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What is claimed and desired to be secured by U.S. Letters Patent is as follows:
1. A method of producing an image of an object in a region from wavefield energy that has been transmitted into and
scattered by the object, said image comprising a map of selected physical characteristics at selected points within the region, said image being stored in a computer memory, and said method comprising the steps of:
(a) transducing an electric signal at each of one or more frequencies into wavefield energy propagated from one or more of transmitter transducer positions, each said transmitter transducer position propagating wavefield energy at at least one
orientation defined by Euler angles with respect to a selected fixed coordinate system;
(b) for one or more receiver positions each having at least one orientation defined by Euler angles with respect to said selected fixed coordinate system, detecting at each of said one or more receiver positions and respective orientations
thereof said wavefield energy;
(c) electronically processing said detected wavefield energy so as to transform said detected wavefield energy into one or more reception stored signals stored in said computer memory and corresponding to a scattered wavefield energy detected;
(d) setting a region characteristics estimate of selected physical characteristics at selected points within the region and storing each said region characteristics estimate in said computer memory;
(e) performing a convergence step comprising the following steps:
(1) preparing, for each said one or more frequencies at each said transmitter transducer positions and respective orientations thereof, an estimate of a total wavefield energy at said selected points derived from a selected incident wavefield
energy for said selected points stored in the computer memory and said region characteristics estimate for said selected points by the steps of:
(i) designating a primary set of surfaces of a plurality of selected surfaces and a different secondary set of surfaces of said selected surfaces, each said selected surface intersecting said region;
(ii) setting the estimate of the total wavefield energy equal to an initial total incident wavefield energy estimate for the primary set of surfaces;
(iii) computing the estimate of the total wavefield energy on the secondary set of surfaces using the region characteristics estimate on the union of the primary and secondary sets of surfaces and the total wavefield energy on the primary set of
surfaces;
(iv) re-designating the primary set of surfaces to include a sub- set of the secondary set of surfaces and re-designating the secondary set of surfaces to include another set of the selected surfaces; and
(v) repeating steps ((iii) through ((iv)) until the estimate of the total wavefield energy is computed for each of the selected surfaces;
(2) deriving, for each of said one or more frequencies at each said transmitter transducer position and orientations thereof, a calculated scattered wavefield energy for one or more of said receiver positions and respective orientations thereof
from at least one of said region characteristics estimate at said selected points and said estimate of said total wavefield energy for a corresponding transmitter transducer position and orientations thereof at said selected points by one or more of the
following:
(i) designating an external surface situated outside said object, and then approximating an integral on the external surface by the sum of:
(a) a first quantity times the estimate of the total wavefield energy on said external surface times a derivative of a Green's function constructed to map to one or more of said receiver positions and respective orientations thereof; and
(b) a second quantity times a derivative of the estimate of the total wavefield energy on said external surface times a Green's function constructed to map to one or more of said receiver positions and respective orientations thereof;
(ii) approximating an integral on at least a portion of the region of the product of:
(a) the estimate of the total wavefield energy at said selected points;
(b) the region characteristics estimate at said selected points; and
(c) a Green's function constructed to map to one or more of said receiver positions and respective orientations thereof;
(iii) performing the steps of:
(a) for each selected point of a portion of the selected points, said potion of the selected points corresponding to one of said one or more receiver positions and respective orientations thereof, setting said calculated scattered wavefield
energy equal to the estimate of the total wavefield energy less said selected incident wavefield energy; and
(b) computing a sum over said portion of said selected points equal to the sum of the calculated scattered wavefield energy for said portion of said selected points times a function constructed to correspond to one or more of said one or more
receiver positions and respective orientations thereof,
(3) for each said transmitter transducer position and orientations thereof and for each said receiver position and orientation thereof, comparing said scattered wavefield energy detected to said calculated scattered wavefield energy to derive
therefrom a comparator; and
(4) when said comparator is greater than a selected tolerance, determining and storing in said computer memory said region characteristics estimate by computing one or more derivatives of the comparator or approximations thereof with respect to
one or more of said selected physical characteristics at one or more of said selected points, and then using said one or more derivatives of the comparator or approximations thereof to compute a region characteristics correction, and then adding said
region characteristics correction to each of said region characteristics estimate for each of said one or more of said selected points, wherein said one or more derivatives of the comparator or approximations thereof is computed from one or more of:
(i) at each said one or more frequencies, said estimate of said total wavefield energy for said selected points for each of said one or more of said transmitter transducer positions and respective orientations thereof;
(ii) at each of said one or more frequencies, said calculated scattered wavefield energy for said one or more receiver positions and respective orientations thereof, and for each of said one or more of said transmitter transducer positions and
respective orientations thereof;
(iii) at each of said one or more frequencies, said scattered wavefield energy detected for said one or more receiver positions and respective orientations thereof, and for each of said one or more of said transmitter transducer positions and
respective orientations thereof, and
(iv) said region characteristics estimate for said selected points;
(f) repeating said convergence step until said comparator is less than or equal to said selected tolerance, and thereafter storing said region characteristics estimate as said image in the computer memory.
