
    Application of Jay P. JOHNSON, Alvin L. Parrack and Delbert R. Lunsford. Application of Alvin L. PARRACK and Delbert R. Lunsford (two cases.)
    Appeal Nos. 76-717 to 76-719.
    United States Court of Customs and Patent Appeals.
    Dec. 7, 1978.
    Rehearing Denied Feb. 15, 1979.
    William J. Beard, attorney of record, Houston, Tex.,, for appellants.
    Joseph F. Nakamura, Washington, D. C., for the Commissioner of Patents; Jere W. Sears, Washington, D. C., of counsel.
    Before MARKEY, Chief Judge, and RICH, BALDWIN, LANE and MILLER, Judges.
   BALDWIN, Judge.

These appeals are from the decisions of the Patent and Trademark Office (PTO) Board of Appeals (board) sustaining the rejections of all claims in three consolidated cases under 35 U.S.C. § 101 for being directed to nonstatutory subject matter. We reverse on all claims.

The Inventions

The inventions before us involve methods for removing undesired components (noise) from seismic data. In seismic prospecting, an acoustic or seismic wave energy source is positioned either in a relatively shallow shot hole on the surface of the earth, or is towed a predetermined distance beneath the surface of a body of water. An acoustic energy impulse of some preselected wave shape and frequency content is generated by the seismic energy source. The acoustic energy generated by the source penetrates through the multiple layers of material comprising the subterranean portion of the earth in the region being prospected. Since the speed of sound is generally different in each layer beneath the surface of the earth, refractions, reflections, and diffractions of the acoustic energy occur at the boundary of each layer. These acoustic energy reflections, refractions, and diffractions cause secondary acoustic energy waves to return toward the surface of the earth. At the surface, the returning acoustic energy waves are detected by a plurality of longitudinally-spaced geophones, hydrophones, or seismic detectors. The individual seismic detectors are located along a generally straight line. These detectors generate analog electrical signals or waveforms which are representative of the arrival of the acoustic energy waves at the detectors. The analog waveforms generated by the seismic detectors are, thus, voltage representations, generated as a function of time, of the amplitude of reflected, refracted, and diffracted secondary acoustic energy waves arriving at the surface of the earth.

The secondary waves detected by the seismic detectors are generally amplified and then recorded or stored in either analog or digital form on a record medium as a function of the time after the seismic “shot” or energy generation. After amplification and prior to recording, thé analog electrical waveform may be digitized by sampling its amplitude at a predetermined rate and then recording the digital amplitude values as a function of time. A time series of digital numbers representative of the amplitude of the analog waveform at each detector as a function of time is thus generated. The recorded representation of seismic energy at a detector location, whether it is recorded in analog or digital form, may be displayed for interpretation in the form of a “wiggle trace” or plot of the amplitude of the arriving acoustic energy waves as a function of time for each geo-phone or seismic detector stationed at a particular surface location. A plurality of such traces forms a record section of the data. These record sections may then be processed to interpret the arriving acoustic energy waves at each seismic detector in terms of the subsurface layering of the earth structure. This analysis, if performed properly, can disclose the location of subterranean earth structures or traps which may contain petroleum deposits. It is quite common for seismic data to be recorded in digital form as described and for digital data processing equipment (i. e., digital computers) to be used in the processing of the seismic data for interpretation in terms of the location of subterranean structures which may be petroleum traps.

The inventions in each of the three applications in these consolidated appeals deal with the removal of unwanted seismic signal components or noise present in the recorded seismic data. Noise removal facilitates interpretation of the seismic data and, thereby, determination of subterranean structure. This undesired acoustic noise which appears on the records of seismic data may be caused by a variety of noise sources. One type of noise, called “multiple reflections,” involves an “echo” effect caused by hard layers near the surface which “trap” and rebroadcast the primary acoustic energy impulse of the source several times rather than just once. The arrival at the detectors of each repetitive reflection (or reverberation) causes the detector to perceive nonexistent deep layers, and the echoes mask the true signal. Other sources of noise are electrical interference from power lines or communication systems in use in the vicinity of the seismic exploration and random acoustic energy noise from other energy sources, such as vehicles moving in the region of the seismic exploration. Thus, the removal of noise or undesired signal components from the recorded data representations comprising a seismic record is a problem in the seismic exploration technique practiced in the petroleum industry.

