Abstract:
The present invention is a propagation resistivity system that utilizes one or more transmitter coil antennas, or “transmitters” and at least two receiver coil antennas, or “receivers”. The system uses a wellbore resistivity tool which may be embodied as a MWD tool or as a wireline tool. Two or more transmitters may be spaced equally on either side of two or more spaced-apart receivers. Two or more frequencies are transmitted and received simultaneously. Multiple frequencies may be transmitted from each transmitter or from separate transmitters at the same time. Multiple frequencies are simultaneously received and analyzed by the receiver electronics, thereby reducing the measurement time for multiple frequency measurements. In one embodiment each of two transmitters transmits simultaneously. One transmitter operates on a high frequency. The second transmitter operates at a lower frequency. The higher frequency signal penetrates a relatively shallow radial distance into the formation and the lower frequency penetrates to a radial depth which exceeds the higher frequency. Composite measurements made at two radial depths are used to compensate for factors having adverse effects on resistivity measurements in the immediate region of the borehole. Such factors include invasion, variations in borehole size, variations in borehole fluid, and the like.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of Invention 
     This invention generally pertains to well logging, and more specifically to well logging apparatus and methods for rapidly developing data for determining such formation properties as resistivity. The apparatus and methods have general applications, but are particularly well suited for measuring while drilling applications employing advanced, high speed drilling apparatus. 
     2. Background of the Art 
     Resistivity is well known parameter used in evaluating earth formations surrounding a well borehole. In the oil and gas exploration and production industry, a measure of resistivity is used to delineate hydrocarbons from saline water within pore space of earth formation penetrated by the borehole. The basic principal underlying the measurement is that for a given formation matrix, the formation containing more resistive hydrocarbon fluid within the pore space will exhibit a greater composite resistivity than the same formation containing less resistive saline liquid within the pore space. 
     In the evolution of the art, resistivity instruments or “tools” were originally conveyed along the wellbore by means of a wireline cable. This technique is still widely used today. Resistivity related measurements are transmitted to the surface by means of the wireline for processing, interpretation and recording. This technique is applicable only in well boreholes that have been previously drilled. 
     In the petroleum industry, it is economically and operationally desirable to evaluate earth formations as they are being penetrated by a drill bit, rather than waiting until the entire well has been drilled as is required in conventional wireline logging. Apparatus and methods for evaluating formations while drilling became commercially available during the 1970s. This technology, known as measurement-while-drilling (MWD) or, alternately, logging-while-drilling (LWD), now includes a wide range of formation evaluation instrumentation which is typically mounted within a drill collar or a drill string, and conveyed along the borehole by the drill string during the drilling operation. Resistivity systems are included in the suite of available MWD systems. In addition to providing timely formation resistivity measurements while the well is being drilled, MWD resistivity measurements can be more accurate than their wireline counterparts. Well boreholes are typically drilled using drilling fluids at a pressure exceeding formation pressure. Over time, drilling fluid “invades” the formation in the vicinity of the borehole thereby perturbing composite resistivity measurements made with a tool within the borehole. Invasion is minimal at the time of drilling and typically increases over time after completion of the drilling operation. MWD resistivity measurements made during the actual drilling operation are, therefore, less perturbed by invasion than wireline resistivity measurements made after the well has been drilled. Invasion, and compensation for the effects of invasion, will be discussed in more detail hereafter. 
     Resistivity measurement tools typically include one or more transmitter coils and one or more receiver coils. Furthermore, more than one transmission frequency is typically used. Generally speaking, multiple transmitter and receiver coils, and multiple transmission frequencies are used to obtain composite resistivity measurements from differing radial depths into the formation in order to compensate for previously-mentioned drilling fluid invasion effects, to measure a wider range of resistivities, to resolve dipping formation beds, to measure formation anisotropy variables, and to measure distance to adjacent beds in geosteering drilling operations. Propagation type resistivity systems, which measure both phase shift and attenuation of transmitted signals, are widely used in prior art MWD systems. At present, this type of system is not used for wireline measurements, but their relative low cost, small physical size and high accuracy forms an attractive addition to the wireline logging arsenal of tools. 