2. A methods as defined in claim 1, wherein said convergence step is a Gauss-Newton step computed using conjugate gradients.
3. A method as defined in claim 1, wherein:
A. model calibration parameters and an imaging system simulation model of said imaging device are used to compute at least one of:
(i) said selected incident wavefield energy and said Green's function constructed to map to one or more of said receiver positions and respective orientations thereof;
(ii) said selected incident wavefield energy and said Green's function constructed to map to one or more of said receiver positions and respective orientations thereof; and
(iii) said selected incident wavefield energy and said function constructed to correspond to one or more of said receiver positions and respective orientations thereof;
B. said model calibration parameters comprising at least one of:
(i) one or more transmitter equivalent source vectors, said one or more transmitter equivalent source vectors being input to one or more transmitter simulators, said one or more transmitter simulators outputting one or more simulated transmitter
wavefields of said interrogating wavefield energy;
(ii) one or more receiver equivalent source vectors, said one or more receiver equivalent source vectors being input to one or more receiver simulators, said one or more receiver simulators outputting one or more simulated receiver sensitivity
functions, said one or more receiver sensitivity functions being electrical responses of said one or more receiver simulators to a point source of interrogating wavefield energy placed at substantially any location in said region;
(iii) one or more transmitter simulation positions, each said one of more transmitter simulation positions having one or more transmitter simulation orientations, each said one or more transmitter simulation orientations being defined by Euler
angles;
(iv) one or more receiver simulation positions, each said one of more receiver simulation positions having one or more receiver simulation orientations, each said one or more receiver simulation orientations being defined by Euler angles; and
(v) one or more electronic system parameters of said imaging device, said electronic system parameters substantially characterizing the analog and digital electronic functions of said imaging device,
C. said calibration parameters are derived by the steps of:
(i) collecting a received wavefield energy by a process comprising the steps of:
I. choosing a substantially known matter distribution in said region from a selected set of one or more substantially known matter distributions;
II. choosing one of said one of more transmitter transducers at one of said one or more transmitter positions and at one of said one or more transmitter orientations;
III. choosing one of said one of more receiver transducers at one of said one or more receiver positions and at one of said one or more receiver orientations;
IV. transmitting interrogating wavefield energy from said one of said one of more transmitter transducers at one of said one or more transmitter positions and at one of said one or more transmitter orientations into said region;
V. receiving interrogating wavefield energy at said one of said one or more transducer receivers at one of said one or more receiver positions and at one of said one or more receiver orientations;
VI. repeating C(III) through C(IV) until a selected portion of said one or more receiver transducers at said one or more receiver positions and orientations thereof have been chosen;
VII. repeating steps C(II) through C(VI) until a selected portion of said one or more transmitter transducers at said one or more transmitter positions and orientations thereof have been chosen;
VIII. repeating steps C(I) through C(VII) until all of said selected set of one or more substantially known matter distributions have been chosen;
(ii) constructing said imaging system simulation model of said imaging device and said imaging process used therewith with an input equal to said model calibration parameters and an output equal to a predicted received wavefield energy, said
predicted received wavefield energy being an approximation of said received wavefield energy, said imaging system simulation model being derived from at least one of:
I. a mathematical theory of said interrogating wavefield energy;
II. a simulation model of the analog and digital electronic functions of said imaging device;
III. said one or more transmitter simulators; and
IV. said one or more receiver simulators;
(iii) setting a portion of said model calibration parameters equal to selected values;
(iv) solving for substantially all other portions of said model calibration parameters using the steps of:
I. defining a comparator, said comparator being a positive scaler value that is a measure of the difference between said received wavefield energy and said predicted received wavefield energy; and
II. using an optimization algorithm to substantially minimize said comparator with respect to said substantially all other portions of said model calibration parameters until said comparator is less than a selected tolerance;
(v) storing said model calibration parameters in a computer memory.
4. A method as defined in claim 1, wherein said convergence step is a Ribiere-Polak step.
5. A method as defined in claim 1, wherein said estimate of said total wavefield energy at said selected points derived from said selected incident wavefield energy for said selected points is prepared, at least in part, by a fast Fourier
transform.
6. A method as defined in claim 1, wherein said scattered wavefield energy detected includes a digital representation of said wavefield energy propagating both into and through said region.