Application serial No. 230,810 • (Appeal No. 76-719) is the first-filed application of the three related applications presently on appeal. The invention disclosed in this application comprises a technique for removing unwanted noise components from the seismic traces in a seismic récord in which certain conventional seismic data processing techniques, such as the correction for “normal move out” and the “stacking” or adding technique which is applied to Common Depth Point (CDP) seismic data, have already been performed. The invention makes use of the physical principle that, because of the manner in which the seismic data are gathered, closely adjacent detectors should receive reflections of essentially the same wave shape from a given layer. A chronologically small portion of a particular seismic trace (termed a reference trace) is examined and is compared with corresponding portions of spatially adjacent seismic traces in order to define a coherent signal component common to all of the traces being examined. The coherent signal component is then separated from the totality of the recorded seismic data present in the portion of the reference trace being examined, and the remainder is considered noise. The assumption present in such processing is that there should be relatively few abrupt changes in the physical characteristics of the subsurface bed boundaries as a function of horizontal distance. Claim 1 in Appeal No. 76-719 recites:

1. A machine implemented method for enhancing digital data in a seismic record, said data having a coherent signal component comprising a measure of the similarity between spatially related time series data, and a noice [sic noise] component, and for improving the signal to noise ratio thereof, comprising the steps of: determining, for a search window defined about a selected time on a selected seismic reference trace, the coherent signal associated with said reference trace and a plurality of adjacent seismic traces;

computing, by use of said coherent signal, the component of said coherent signal extant in said reference trace and replacing in time alignment with said reference trace on an output signal record medium, that portion of said reference trace included in said search window with said component of the reference trace comprising said coherent signal portion;

replacing, in time alignment with said reference trace on an output noise record medium, that portion of said reference trace included in said search window, with the remainder of said reference trace which does not comprise said coherent signal portion; and repeating the above steps for other selected times and other selected reference traces until all data comprising said record is so processed.

Claim 10 in this appeal recites:

10. A machine implemented method for enhancing digital data in a Common Depth Point, moveout corrected and stacked seismic data record, said data having á coherent signal component comprising a measure of the similarity between spatially related time series data, and a noise component, and for improving the signal to noise ratio thereof, comprising the steps of:

determining, for a search window defined about a selected time on a selected seismic reference trace, the shape of the coherent signal associated with said selected reference trace and a plurality of space wise adjacent seismic traces;

determining, for said search window, the amplitude of said coherent signal;

computing, as a function of the amplitude and shape information pertaining to said coherent signal, the component portion of said selected reference trace corresponding to said coherent signal;

replacing, in time alignment with said selected reference trace, on an output signal record medium the portion of said selected reference trace in said search window, with said coherent signal component portion; and repeating the above steps for other selected times and other selected reference traces until all data comprising said record is so processed.

The remaining independent claim in Appeal No. 76-719 is claim 16 which states:

16. A machine implemented method for enhancing plural raw digital data records, not moveout corrected, said data having a coherent signal component comprising a measure of the similarity between spatially related time series data, and a noise component, and for improving the signal to noise ratio thereof, comprising the steps of:

compiling, from said plurality of raw data records, a synthetic data record of common range traces;

determining, for a search window defined about a selected time on a selected reference trace on said synthetic data record, the shape and amplitude of the coherent signal associated with said reference trace and a plurality of spacewise adjacent seismic traces on said synthetic record;

computing, as a function of the amplitude and shape of said coherent signal, the component portion of said selected reference trace corresponding to said coherent signal;

replacing, in time alignment on said synthetic data record, on an output signal record medium, the portion of said reference trace in said search window, with said coherent signal component portion;

repeating the above steps for other selected times and other selected reference traces until all data comprising said synthetic record is so processed; and repeating all the above steps for different common shotpoint-detector ranges, thereby enhancing the data on all of said raw data records.

The examiner, by letter of October 24, 1973, found a rejection of claims 1 — 7, 10, 12 and 14 under 35 U.S.C. § 103 to be overcome by applicants’ arguments in an amendment of September 26,1973, and only the rejection under 35 U.S.C. § 101 was maintained.

The second-filed application in the present appeals (application serial No. 305,-386, Appeal No. 76-717), extends the method of the first application to the processing of seismic data in raw form, that is, data upon which “move out” corrections and CDP “stacking” procedures have not been performed. This is accomplished by deriving those segments of spatially related adjacent traces which correspond chronologically to the portion of the reference trace being examined at a given step in processing by projecting the reference trace portion or “window” onto spatially related adjacent traces along a predetermined hyperbolic curve. This hyperbolic projection takes into account the “normal move out” correction which would otherwise be applied to the seismic data prior to its comparison to spatially related traces in order to determine the coherent signal in the technique recited in Appeal No. 76-719. Claim 1 in Appeal No. 76-717 is:

1. A method for enhancing digital seismic data said data having a coherent signal component comprising a measure of similarity between spatially related time series data, and a noise component in unmoved out form, comprising the steps of:

a) determining for a selected time TR on a selected seismic trace R, the estimated times Tx on one or more additional traces included in the data at which possible events common to a possible event at Te occur;

b) determining, for a search window having edges equally spaced on either side of times Tr the coherent signal component;

c) computing, by use of said coherent signal component, the component of said coherent signal extant in said selected trace TR [sic R] with replacing in time alignment with said selected trace on an output signal record medium, that portion of said selected trace Tr [sic R] included in said search window with said component of the selected trace comprising said coherent signal portion; and

' d) repeating the recited steps for other selected times and other selected traces until all said seismic data are so processed.