     U.S. Pat. No. 5,581,024 to Meyer, Deady and Wisler discloses a depth correction and computation apparatus and methods for combining multiple borehole resistivity measurements. U.S. Pat. No. 5,594,343 to Clark, Wu, and Grijalva discloses resistivity well logging apparatus and methods with borehole compensation including multiple transmitters asymmetrically disposed about a pair of receiving antennas. U.S. Pat. No. 5,672,971 to Meador, Meisner, Hall, Thompson and Murphy discloses a resistivity well logging system arranged for stable, high sensitivity reception of propagating electromagnetic waves. U.S. Pat. No. 5,682,099 to Thompson, Wisler, and Schneider discloses a method for bandpass sampling in MWD systems, which is applicable to multiple frequency resistivity systems. This patent is intended to be incorporated herein by reference for disclosure such as the use of transmitters and receivers to garner information on the resistivity of the formation in the region of a wellbore. U.S. Pat. No. 5,892,361 to Meyer, Thompson, Wisler, and Wu discloses the use of raw amplitude and phase in propagation resistivity measurements to measure borehole environment. U.S. Pat. No. 5,329,235 to Zhou, Hilliker and Norwood discloses a method for processing signals from a MWD resistivity logging tool to enhance vertical resolution. There are other disclosures in the art, which discuss various configurations, frequencies, and processing methods of resistivity logging tools. 
     In prior art systems employing multiple transmission frequencies, measurements are made sequentially using one transmitter and one frequency at a time. Because of the relatively slow drilling penetration rates of earlier MWD measurement systems, the time consuming sequential multiple frequency transmission has not presented a significant vertical depth resolution problem. The industry is, however, evolving toward more and faster MWD measurements, especially when the measurements are made when the drill stem is being removed or “tripped” from the borehole for purposes of changing a drill bit or for some other purpose. Sequential frequency transmission systems are detrimental to these faster methods. In addition, since wireline logging tools are conveyed along the borehole at a much faster rate than their MWD counterparts, sequential rather than simultaneous multiple frequency transmission is even more detrimental. No known prior art discloses a MWD resistivity logging system, which used multiple transmitter and receivers and multiple transmission frequencies that are transmitted simultaneously rather than sequentially. 
     SUMMARY OF THE INVENTION 
     In view of the prior art systems discussed above, an object of the present invention is to provide a propagation resistivity MWD logging system which employs at least two transmission frequencies transmitted simultaneously. 
     Another object of the present invention is to provide a MWD propagation resistivity logging system which utilizes at least two transmitters to transmit at least two different frequencies simultaneously. 
     Yet another object of the invention is to provide a MWD propagation resistivity logging system in which a single transmitter transmits at two different frequencies at the same time. 
     Still another object of the present invention is to provide a MWD propagation resistivity logging system employing at least two transmitters and two receivers which measure signals that are subsequently combined to yield phase difference and attenuation factor measurements that are compensated for adverse effect of systematic transmitter and receiver error. 
     Still another object of the invention is to provide a propagation resistivity measurement system that meets the above mentioned objects and that can be configured as a tool for wireline logging operations. 
     There are other objects and applications of the present invention that will become apparent in the following disclosure. 
     The present invention is a propagation resistivity system that utilizes one or more transmitter coil antennas, or “transmitters” and at least two receiver coil antennas, or “receivers”. The system uses a wellbore resistivity tool or well-logging device which as illustrated may be embodied as a MWD tool, but can alternately be embodied as a wireline tool. The invention will be described using only two transmitters, two receivers, and two frequencies. Extension to three or more transmitters and/or frequencies is straight forward and would be understood by one of ordinary skill in the art. Two transmitters may be spaced equally on either side of two spaced-apart receivers. Each of the two transmitters transmits simultaneously. One transmitter operates on a high frequency, such as 2 megaHertz (MHz), which is an industry standard. The second transmitter operates at a lower frequency, which may be nominally as low as about 100 kiloHertz (kHz). The higher frequency signal penetrates a relatively shallow radial distance into the formation and the lower frequency penetrates to a radial depth which exceeds the penetration of the higher frequency. Composite measurements made at two radial depths are used to compensate for factors having adverse effects on resistivity measurements in the immediate region of the borehole. Such factors include invasion, variations in borehole size, variations in borehole fluid, and the like. 
