of said one or more sources approximate one or more cylindrical waves of a given phase tilt; b) one or more detecting means for detecting as a function of time the one or more fields produced by the waves interacting with said earth formation; c) signal producing means for producing signals which are a function of said one or more fields; and d) filter means for filtering said produced signals according to a filtered backpropagation technique to generate a two-dimenstional array representing the partial reconstruction of the subsurface formation.

Claim 49

Dependent Claim 53 words

A system for tomographic reconstruction of a subsurface earth formation according to claim 38 characterized by: e) interpolation means for interpolating said partial reconstruction array onto a master array; and f) phase tilt changing means for changing the phase tilt of said one or more waves of energy directed into said earth format.

Claim 50

Dependent Claim 27 words

A system for tomographic reconstruction of a subsurface earth formation comprising claim 39 characterized by: g) display means for displaying said two-dimensional reconstruction of the earth formation.

Claim 51

Dependent Claim 41 words

A system according to claim 39 characterized by: said one or more sources of waves are located on the surface of said earth formation; and said one more detecting means are located in at least one borehole in said earth formation.

Claim 52

Dependent Claim 42 words

A system according to claim 39 characterized in that: said one or more sources of waves are located in at least one borehole of said earth formation; and said one or more detecting means are located on the surface of said formation.

Claim 53

Dependent Claim 47 words

A system according to claim 39 characterized in that: said one or more source of waves are located in at least one borehole in said earth formation formation; and said one or more detecting means are located in at least one other borehole in said earth formation.

Claim 54

Dependent Claim 26 words

A system according to claim 39 characterized by: preprocessing means for preprocessing said produced signals, wherein said produced signals of said filter means are preprocessed signals.

Claim 55

Dependent Claim 39 words

A system according to claim 39 characterized by: said one or more sources of waves are a plurality of spherical wave point source emitters which approximate a cylindrical wave by emitting with a variable phase delay between each source.

Claim 56

Dependent Claim 50 words

A system according to claim 44 characterized by: said one or more sources of waves comprise a plurality of spherical wave point source emitters which in conjunction with said preprocessing means approximate a cylindrical wave by sequentially pulsing, wherein said preprocessing means comprises a stacker for stacking said detected signal.

Claim 57

Dependent Claim 81 words

A system accoring to claim 44 characterized in that said preprocessing means comprises; converting means for converting said produced signals from anolog to digital form; Fourier transforming means for transforming said analog signals over time with a Fourier transformer; normalizing means for normalizing said Fourier transformed signals; complex phase converting means for complex phase convering said normalizing signals; and phase unwrapping means for phase unwrapping said complex phase converted signals to produce a one-dimensional array for input into said filtering step.

Claim 58

Dependent Claim 89 words

A system according to claim 44 characterized in that said directed wave of energy comprises a very short pulse and said preprocessing means comprises; an analog to digital converter; delay timing means for timing the delay between the directing and detecting of said pulse; amplitude measuring means for measuring the peak amplitude of said detected fields; and means for receiving the outputs of said delay timing means and amplitude measuring means and for converting said timed and measured signals into a two-dimensional array for input into said filter means.

Claim 59

Dependent Claim 57 words

A system according to claim 44 characterized in that said preprocessing means comprises: an analog to digital converter for converting said produced signals for analog to digital form; a Fourier transformer for transforming said signals over time; a normalizer for normalizing said transformed signals, and a processor for processing said normalized signals according to the Born approximation.

Claim 60

Dependent Claim 28 words

The system of claim 38 characterized in that said filtering means comprises: ccnvolutional, phase-tilt dependent, deblurring filtering means; and backprogation filter means for backpropagating the filtered preprocessed signals.

Claim 61

Dependent Claim 143 words

A system according to claim 50 characterized in that: said preprocessed signals are filtered and backpropagated according to a filtered backpropagation technique wherein q , m is a filtered backpropagation technique for object depth x q , and m indexes sample values of preprocessed signals; m is a convolutional, phase-tilt dependent, deblurring filter; γ m = k , where M is the number of detectors detecting said fields; k is the wavenumber associated with the frequency of said directed waves; x q is the distance of the investigated object depth q from the axis of rotation of said object; x is the x axis unit vector; l o is the distance between the axis of rotation of said object and the detector array; and s o . r is a scalar product between the unit propagation vector s and the position vector r.

Diffraction tomography systems and methods

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