Claim 13 in this appeal recites:

13. A method of enhancing unmoved out seismic data in a gather of common depth point seismogram traces, said data having a coherent signal component comprising a measure of the similarity between spatially related time series data, and a noise component, comprising the steps of:

a) selecting a trace in said gather to function as a reference trace R;

b) selecting a tiine TR on said trace R;

c) determining times Tx on one or more traces X included in said gather at which possible events common to a possible event at TR on trace R occur;

d) cross correlating equal time length trace segments on traces X and R to derive time alignments for producing a coherent signal component segment COH from a segment of said reference trace R;

e) forming said coherent signal component segment COH on an output record medium in time alignment with said reference trace segment; and

f) repeating steps a), b), c), d), and e) with each trace in the gather functioning as the reference trace until all of said gather is processed to form an enhanced gather of coherent seismogram traces on said output record medium.

In a first Office Action, the examiner rejected all of the claims of this application under 35 U.S.C. § 101 and claims 1-4 and 13-15 under 35 U.S.C. § 103 over a combination of references. This § 103 rejection was not repeated after applicants’ amendment of December 19, 1973.

The third application concerned in these consolidated appeals (application serial No. 327,267, Appeal No. 76-718), utilizes the same general physical principles for the detection and removal of “multiple” events in a seismic signal trace. The assumption here is that the multiple events have occurred because of the reflection of acoustic energy from the same (or closely adjacent) points on the subsurface boundaries and that the seismic signal or analog waveform produced by such reflections at the surface seismic detectors has the same characteristic shape (although its amplitude may be greatly diminished) after each such multiple reflection or reverberation. Thus, a particular time interval or “window” of a reference seismic trace is examined and compared against the same time duration interval (or window) of the same trace occurring at a later time. The shape of the trace in each of the intervals or time “windows” being examined can, if the assumptions about the nature of the process are valid, be used to extract multiple reflections by defining the existence of such a multiple reflection in the later occurring portion of the trace. With the multiple reflection thus defined, it may be removed from the trace by a subtraction process, thereby leaving the portion or component of the trace which is not attributable to this noise source. Claim 1 in Appeal No. 76-718 is representative:

1. A process for suppressing multiple events in seismic traces comprising the steps of:

a) comparing a first seismic trace segment with a second segment of the same trace to select.that portion of the second segment which most closely resembles said first segment;

b) determining the degree of similarity between said selected portion and said first segment; and

c) extracting a part of said selected portion fro'm said first portion, said part being a function of the degree of similarity between said selected portion and said first segment.

The examiner rejected all the claims of this application under 35 U.S.C. §§ 101 and 102, but the board reversed the 102 grounds upon finding that the reference did not suggest or anticipate the limitation that the extracted part be a function of the similarity between the selected portion and the first segment.

The Board

The board, in three separate opinions, affirmed the rejection of all of the claims before us as directed to nonstatutory subject matter under 35 U.S.C. § 101. It was the board’s position that Gottschalk v. Benson, 409 U.S. 63, 93 S.Ct. 253, 34 L.Ed.2d 273, 175 USPQ 673 (1972), and In re Christensen, 478 F.2d 1392, 178 USPQ 35 (CCPA 1973), preclude a patent grant for any “subject matter which is algorithmic in character.” The board found the claims on appeal to be special methods for solving problems involving seismic data and, therefore, algorithms not embraced within 35 U.S.C. § 101.

Issue

The sole issue before this court is whether the methods recited in the claims of the three cases constitute statutory subject matter under 35 U.S.C. § 101.

OPINION

Initially, we recognize that the board considered these appeals without the benefit of the Supreme Court’s decision in Parker v. Flook, supra. While a degree of uncertainty existed concerning the proper interpretation of Gottschalk v. Benson, supra, it is clear after Flook that the board’s conclusion that patent protection is proscribed for all inventions “algorithmic in character” is overbroad and erroneous.

In Benson, the Supreme Court determined that the claimed method for converting pure binary numbers to binary coded decimals (BCD) was not patentable subject matter under 35 U.S.C. § 101. The Court set forth its reasons in the following “nutshell” holding: an idea may not be patented and a claim may not issue which would preempt a mathematical formula. In the viewpoint of the Court, Benson’s claims could not be allowed because to do so would grant him the right to exclude the use of a mathematical formula by others. 409 U.S. at 71-2, 93 S.Ct. 253, 175 USPQ at 676.

In the six years following Benson, this Court applied the “nutshell” analysis in a series of cases involving different factual situations. See, e. g., In re Freeman, 573 F.2d 1237, 197 USPQ 464 (CCPA 1978); In re Richman, 563 F.2d 1026, 195 USPQ 340 (CCPA 1977); In re de Castelet, 562 F.2d 1236, 195 USPQ 439 (CCPA 1977); In re Chatfield, 545 F.2d 152, 191 USPQ 730 (CCPA 1976), cert. denied, 434 U.S. 875, 98 S.Ct. 226, 54 L.Ed.2d 155, 195 USPQ 465 (1977).