7. A method as defined in claim 1, wherein said step of transducing said electric signal at each of one or more frequencies into wavefield energy propagated from one or more of transmitter transducer positions, each said transmitter transducer
position propagating wavefield energy comprises the steps of:
positioning a transducer array adjacent to said object, said transducer array comprising said one or more of transmitter transducer positions and said one or more receiver positions;
sending said electric signal at a first frequency to each said transmitter transducer positions so that each said transmitter transducer positions will in turn propagate wavefield energy at said first frequency; and
thereafter changing the frequency of said signal and sending said electrical signal at said changed frequency to each said transmitter transducer position so as to sequentially propagate wavefield energy from each said transmitter transducer
position at said changed frequency.
8. A method as defined in claim 7, wherein said transducer array is configured to enclose at least a portion of said object.
9. A method as defined in claim 1, wherein said step of transducing said electric signal at each of one or more frequencies into wavefield energy propagated from one or more of transmitter transducer positions, each said transmitter transducer
position propagating wavefield energy, comprises the steps of:
positioning a transducer array adjacent to at least a portion of said region, said transducer array comprising said one or more of transmitter transducer positions and said one or more receiver positions;
generating said electric signal in the form of a waveform which is characterized by one or more different frequencies; and
sending said generated waveform in turn to each said transmitter transducer position so as to propagate wavefield energy at said one or more frequencies from each said transmitter transducer position.
10. A method as defined in claim 9, wherein said transducer array is configured to enclose at least a portion of said region.
11. A method as defined in claim 1, wherein said step of detecting at each of said one or more receiver positions and respective orientations thereof said wavefield energy comprises the steps of:
positioning a transducer array adjacent to said object, said transducer array comprising said one or more of transmitter transducer positions and said one or more receiver positions; and
after wavefield energy is transmitted from one of said transmitter transducer positions, sequencing each of said one or more receiver positions so as to detect said scattered wavefield energy at each of said one or more receiver positions in
turn.
12. A method as defined in claim 11, wherein said step of electronically processing said detected wavefield energy comprises the steps of:
transducing the wavefield energy detected by each of said one or more receiver positions into a corresponding electric signal;
amplifying said corresponding electric signal to produce an amplified signal; and
thereafter processing each said amplified signal so as to generate two signals which correspond to mathematical real and imaginary parts of a representation of each said amplified signal.
13. A method as defined in claim 12, wherein the step of processing each said amplified signal comprises the steps of:
inputting each said amplified signal detected at each of said one or more receiver positions to first and second multiplier circuits and multiplying each said amplified signal input to said first multiplier circuit by each said electric signal
sent to each of said one or more transmitter transducer positions;
shifting by 90.degree. the phase of an electric signal that is the duplicate of each said electric signal input to said first multiplier circuit, and thereafter multiplying each said amplified signal input to said second multiplier circuit by
each said electric signal that is shifted by 90.degree.; and
filtering the output of each said multiplier circuit with a low-pass filter and thereafter integrating and digitizing the output of each said low-pass filter.
14. A method as defined in claim 12, wherein said step of processing each said amplified signal comprises the steps of:
inputting each said amplified signal to a high speed analog-to-digital converter so as to digitize each said amplified signal; and
inputting each said digitized signal from said high speed analog-to-digital converter into a parallel processor programmed to take the complex fast Fourier transform of each said digitized signal.
15. A method as defined in claim 11, wherein said transducer array is configured to substantially enclose said region.
16. A method as defined in claim 1, wherein said primary set of surfaces has only one element, and said secondary set of surfaces has only one element.
17. A method as defined in claim 1, wherein said region characteristics estimate of said selected physical characteristics at said selected points within the region is initialized to an average value determined by an estimated average of said
region characteristics estimate.
18. A method as defined in claim 1, wherein said estimate of the total wavefield energy at said selected points for said one or more transmitter transducer positions and respective orientations thereof are obtained separately at each said
frequency sequentially.
19. A method as defined in claim 1, wherein said region characteristics estimate of said selected physical characteristics at said selected points within the region is formulated using a plurality of frequency-independent components represented
as a vector .GAMMA. multiplied by a frequency-dependent matrix M, and wherein said vector .GAMMA. is updated so as to determine said region characteristics estimate of said selected physical characteristics at said selected points within the region.
20. A method as defined in claim 19, wherein said vector .GAMMA. is updated using a conjugate gradient method.
21. A method as defined in claim 1, wherein said region characteristics correction is determined by a conjugate gradient method.