     The higher frequency signal may be transmitted from the first transmitter T 1 , and the lower frequency signal may be transmitted simultaneously from the second transmitter T 2  during a time interval t a . At a later time interval t b , the reverse occurs. That is, there is simultaneous transmission of the high frequency signal from transmitter T 2  and the lower frequency signal from T 1 . Alternately, both high and low frequencies can be transmitted simultaneously from T 1 , and subsequently both high and low frequencies can be transmitted simultaneously from T 2 . In either embodiment, two frequencies are transmitted simultaneously from the tool to propagate into the formation and to produce signals, which are subsequently detected by the receivers. 
     Using the first transmission sequence, the high frequency or first frequency signal from T 1  is received at the closer spaced receiver R 1  with a phase φ 111  measured in degrees or radians and relative to the phase of the transmitted signal (the first number after the φ indicating the transmitter from which the signal originated, the second number after the φ indicating the signal is received by the first receiver, and the third number indicating the signal is propagated at a first frequency). The high or first frequency signal from the first transmitter T 1  is also received at the first receiver R 1  having been attenuated relative to the transmitter signal by an amount α 111  measured in decibels or nepers. The numbers after the α indicate the same as the three numbers after the phase. Simultaneously, phase and attenuation of the signal from transmitter T 1  is received at receiver R 2 , at frequency  1 , φ 121  and α 121 . It is well known in the art that the phase difference φ 121 -φ 111  and the attenuation difference α 121 -α 111  are functions of formation properties and conditions in the vicinity of the borehole and receiver antennas, and may be defined as a phase difference Δφ 11  and attenuation difference Δα 11 . In each case the first number after the Δφ or Δα indicates from transmitter T 1  and the second number indicates at frequency  1 . In particular the phase difference and attenuation difference are functions of resistivity of the formation. T 2  simultaneously transmits a signal at the lower frequency, denoted by the subscript 2, which is received by R 2  and by R 1  thereby defining a phase difference Δφ 22  and attenuation difference Δα 22 . Next in the measurement sequence T 2  then transmits the high frequency, which is received at R 2  and R 1  and thereby defines a phase and attenuation difference Δφ 21  and Δα 21 . T 1  simultaneously transmits a signal at the lower frequency which is received by R 1  and R 2 , thereby defining a phase and attenuation difference Δφ 12  and Δα 12 . The terms Δφ 11  and Δφ 21  are combined to yield a compensated phase difference Δφ C1 =(Δφ 11 +Δφ 21 )*½. Similarly the terms Δα 11  and Δα 21  are combined to yield a compensated attenuation difference Δα C1 =(Δα 11 +Δα 21 )*½. And in like manner the terms Δφ 12 , Δφ 22 , Δα 12 , and Δα 22  are combined to yield compensated phase difference Δφ C2 =(Δφ 12 +Δφ 22 )*½ and attenuation difference Δα C2 =(Δα 12 +Δα 22 )*½. 
     Transmission is switched from transmitter T 1  to T 2  and back again to transmitter T 1  in the first embodiment of the invention. In the second embodiment T 1  simultaneously emits high and low frequencies, and next in the measurement sequence T 2  simultaneously emits high and low frequencies. Compensated values ø CH , ø CL , as well as α CH  and α CL , are computed in the same manner. 
     As is well known in the industry compensated values Δφ C1 , Δφ C2 , Δα C1 , and Δα C2 , are then used separately and/or combined to determine formation resistivities, and subsequently formation hydrocarbon saturation, despite the effects of invasion, borehole fluids, and systematic equipment error. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 shows a resistivity tool embodied as a MWD system; 
     FIG. 2 shows a resistivity tool embodied as a wireline logging system; 
     FIG. 3 shows a resistivity tool with one pair of receivers and N/2 pairs of transmitters; 
     FIG. 4 shows the circuitry controlling the operation of transmitters and receivers of a resistivity tool; 
     FIG. 5 is a timing diagram of a tool which simultaneously transmits two different frequencies using two transmitters; 
     FIG. 6 is a timing diagram of a tool which simultaneously transmits two different frequencies from the same transmitter; and 
     FIG. 7 is a flow chart for the method of measuring phase and amplitude parameters, compensating these measurements for systematic transmitter and receiver error, and combining compensated phase and amplitude measurements made at multiple frequencies to obtain formation resistivity. 