It was not until its decision in Parker v. Flook, supra, that the Supreme Court again directly spoke on the § 101 issue involving algorithmic type inventions. The claims at issue in Flook recited methods of updating alarm limits during the catalytic conversion of petroleum. The applicant admitted that the novelty of his process rested solely in the mathematical formula for computing the updated alarm limits. The final result of practicing Flook’s process as claimed was a number or value to serve as a new alarm limit. This number or value was calculated from previous alarm limits and other data inputs.

The Supreme Court held Flook’s process to be a method of calculation and, hence, nonstatutory even though limited to a specific technology and end use. Flook, supra, 98 S.Ct. at 2528 n.18, 198 USPQ at 199 n.18. In reaching this decision, the Court simplified the “nutshell” of Benson into a single kernel of principle: the discovery of a mathematical formula is not patentable even though the formula is novel and useful. Id., 98 S.Ct. at 2523, 198 USPQ at 195. Further, the Court stated that the plain language of 35 U.S.C. § 101 is not to be read literally when determining what is statutory subject matter. Id., 98 S.Ct. at 2525, 198 USPQ at 196. This is evidenced by prior judicial decisions which have excised certain categories of invention from the classes of statutory subject matter. See, e. g., O’Reilly v. Morse, 56 U.S. 62, 15 How. 62, 14 L.Ed. 601 (1853) (phenomena of nature); Rubber-Tip Pencil Co. v. Howard, 87 U.S. 498, 20 Wall. 498, 22 L.Ed. 410 (1874) (mere ideas); Hotel Security Checking Co. v. Lorraine Co., 160 F. 467 (2d Cir. 1908) (method of doing business).

While in Flook, the Supreme Court acknowledged, supra, 98 S.Ct. at 2525, 198 USPQ at 197, that “[t]he line between a patentable ‘process’ and an unpatentable ‘principle’ does not always shimmer with clarity,” and, thus, turns on the claimed subject matter of each application, there are significant consistencies evident in the Benson and Flook opinions. First, the definition assigned in Benson to the term “algorithm” was reiterated in Flook, i. e., “a procedure for solving a given type of mathematical problem." Id., 98 S.Ct. at 2523 n.1, 198 USPQ at 195 n.1, quoting, Benson, supra at 65, 93 S.Ct. 253, 175 USPQ 674. (Emphasis added.) Also, the Court, in Flook, reiterated that although a law of nature cannot be patented, “a process is not unpatentable simply because it contains a law of nature or. a mathematical algorithm.” Id., 98 S.Ct. at 2526, 198 USPQ at 197. Additionally, the Court in both Benson and Flook refused to hold computer programs nonstatutory subject matter per se.

Following the Supreme Court’s decision in Benson, and before its decision in Flook, numerous appeals to this Court necessitated the application of the principles expressed in Benson to both apparatus and process claims rejected under 35 U.S.C. § 101. Besides the differing language of the claims in these appeals, the nature of the inventions recited therein varied greatly.

One of these appeals led to our decision in In re Chatfield, supra, which set forth certain guidelines for determining whether claims recite statutory subject matter or mathematical algorithms properly rejecta-ble under the Benson principles. In Chat- field we indicated that no basis exists in Benson or the statute for treating a claimed computer-implemented process differently from a process performed by any other machine system when considering whether statutory subject matter is recited. Chat-field, supra, 545 F.2d at 157,191 USPQ 734. Judge Rich stated in his dissent that Benson applies equally whether an invention is claimed as an apparatus or process, because the form of the claim is often an exercise in drafting. Id. at 160, 191 USPQ 737. This viewpoint was adopted by this entire Court in In re Freeman, supra, 573 F.2d at 1247, 197 USPQ at 472.

Further, this court’s opinion in Chat-field. emphasized that the meaning of the term “algorithm” is no longer in question when we stated:

The Supreme Court carefully supplied a definition of the particular algorithm before it, i. e., “[a] procedure for solving a given type of mathematical problem.” The broader definition of algorithm is “a step-by-step procedure for solving a problem or accomplishing some end.” Web-, ster’s New Collegiate Dictionary (1976). It is axiomatic that inventive minds seek and develop solutions to problems and step-by-step solutions often attain the status of patentable invention. It would be unnecessarily detrimental to our patent system to deny inventors patent protection on the sole ground that their contribution could be broadly termed an “algorithm." [Emphasis in original.]

Id., 545 F.2d at 156 n. 5,191 USPQ at 734 n. 5. This court additionally held that each claim must be judged in its entirety when determining whether statutory subject matter is recited. Id., at 158, 191 USPQ at 736. Therefore, a claim does not recite nonstatutory subject matter merely because, an element or a step, when considered out of the context of the rest of the claim, is found to contain a natural law or mathematical algorithm. See Flook, supra, 98 S.Ct. at 2526,198 USPQ at 197; Eibel Process Co. v. Minnesota and Ontario Paper Co., 261 U.S. 45, 43 S.Ct. 322, 67 L.Ed. 523 (1923).