22. A method as defined in claim 1, wherein the each of said plurality of selected surfaces is a plane and where the step of computing the estimate of the total wavefield energy on the secondary set of surfaces using the region characteristics
estimate on the union of the primary and secondary sets of surfaces and the total wavefield energy on the primary set of surfaces is computed using a Fast-Fourier-Transform implemented propagator, where said propagator does not involve any approximation
to the square root function.
23. The method as defined in claim 1, wherein computing said region characteristics estimate from one or more derivatives of the comparator or approximations thereof with respect to one or more of said selected physical characteristics at one or
more of said selected points constructs a steepest descent direction; and then setting said region characteristics estimate equal to a sum of:
(a) a selected quantity times said steepest descent direction; and
(b) a selected function on said one or more of said selected points, wherein said selected quantity and said selected function are selected to reduce the comparator.
24. A method for producing an image of an object in a region from wavefield energy that has been transmitted into and scattered by the object, said image comprising a map of selected physical characteristics at selected points within the region,
said image being stored in a computer memory, and said method comprising the steps of:
(a) transducing an electric signal at each of one or more frequencies into wavefield energy propagated from one or more of transmitter transducer positions, each said transmitter transducer position propagating wavefield energy at at least one
orientation defined by Euler angles with respect to a selected fixed coordinate system;
(b) for one or more receiver positions each having at least one orientation defined by Euler angles with respect to said selected fixed coordinate system, detecting at each of said one or more receiver positions and respective orientations
thereof said wavefield energy;
(c) electronically processing said detected wavefield energy so as to transform said detected wavefield energy into one or more reception stored signals stored in said computer memory and corresponding to a scattered wavefield energy detected;
(d) setting a region characteristics estimate of selected physical characteristics at selected points within the region and storing each said region characteristics estimate in said computer memory;
(e) performing a convergence step comprising the following steps:
(1) preparing, for each said one or more frequencies at each said transmitter transducer positions and respective orientations thereof, an estimate of a total wavefield energy at said selected points derived from a selected incident wavefield
energy for said selected points stored in the computer memory and said region characteristics estimate for said selected points by the steps of:
(i) designating a primary set of surfaces of a plurality of selected surfaces and a different secondary set of surfaces of said selected surfaces, each said selected surface intersecting said region;
(ii) setting the estimate of the total wavefield energy equal to an initial total incident wavefield energy estimate for the primary set of surfaces;
(iii) computing the estimate of the total wavefield energy on the secondary set of surfaces using the region characteristics estimate on the union of the primary and secondary sets of surfaces and the total wavefield energy on the primary set of
surfaces;
(iv) re-designating the primary set of surfaces to include a sub- set of the secondary set of surfaces and re-designating the secondary set of surfaces to include another set of the selected surfaces; and
(v) repeating steps ((iii) through ((iv)) until the estimate of the total wavefield energy is computed for each of the selected surfaces;
(2) deriving, for each of said one or more frequencies at each said transmitter transducer position and orientations thereof, a calculated scattered wavefield energy for one or more of said receiver positions and respective orientations thereof
from at least one of said region characteristics estimate at said selected points and said estimate of said total wavefield energy for a corresponding transmitter transducer position and orientations thereof at said selected points by designating an
external surface situated outside said object, and then approximating an integral on the external surface by the sum of:
(i) a first quantity times the estimate of the total wavefield energy on said external surface times a derivative of a Green's function constructed to map to one or more of said receiver positions and respective orientations thereof; and
(ii) a second quantity times a derivative of the estimate of the total wavefield energy on said external surface times a Green's function constructed to map to one or more of said receiver positions and respective orientations thereof;
(3) for each said transmitter transducer position and orientations thereof and for each said receiver position and orientation thereof, comparing said scattered wavefield energy detected to said calculated scattered wavefield energy to derive
therefrom a comparator; and
(4) when said comparator is greater than a selected tolerance, determining and storing in said computer memory said region characteristics estimate by computing one or more derivatives of the comparator or approximations thereof with respect to
one or more of said selected physical characteristics at one or more of said selected points, and then using said one or more derivatives of the comparator or approximations thereof to compute a region characteristics correction, and then adding said
region characteristics correction to each of said region characteristics estimate for each of said one or more of said selected points, wherein said one or more derivatives of the comparator or approximations thereof is computed from one or more of:
(i) at each said one or more frequencies, said estimate of said total wavefield energy for said selected points for each of said one or more of said transmitter transducer positions and respective orientations thereof;
(ii) at each of said one or more frequencies, said calculated scattered wavefield energy for said one or more receiver positions and respective orientations thereof, and for each of said one or more of said transmitter transducer positions and
respective orientations thereof;
(iii) at each of said one or more frequencies, said scattered wavefield energy detected for said one or more receiver positions and respective orientations thereof, and for each of said one or more of said transmitter transducer positions and
respective orientations thereof; and
(iv) said region characteristics estimate for said selected points;
(f) repeating said convergence step until said comparator is less than or equal to said selected tolerance, and thereafter storing said region characteristics estimate as said image in the computer memory.
25. A methods as defined in claim 24, wherein said convergence step is a Gauss-Newton step computed using conjugate gradients.
26. A method as defined in claim 24, wherein:
A. model calibration parameters and an imaging system simulation model of said imaging device are used to compute:
(i) said selected incident wavefield energy;
(ii) said Green's function constructed to map to one or more of said receiver positions and respective orientations thereof; and
(iii) said derivative of a Green's function constructed to map to one or more of said receiver positions and respective orientations thereof;
B. said model calibration parameters comprising at least one of:
(i) one or more transmitter equivalent source vectors, said one or more transmitter equivalent source vectors being input to one or more transmitter simulators, said one or more transmitter simulators outputting one or more simulated transmitter
wavefields of said interrogating wavefield energy;
(ii) one or more receiver equivalent source vectors, said one or more receiver equivalent source vectors being input to one or more receiver simulators, said one or more receiver simulators outputting one or more simulated receiver sensitivity
functions, said one or more receiver sensitivity functions being electrical responses of said one or more receiver simulators to a point source of interrogating wavefield energy placed at substantially any location in said region;
(iii) one or more transmitter simulation positions, each said one of more transmitter simulation positions having one or more transmitter simulation orientations, each said one or more transmitter simulation orientations being defined by Euler
angles;
(iv) one or more receiver simulation positions, each said one of more receiver simulation positions having one or more receiver simulation orientations, each said one or more receiver simulation orientations being defined by Euler angles; and
(v) one or more electronic system parameters of said imaging device, said electronic system parameters substantially characterizing the analog and digital electronic functions of said imaging device,
C. said calibration parameters are derived by the steps of:
(i) collecting a received wavefield energy by a process comprising the steps of:
I. choosing a substantially known matter distribution in said region from a selected set of one or more substantially known matter distributions;
II. choosing one of said one of more transmitter transducers at one of said one or more transmitter positions and at one of said one or more transmitter orientations;
III. choosing one of said one of more receiver transducers at one of said one or more receiver positions and at one of said one or more receiver orientations;
IV. transmitting interrogating wavefield energy from said one of said one of more transmitter transducers at one of said one or more transmitter positions and at one of said one or more transmitter orientations into said region;
V. receiving interrogating wavefield energy at said one of said one or more transducer receivers at one of said one or more receiver positions and at one of said one or more receiver orientations;
VI. repeating C(III) through C(IV) until a selected portion of said one or more receiver transducers at said one or more receiver positions and orientations thereof have been chosen;
VII. repeating steps C(II) through C(VI) until a selected portion of said one or more transmitter transducers at said one or more transmitter positions and orientations thereof have been chosen;
VIII. repeating steps C(I) through C(VII) until all of said selected set of one or more substantially known matter distributions have been chosen;
(ii) constructing said imaging system simulation model of said imaging device and said imaging process used therewith with an input equal to said model calibration parameters and an output equal to a predicted received wavefield energy, said
predicted received wavefield energy being an approximation of said received wavefield energy, said imaging system simulation model being derived from at least one of:
I. a mathematical theory of said interrogating wavefield energy;
II. a simulation model of the analog and digital electronic functions of said imaging device;
III. said one or more transmitter simulators; and
IV. said one or more receiver simulators;
(iii) setting a portion of said model calibration parameters equal to selected values;
(iv) solving for substantially all other portions of said model calibration parameters using the steps of:
I. defining a comparator, said comparator being a positive scaler value that is a measure of the difference between said received wavefield energy and said predicted received wavefield energy; and
II. using an optimization algorithm to substantially minimize said comparator with respect to said substantially all other portions of said model calibration parameters until said comparator is less than a selected tolerance;
(v) storing said model calibration parameters in a computer memory.
27. A method as defined in claim 24, wherein said convergence step is a Ribiere-Polak step.
28. A method as defined in claim 24, wherein said estimate of said total wavefield energy at said selected points derived from said selected incident wavefield energy for said selected points is prepared, at least in part, by a fast Fourier
transform.
29. A method as defined in claim 24, wherein said scattered wavefield energy detected includes a digital representation of said wavefield energy propagating both into and through said region.