In our subsequent decision in In re Freeman, supra, we set forth a two-step procedure for analyzing a claim to determine whether or not it preempts a mathematical algorithm. This determination is critical since Benson declared claims which preempt mathematical algorithms to be nonstatuto-ry-

The first step of the Freeman analysis is to determine whether a method claim directly or indirectly recites “process steps which are themselves calculations, formulae or equations.” Id., 573 F.2d at 1246, 197 USPQ at 471. Only if such steps are recited is the claim to be further analyzed to ascertain whether the claim merely recites a mathematical formula or a method of calculation as in Benson and Flook. In Freeman and the subsequent case of In re Toma, 575 F.2d 872, 197 USPQ 852 (CCPA 1978), the steps of the claims did not directly or indirectly recite mathematical calculations, formulae or equations, and hence the second step of the analysis was not reached.

Our decision in In re Richman, supra, was handed down between the Chatfield and Freeman decisions and appears to have foreshadowed the Supreme Court’s holding in Flook. The claims in Richman recited a method of calculating an average boresight correction angle within a signal-processing radar apparatus. We held the claims to recite nonstatutory subject matter, not because a mathematical expression appeared in steps of the claims, but because each claim, when considered in its entirety, recited “a method of calculating using a mathematical formula.” Id., 563 F.2d at 1030,195 USPQ at 343. In Flook as in Richman, the result of performing the claimed process was a value or number and in each case the claims were held to be nonstatutory recitations of methods for computing the numbers.

Turning to the claims at issue, we must apply the Supreme Court precedents of Benson and Flook to the three sets of claims on appeal. Initially, we note that there are two important factual distinctions between the claims at issue and the claims in Flook. First, in Flook the applicant alleged that his claims recited a novel mathematical procedure for computing a number called an alarm limit. The applicants in the instant appeals, however, allege no such novel mathematical procedures and do not seek a patent on a mathematical formula. Second, while the purpose of performing the process in Flook was to compute a new value for an alarm limit, the purpose of applicants’ methods are to filter out extraneous and erroneous components and to physically record a noiseless seismic trace on a record medium. Any computations required in performing applicants’ processes are admitted to be well-known operations mandated by applicants’ preference to perform the filtering process with a digital computer. The products produced by applicants’ claimed processes are new, noiseless seismic traces recorded on a record medium and not mere mathematical values. Thus, the significant limitations recited in the claims of operating on a recorded, unenhanced, seismic trace to produce and record a new seismic trace lead us to find the claims to recite statutory processes and not methods of calculating as were present in Flook.

Finding the claims at issue to be statutory under the Flook criterion is not the end of the required analysis, because even though, as has been pointed out, there are significant overlaps between the analyses in the Supreme Court’s Benson and Flook opinions, we still consider it necessary to determine whether the claims recite mathematical algorithms in a nonstatutory manner under the Benson “nutshell” holding. We choose to conduct this inquiry with the aid of a two-part analysis as was done in In re Freeman, supra. Our search for directly or indirectly recited mathematical algorithms in the instant cases begins by applying the first part of the Freeman inquiry to each of the claims before us. In Appeal No. 76-717, step “c” of claim 1 recites “computing, by use of said coherent signal component, the component of said coherent signal extant in said selected trace.” (Emphasis ours.) The term “compute” at least suggests the execution of a mathematical algorithm in the form of one or a sequence of mathematical operations, and thus, claim 1 and claims 2-12 which depend therefrom must be subjected to further analysis under the Benson and Flook precedents.

Claim 13 of Appeal No. 76-717 is the only other independent claim in that case. Step “c” of this claim recites “determining times Tx on one or more traces X included in said gather at which possible events common to a possible event at Tr on trace R occur” and step “d” recites “cross correlating equal time length trace segments on traces X and R to derive time alignments for producing a coherent signal component COH from a segment of said reference trace R.” While “determining” and “cross correlating” are not prima facie mathematical calculations, formulae, or equations, these steps cannot be analyzed in a vacuum. Reference to the specification must be made to determine whether such terms indirectly recite mathematical calculations, formulae, or equations. Although appellants’ specification in this case does not equate either the step of “determining” or the step of “correlating” with the execution of a mathematical algorithm, the flow diagrams which form part of the specification disclose explicit mathematical equations which are to be used in conjunction with each of these steps. Thus, claims 13-17 will also be made the subject of the second Freeman inquiry.

Claim 1, the only independent claim in Appeal No. 76-718, recites the steps of “comparing a first seismic trace segment with a second segment of the same trace” and “determining the degree of similarity” between two portions of the seismic trace. Reference to the specification indicates that the step of “determining the degree of similarity” requires the execution of mathematical equations and, thus, all of the claims of this case will be further analyzed to determine whether a mathematical algorithm is being preempted.