30. A method as defined in claim 24, wherein said step of transducing said electric signal at each of one or more frequencies into wavefield energy propagated from one or more of transmitter transducer positions, each said transmitter transducer
position propagating wavefield energy comprises the steps of:
positioning a transducer array adjacent to said object, said transducer array comprising said one or more of transmitter transducer positions and said one or more receiver positions;
sending said electric signal at a first frequency to each said transmitter transducer positions so that each said transmitter transducer positions will in turn propagate wavefield energy at said first frequency; and
thereafter changing the frequency of said signal and sending said electrical signal at said changed frequency to each said transmitter transducer position so as to sequentially propagate wavefield energy from each said transmitter transducer
position at said changed frequency.
31. A method as defined in claim 30, wherein said transducer array is configured to enclose at least a portion of said object.
32. A method as defined in claim 24, wherein said step of transducing said electric signal at each of one or more frequencies into wavefield energy propagated from one or more of transmitter transducer positions, each said transmitter transducer
position propagating wavefield energy, comprises the steps of:
positioning a transducer array adjacent to at least a portion of said region, said transducer array comprising said one or more of transmitter transducer positions and said one or more receiver positions;
generating said electric signal in the form of a waveform which is characterized by one or more different frequencies; and
sending said generated waveform in turn to each said transmitter transducer position so as to propagate wavefield energy at said one or more frequencies from each said transmitter transducer position.
33. A method as defined in claim 32, wherein said transducer array is configured to enclose at least a portion of said region.
34. A method as defined in claim 24, wherein said step of detecting at each of said one or more receiver positions and respective orientations thereof said wavefield energy comprises the steps of:
positioning a transducer array adjacent to said object, said transducer array comprising said one or more of transmitter transducer positions and said one or more receiver positions; and
after wavefield energy is transmitted from one of said transmitter transducer positions, sequencing each of said one or more receiver positions so as to detect said scattered wavefield energy at each of said one or more receiver positions in
turn.
35. A method as defined in claim 34, wherein said step of electronically processing said detected wavefield energy comprises the steps of:
transducing the wavefield energy detected by each of said one or more receiver positions into a corresponding electric signal;
amplifying said corresponding electric signal to produce an amplified signal; and
thereafter processing each said amplified signal so as to generate two signals which correspond to mathematical real and imaginary parts of a representation of each said amplified signal.
36. A method as defined in claim 35, wherein the step of processing each said amplified signal comprises the steps of: inputting each said amplified signal detected at each of said one or more receiver positions to first and second multiplier
circuits and multiplying each said amplified signal input to said first multiplier circuit by each said electric signal sent to each of said one or more transmitter transducer positions;
shifting by 90.degree. the phase of an electric signal that is the duplicate of each said electric signal input to said first multiplier circuit, and thereafter multiplying each said amplified signal input to said second multiplier circuit by
each said electric signal that is shifted by 90.degree.; and
filtering the output of each said multiplier circuit with a low-pass filter and thereafter integrating and digitizing the output of each said low-pass filter.
37. A method as defined in claim 35, wherein said step of processing each said amplified signal comprises the steps of:
inputting each said amplified signal to a high speed analog-to-digital converter so as to digitize each said amplified signal; and
inputting each said digitized signal from said high speed analog-to-digital converter into a parallel processor programmed to take the complex fast Fourier transform of each said digitized signal.
38. A method as defined in claim 34, wherein said transducer array is configured to substantially enclose said region.
39. A method as defined in claim 24, wherein said primary set of surfaces has only one element, and said secondary set of surfaces has only one element.
40. A method as defined in claim 24, wherein said region characteristics estimate of said selected physical characteristics at said selected points within the region is initialized to an average value determined by an estimated average of said
region characteristics estimate.
41. A method as defined in claim 24, wherein said estimate of the total wavefield energy at said selected points for said one or more transmitter transducer positions and respective orientations thereof are obtained separately at each said
frequency sequentially.
42. A method as defined in claim 24, wherein said region characteristics estimate of said selected physical characteristics at said selected points within the region is formulated using a plurality of frequency-independent components represented
as a vector .GAMMA. multiplied by a frequency-dependent matrix M, and wherein said vector .GAMMA. is updated so as to determine said region characteristics estimate of said selected physical characteristics at said selected points within the region.
43. A method as defined in claim 42, wherein said vector .GAMMA. is updated using a conjugate gradient method.
44. A method as defined in claim 24, wherein said region characteristics correction is determined by a conjugate gradient method.
45. A method as defined in claim 24, wherein the each of said plurality of selected surfaces is a plane and where the step of computing the estimate of the total wavefield energy on the secondary set of surfaces using the region characteristics
estimate on the union of the primary and secondary sets of surfaces and the total wavefield energy on the primary set of surfaces is computed using a Fast-Fourier-Transform implemented propagator, where said propagator does not involve any approximation
to the square root function.