Appeal No. 76-719 contains three independent claims — claims 1, 10 and 16. Each of these claims includes a step which specifically recites “computing.” As we stated in connection with our analysis of claim 1 of Appeal No. 76-717, the term “computing” connotes the execution of one or a sequence of mathematical operations. Since all of the claims of Appeal No. 76-719 either directly or indirectly recite a “compute” step, they too must be analyzed under the second part of the Freeman inquiry.

Under the second step of our analysis, we must determine whether each claim as a whole, including all of its steps, merely recites a mathematical formula or a method of calculation. This analysis requires careful interpretation of each claim in the light of its supporting disclosure to determine whether or not it merely defines a method of solving a mathematical problem. If it does not, then it defines statutory subject matter, namely, a “process.”

Considering Appeal No. 76-717, claim 1 recites “a selected seismic trace R” having “a coherent signal component” and .“a noise component” indicative of a noise event. One or more “additional traces” are chosen which also contain the coherent signal component. The coherent signal (the reference trace without the noise component) is determined and reproduced on an “output signal record medium” in place of the reference trace. Even assuming arguendo that the “computing” step recited in the claim entails performing mathematical calculations, the process is explicitly claimed within the framework of a method for producing an output seismic trace which is different from, and an enhancement of, an input seismic trace. Thus, any calculations which may be performed in practicing the process of claim 1 are but a part of that process which includes the other recited steps.

Claim 13 recites a method for enhancing seismic data which begins with a “reference trace R” (from a gather of seismic data) containing both coherent and noise components. By performing the “determining” and “cross correlating” steps set forth in the claim on selected portions of the reference trace and other traces selected from the gather, a coherent (noise-free) signal component segment is produced from a segment on the reference trace. This coherent signal segment is then recited to be formed on an “output record medium” in a specific manner. Again, any mathematical operations performed in practicing the method recited in claim 13 are incident to producing a noise-free signal trace from a reference trace, and by no interpretation can claim 13 be construed to be a mere procedure for solving a given type of mathematical problem.

Appellants admitted in their supplemental brief that any calculations incident to performing the processes claimed in this appeal and Appeal Nos? 76-718 and 76-719 are well known and form no basis for pat-entability. This is a significant factual distinction from the situation in Flook where patentability was predicated upon a particular formula for computing alarm limits and the situation in Benson where the claims recited a mathematical algorithm for converting numbers from pure binary to binary coded decimals. It is apparent that any calculations required in practicing the processes appellants recite in claims 1 and 13 result from the selection of a general purpose computer and digital processing techniques to analyze, filter and record the seismic traces instead of using banks of analog filters or other devices. Our decisions in Chatfield, supra, and Deutsch, supra, held computer-implemented processes to be statutory subject matter, and we reach a similar conclusion with respect to claims 1 and 13. Furthermore, the Supreme Court’s decisions in Benson and Flook support this result because these claims, when considered as a whole, do not merely recite methods of calculation or mathematical formulas.

We see nothing in claims 2-12, which depend from claim 1, or in claims 14 — 17, which depend from claim 13, which would cause them to be nonstatutory. Since dependent claims, when properly drafted, are by nature less inclusive than their associated independent claims, and since we have found the independent claims to recite statutory processes under 35 U.S.C. § 101, we reverse the board’s holding as to claims 1-17 in Appeal No. 76-717.

In Appeal No. 76-718, the process recited by claim 1 begins with a seismic trace and compares a first segment (containing multiple event noise) of the trace with a second segment of the trace to determine the selected portion of the second segment which most closely resembles the first segment. The next step recited determines the “degree of similarity” between the first segment and the selected portion. The final step recites “extracting a part of said selected portion from said first portion.” If we assume that the determining step is in actuality a mathematical operation performed on the digital representation of the physical seismic trace, the claim when analyzed in its entirety still defines a process for producing a segment of a seismic trace, which is free from a multiple noise event, from a segment of the trace which includes the multiple noise event. Thus) while the steps recited in the claim may include the execution of a mathematical procedure, it is clear that the claim as a whole defines a sequence of steps for operating upon a seismic data trace to produce a different, noise-free seismic data trace. As is the case in Appeal No. 76-717, we do not find that claim 1 merely recites a mathematical formula or method of calculation and, thus, we conclude claim 1 recites a statutory process. We also find the dependent claims in this case to recité statutory processes under the reasoning set forth with regard to the dependent claims in Appeal No. 76-717.

In Appeal No. 76-719, claim 1, and therefore claims 2-9 dependent thereon, begin with a seismic record having a coherent component and a noise component. One trace is compared with other traces of the record to determine the coherent component and, using the coherent component, the noise component. The coherent component and the noise component are then separately placed on an output signal record medium and an output noise record medium, respectively. The result is a seismic record with the noise removed and a physical record of the noise which has been removed.

Claim 10, and claims 11-15 dependent thereon, begin with a common depth point, moveout-corrected, and stacked seismic data record having a coherent component and a noise component. The shape and amplitude of the coherent signal common to a reference trace and a plurality of other traces are determined. The portion of the reference trace corresponding to the coherent signal is computed and recorded on an output signal record medium. ■

The analysis of each of the claims in Appeal No. 76-719 necessarily follows the analysis set forth above in Appeal Nos. 76 — 717 and 76-718. Although the specification makes it clear that the “compute” steps recited in each of the independent claims of this case refer to the execution of mathematical operations on the seismic traces, the claims recite such executions within the framework of a process for filtering out or removing noise from the seismic trace to produce noiseless traces which are recorded on an output signal medium. Each of these independent claims recites processes which include the performance of mathematical calculations as but one of a sequence of substantive steps. The claims in their en-tireties are not, however, mere procedures for solving mathematical problems. The determination of whether the processes as claimed are statutory requires an analysis of each of the claims as a whole. Appellants do not assert a recitation of a formula or a method of calculation as a basis for patentability of the recited processes, and it is clear that any mathematical operations performed in practicing the processes are incidental to the recited series of steps whereby a seismic data record is analyzed and processed in a specific manner to produce and record a noiseless seismic data record.

As we stated above (see p. 1080), appellants’ selection of a general purpose computer and digital data processing techniques to implement the processes does not determine whether these claimed processes are statutory. Since the claims before us do not merely recite mathematical formulas or methods of calculation, we reverse the board’s decision that claims 1 — 21 in Appeal No. 76-719 are nonstatutory.

The Solicitor argues in his supplemental brief that the claims at issue are not statutory subject matter because they are computer programs and computer programs are not patentable under Benson and Flook. This broad statement is not at all germane to the considerations before this court and is an erroneous statement of the law. We stated in In re Chatfield, 545 F.2d supra at 155, 191 USPQ at 733, that “the mere labeling of an invention as ‘a computer program’ does not aid in decision making” and the Supreme Court declined to decide either Benson or Flook on such broad, non-substantive grounds but rather considered the specific recitations in the claims. There is no reason for the Solicitor or the PTO to shortcut the analytical framework set forth in Benson, Flook, and decisions of this Court by relying on unfounded generalities.

Although the board stated that it felt “constrained” by our decision in In re Christensen, 478 F.2d 1392, 178 USPQ 35 (CCPA 1973), to find the claims of the three applications nonstatutory, we find the results reached here to be harmonious with our decision in Christensen. The claims in Christensen, when considered in their entirety, recited data-gathering steps in conjunction with solving a mathematical equation. Such is not the situation with the instant claims, however, which recite statutory methods for producing new and different, noise-free seismic traces from seismic data traces which contain noise.

Because we find each of the claims in all three appeals to recite statutory processes, we reverse the decision of the board in each of the three appeals.

REVERSED. 
      
      . Claims 1-17 of Appeal No. 76-717, application serial No. 305,386, filed November 10, 1972, for “Method of Enhancing Common Depth Point Seismic Data,” claims 1-22 of Appeal No. 76-718, application serial No. 327,267, filed January 29, 1973, for “Method for Reducing Multiple Events in a Seismic Record,” and claims 1-21 of Appeal No. 76-719, application serial No. 230,810, filed March 1, 1972, for “Method for Enhancing Seismic Data.”
     
      
      . The Supreme Court handed down its decision in Parker v. Flook, 437 U.S. 584, 98 S.Ct. 2522, 57 L.Ed.2d 451, 198 USPQ 193 (1978), after the oral argument of these appeals. Due to the similarity of issues in Flook and the instant appeals, these appeals were restored to the calendar on July 13, 1978, by an order of this court, and the parties were requested to file supplementary briefs on the bearing that decision might have on the issues before us.
     
      
      . 35 U.S.C. § 101 provides:
      Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
      35 U.S.C. § 100(b) provides:
      The term “process” means process, art or method, and includes a new use of a known process, machine, manufacture, composition of matter, or material.
     
      
      . The following is a representative claim from Flook’s application:
      1. A method for updating the value of at least one alarm limit on at least one process variable involved in a process comprising the catalytic chemical conversion of hydrocarbons wherein said alarm limit has a current value of
      Bo + K
      wherein Bo is the current alarm base and K is a predetermined alarm offset which comprises:
      (1) Determining the present value of said process variable, said present value being defined as PVL;
      (2) Determining a new alarm base, Bl, using the following equation:
      Bl =Bo(1.0-F) + PVL(F)
      where F is a predetermined number greater than zero and less than 1.0;
      (3) Determining an updated alarm limit which is defined as Bl + K; and thereafter
      (4) Adjusting said alarm limit to said updated alarm limit value.
     
      
      . The mere presence of a mathematical formula in a patent claim is not prima facie grounds for holding the claim nonstatutory. This conclusion is supported by the Supreme Court’s decision in MacKay Co. v. Radio Corp., 306 U.S. 86, 59 S.Ct. 427, 83.L.Ed. 506, 40 USPQ 199 (1939), where the claim in issue recited:
      15. An antenna comprising a pair of relatively long conductors disposed with respect to each other at an angle substantially equal to twice
      
        
      
      degrees, I being the length of the wire and a the operating wave length in like units, and means in circuit with said antenna for exciting the conductors in phase opposition whereby standing waves of opposite instantaneous polarity are formed on the conductors throughout their length.
      