46. The method as defined in claim 24, wherein computing said region characteristics estimate from one or more derivatives of the comparator or approximations thereof with respect to one or more of said selected physical characteristics at one
or more of said selected points constructs a steepest descent direction; and then setting said region characteristics estimate equal to a sum of:
(a) a selected quantity times said steepest descent direction; and
(b) a selected function on said one or more of said selected points, wherein said selected quantity and said selected function are selected to reduce the comparator.
47. A method for producing an image of an object in a region from wavefield energy that has been transmitted into and scattered by the object, said image comprising a map of selected physical characteristics at selected points within the region,
said image being stored in a computer memory, and said method comprising the steps of:
(a) transducing an electric signal at each of one or more frequencies into wavefield energy propagated from one or more of transmitter transducer positions, each said transmitter transducer position propagating wavefield energy at at least one
orientation defined by Euler angles with respect to a selected fixed coordinate system;
(b) for one or more receiver positions each having at least one orientation defined by Euler angles with respect to said selected fixed coordinate system, detecting at each of said one or more receiver positions and respective orientations
thereof said wavefield energy;
(c) electronically processing said detected wavefield energy so as to transform said detected wavefield energy into one or more reception stored signals stored in said computer memory and corresponding to a scattered wavefield energy detected;
(d) setting a region characteristics estimate of selected physical characteristics at selected points within the region and storing each said region characteristics estimate in said computer memory;
(e) performing a convergence step comprising the following steps:
(1) preparing, for each said one or more frequencies at each said transmitter transducer positions and respective orientations thereof, an estimate of a total wavefield energy at said selected points derived from a selected incident wavefield
energy for said selected points stored in the computer memory and said region characteristics estimate for said selected points by the steps of:
(i) designating a primary set of surfaces of a plurality of selected surfaces and a different secondary set of surfaces of said selected surfaces, each said selected surface intersecting said region;
(ii) setting the estimate of the total wavefield energy equal to an initial total incident wavefield energy estimate for the primary set of surfaces;
(iii) computing the estimate of the total wavefield energy on the secondary set of surfaces using the region characteristics estimate on the union of the primary and secondary sets of surfaces and the total wavefield energy on the primary set of
surfaces;
(iv) re-designating the primary set of surfaces to include a sub- set of the secondary set of surfaces and re-designating the secondary set of surfaces to include another set of the selected surfaces; and
(v) repeating steps ((iii) through ((iv)) until the estimate of the total wavefield energy is computed for each of the selected surfaces;
(2) deriving, for each of said one or more frequencies at each said transmitter transducer position and orientations thereof, a calculated scattered wavefield energy for one or more of said receiver positions and respective orientations thereof
from at least one of said region characteristics estimate at said selected points and said estimate of said total wavefield energy for a corresponding transmitter transducer position and orientations thereof at said selected points by approximating an
integral on at least a portion of the region of the product of:
(i) the estimate of the total wavefield energy at said selected points;
(ii) the region characteristics estimate at said selected points; and
(iii) a Green's function constructed to map to one or more of said receiver positions and respective orientations thereof;
(3) for each said transmitter transducer position and orientations thereof and for each said receiver position and orientation thereof, comparing said scattered wavefield energy detected to said calculated scattered wavefield energy to derive
therefrom a comparator; and
(4) when said comparator is greater than a selected tolerance, determining and storing in said computer memory said region characteristics estimate by computing one or more derivatives of the comparator or approximations thereof with respect to
one or more of said selected physical characteristics at one or more of said selected points, and then using said one or more derivatives of the comparator or approximations thereof to compute a region characteristics correction, and then adding said
region characteristics correction to each of said region characteristics estimate for each of said one or more of said selected points, wherein said one or more derivatives of the comparator or approximations thereof is computed from one or more of:
(i) at each said one or more frequencies, said estimate of said total wavefield energy for said selected points for each of said one or more of said transmitter transducer positions and respective orientations thereof;
(ii) at each of said one or more frequencies, said calculated scattered wavefield energy for said one or more receiver positions and respective orientations thereof, and for each of said one or more of said transmitter transducer positions and
respective orientations thereof;
(iii) at each of said one or more frequencies, said scattered wavefield energy detected for said one or more receiver positions and respective orientations thereof, and for each of said one or more of said transmitter transducer positions and
respective orientations thereof; and
(iv) said region characteristics estimate for said selected points;
(f) repeating said convergence step until said comparator is less than or equal to said selected tolerance, and thereafter storing said region characteristics estimate as said image in the computer memory.