      
      . Numerous legal writers have addressed the question of whether computer programs are patentable under the present statute. See Comment, Computer Programs: Should They Be Patentable?, 68 Colum.L.Rev. 241 (1968); Comment, Computer Program Protection: The Need To Legislate A Solution, 54 Cornell L.Rev. 586 (1969); Comment, Computer Program Classification: A Limitation On Program Patentability As A Process, 53 Ore.L.Rev. 501 (1974); Note, Protection of Computer Programs: Resurrection of the Standard, 50 Notre Dame Law., 333 (1974). The Supreme Court did not definitively answer this question in either Benson or Fiook because it said the issue was more appropriately within the jurisdiction of Congress, See Benson, supra at 73, 175 USPQ 677; Flook, supra, 98 S.Ct. at 2528, 198 USPQ 199-200. The thrust of the Benson opinion was that certain claims reciting a mathematical algorithm were not statutory, and the holding in Flook was “that a claim for an improved method of calculation, even when tied to a specific end use, is unpatentable under [35 USC] § 101.” (Emphasis added.) Flook, supra, 98 S.Ct. at 2528 n.18, 198 USPQ at 199 n.18.
     
      
      . The Supreme Court endorsed this holding in Flook when it stated:
      Section 103, by its own terms, requires that a determination of obviousness be made by considering “the subject matter as a whole.” 35 U.S.C. § 103. Although this does not necessarily require that analysis of what is patentable subject matter under § 101 proceed on the same basis, we agree that it should. [Emphasis in original.]
      
        Id., 98 S.Ct. at 2528 n. 16, 198 USPQ at 199 n. 16.
     
      
      . No statutory basis exists for declaring claimed processes nonstatutory merely because they are implemented by a computer system. The Supreme Court has looked to the nature of the invention as recited by the claims and not to how the process is carried out. We see no reason or precedent for treating a computer implemented process differently than any other machine-implemented process. See In re Deutsch, 553 F.2d 689, 193 USPQ 645 (CCPA 1977); In re Chatfíeld, supra.
     
      
      . The “determining” step is explained in the flow diagrams as follows:
      
        FIND AND TIME Tx OF THE EVENT COMMON TO THE EVENT AT TR ON TRACE X IN THE WINDOW USING THE EQUATION
      
      
        
      
      
        WHERE
      
      ^ BETWEEN OCCURANCE OF SOURCE WAVE AND RECEIPT BY DETECTOR xx: RANGE OF DETECTOR PRODUCING TRACE X V„F STACKING VELOCITY OFSOURCE WAVE BETWEEN * SOURCE, REFLECTOR AND DETECTOR tQ * VERTICAL TRAVEL TIME OF SOURCE WAVE BETWEEN SURFACE AND REFLECTOR
      
      The “cross correlating” step, according to the flow diagrams, is accomplished as follows:
      
        CROSS CORRELATE TRACE R WITH TRACE X / e COMPUTE CORRELATION COEFFICIENT C
      
      
        
      
      
        WHERE i IS MEA SURED FROM THE LEFT WINDOW EDGES
      
       
      
      . According to the specification, the degree of similarity, K, is derived from the relationship:
      
        
      
      where:
      Alj is the amplitude of the waveform in window A1 at *: point i from the left edge of window Al;
      Bl; is the amplitude of the waveform in window Bl at a point i from the left edge of window Bl;
      i ranges incrementally at data point spacings from the left edge to the right edge of the windows Al and Bl.
      
      
      . Again, we note legal precedent which states that the mere presence of a mathematical expression or calculation in an apparatus or process is not sufficient to find the claim, as a whole, to recite nonstatutory subject matter. In Flook, the Supreme Court stated “a process is not unpatentable simply because it contains a law of nature or a mathematical algorithm,” supra, 98 S.Ct. at 2526, 198 USPQ 197. In our decision in In re Chatfield, supra, we found the dependent claims to recite statutory methods for operating a computer system even though the dependent claims set forth specific formulas for use in implementing the methods.
     
      
      . Very simply, our decision today recognizes that modern technology has fostered a class of inventions which are most accurately described as computer-implemented processes. Such processes are encompassed within 35 U.S.C. § 101 under the same principles as other machine-implemented processes, subject to judicially determined exceptions, inter alia, mathematical formulas, methods of calculation, and mere ideas. The overbroad analysis of the PTO errs in failing to differentiate between a computer program, i. e., sets of instructions within a computer, and computer-implemented processes wherein a computer or other automated machine performs one or more of the recited process steps. This distinction must not be overlooked because there is no reason for treating a computer differently from any other apparatus employed to perform a recited process step.
     