48. A methods as defined in claim 47, wherein said convergence step is a Gauss-Newton step using conjugate gradients.
49. A method as defined in claim 47, wherein:
A. model calibration parameters and an imaging system simulation model of said imaging device are used to compute:
(i) said selected incident wavefield energy; and
(ii) said Green's function constructed to map to one or more of said receiver positions and respective orientations thereof;
B. said model calibration parameters comprising at least one of:
(i) one or more transmitter equivalent source vectors, said one or more transmitter equivalent source vectors being input to one or more transmitter simulators, said one or more transmitter simulators outputting one or more simulated transmitter
wavefields of said interrogating wavefield energy;
(ii) one or more receiver equivalent source vectors, said one or more receiver equivalent source vectors being input to one or more receiver simulators, said one or more receiver simulators outputting one or more simulated receiver sensitivity
functions, said one or more receiver sensitivity functions being electrical responses of said one or more receiver simulators to a point source of interrogating wavefield energy placed at substantially any location in said region;
(iii) one or more transmitter simulation positions, each said one of more transmitter simulation positions having one or more transmitter simulation orientations, each said one or more transmitter simulation orientations being defined by Euler
angles;
(iv) one or more receiver simulation positions, each said one of more receiver simulation positions having one or more receiver simulation orientations, each said one or more receiver simulation orientations being defined by Euler angles; and
(v) one or more electronic system parameters of said imaging device, said electronic system parameters substantially characterizing the analog and digital electronic functions of said imaging device,
C. said calibration parameters are derived by the steps of:
(i) collecting a received wavefield energy by a process comprising the steps of:
I. choosing a substantially known matter distribution in said region from a selected set of one or more substantially known matter distributions;
II. choosing one of said one of more transmitter transducers at one of said one or more transmitter positions and at one of said one or more transmitter orientations;
III. choosing one of said one of more receiver transducers at one of said one or more receiver positions and at one of said one or more receiver orientations;
IV. transmitting interrogating wavefield energy from said one of said one of more transmitter transducers at one of said one or more transmitter positions and at one of said one or more transmitter orientations into said region;
V. receiving interrogating wavefield energy at said one of said one or more transducer receivers at one of said one or more receiver positions and at one of said one or more receiver orientations;
VI. repeating C(III) through C(IV) until a selected portion of said one or more receiver transducers at said one or more receiver positions and orientations thereof have been chosen;
VII. repeating steps C(II) through C(VI) until a selected portion of said one or more transmitter transducers at said one or more transmitter positions and orientations thereof have been chosen;
VIII. repeating steps C(I) through C(VII) until all of said selected set of one or more substantially known matter distributions have been chosen;
(ii) constructing said imaging system simulation model of said imaging device and said imaging process used therewith with an input equal to said model calibration parameters and an output equal to a predicted received wavefield energy, said
predicted received wavefield energy being an approximation of said received wavefield energy, said imaging system simulation model being derived from at least one of:
I. a mathematical theory of said interrogating wavefield energy;
II. a simulation model of the analog and digital electronic functions of said imaging device;
III. said one or more transmitter simulators; and
IV. said one or more receiver simulators;
(iii) setting a portion of said model calibration parameters equal to selected values;
(iv) solving for substantially all other portions of said model calibration parameters using the steps of:
I. defining a comparator, said comparator being a positive scaler value that is a measure of the difference between said received wavefield energy and said predicted received wavefield energy; and
II. using an optimization algorithm to substantially minimize said comparator with respect to said substantially all other portions of said model calibration parameters until said comparator is less than a selected tolerance;
(v) storing said model calibration parameters in a computer memory.
50. A method as defined in claim 47, wherein said convergence step is a Ribiere-Polak step.
51. A method as defined in claim 47, wherein said estimate of said total wavefield energy at said selected points derived from said selected incident wavefield energy for said selected points is prepared, at least in part, by a fast Fourier
transform.
52. A method as defined in claim 47, wherein said scattered wavefield energy detected includes a digital representation of said wavefield energy propagating both into and through said region.
53. A method as defined in claim 47, wherein said step of transducing said electric signal at each of one or more frequencies into wavefield energy propagated from one or more of transmitter transducer positions, each said transmitter transducer
position propagating wavefield energy comprises the steps of:
positioning a transducer array adjacent to said object, said transducer array comprising said one or more of transmitter transducer positions and said one or more receiver positions;
sending said electric signal at a first frequency to each said transmitter transducer positions so that each said transmitter transducer positions will in turn propagate wavefield energy at said first frequency; and
thereafter changing the frequency of said signal and sending said electrical signal at said changed frequency to each said transmitter transducer position so as to sequentially propagate wavefield energy from each said transmitter transducer
position at said changed frequency.
54. A method as defined in claim 53, wherein said transducer array is configured to enclose at least a portion of said object.
55. A method as defined in claim 47, wherein said step of transducing said electric signal at each of one or more frequencies into wavefield energy propagate | | |