    
    
     DETAILED DESCRIPTION 
     The resistivity tool as illustrated may be embodied as a MWD tool, or as a wireline system. Both embodiments will be disclosed. 
     FIG. 1 shows the invention embodied as a MWD system. Receivers R 1  and R 2 , denoted at  22  and  20 , respectively are spaced apart a distance  28  on the outer surface of a preferably stainless steel mandrel  10  which is typically a drill collar. Transmitters T 1  and T 2 , denoted at  16  and  18  respectively, are equally spaced a distance  26  from receivers R 1  and R 2 , respectively. Dimension  28  may be, for example about 6 inches (in), and dimension  26  may be, for example, about 30 in. The transmitters and receivers are powered and controlled by an electronic package  29 , which is mounted within the wall of mandrel  10 . The package  29  can also contain telemetry equipment to transmit measured data to the surface in real time, or to alternately record the data for subsequent playback, processing and analysis. The MWD tool is a component of a drill string which is terminated at the lower end by drill bit  24 , and is conveyed along borehole  14  by drill pipe  12 . Resistivity of formation  11  penetrated by borehole  14  can be measured as the drill string advances in the borehole, or as the drill string is removed or “tripped” from the borehole. The drill string is operated in a manner well known in the art using a drilling rig and associated equipment (not shown) located at the surface  32  of the earth. 
     Still referring to FIG. 1, one pair of transmitters T 1 , T 2  and one pair of receivers R 1 , R 2  are illustrated. Measured signals from the transmitters T 1 , T 2  are processed to yield compensated measures of signal phase and attenuation at two different radial depths of investigation into the formation  11 . As mentioned previously, borehole conditions and drilling fluid invasion can adversely affect such measurements in the vicinity of the borehole, and measures at multiple radial depths of investigation can be used to minimize these adverse effects. It is possible to use additional pairs of spaced transmitters to obtain additional measures at varying depths of investigation. Additional pairs of receivers can also be used to obtain additional measurements at varying vertical resolutions. A system using N/2 pairs of transmitters will be discussed in a subsequent section of the specification. 
     FIG. 2 shows the system embodied as a wireline logging system. Receivers R 1  and R 2 , denoted at  42  and  40 , respectively, are spaced apart a distance  28 ′ on the outer surface of a logging tool  50  which is typically a stainless steel pressure housing. Transmitters T 1  and T 2 , denoted at  46  and  48 , respectively, are equally spaced a distance  26 ′ from receivers R 1  and R 2 , respectively. Dimension  28 ′ may be, for example, about 6 inches (in), and dimension  26 ′ may be, for example about 30 in. Note that the transmitter and receiver spacing in the wireline embodiment of FIG. 2 are not necessarily the same as the respective spacing in the MWD embodiment shown in FIG.  1 . 
     Referring to FIG. 2, the transmitters T 1 , T 2  and receivers R 1 , R 2  are powered and controlled by an electronic package  49 , which is mounted within the pressure housing  50 . The tool  50  is attached to a logging cable  54  by means of a cable head  52 . The logging cable  54 , which typically contains multiple electrical or fiber optic conductors, serves both as a communication path between the tool  50  and the surface of the earth  32 , and also provides a means for conveying the tool  10  along the borehole  14  using works (not shown) at the surface of the earth. Resistivity of the formation  11  penetrated by the borehole  14  can be measured as a function of depth within the borehole which is typically measured as the tool  10  is moved up the borehole  14 . 
     FIG. 3 illustrates the resistivity tool with a plurality of transmitter pairs equally spaced about a receiver R 1 , R 2  pair  62  on a mandrel  60  (additional receiver pairs may be added, e.g., shown as R 3  and R 4  and treated the same as R 1  and R 2 ). The transmitters and receivers are referenced similar to the previous discussions, with the multiple transmitter embodiment in FIG. 3 containing N/2 pairs of transmitters (where N is an even number). This yields multiple depths of investigation and additional borehole compensation. Phase and attention measurements are generally the same as with the single pair transmitter embodiment. Furthermore, systematic apparatus error correction is the same as with the single pair transmitter embodiment. 
     FIG. 4 illustrates the basic elements of the circuitry to control the transmitters and receivers of the system, and is identified as a whole by the reference number  29 ′. Transmitter coils  70  and  72  (FIGS. 1-4) transmit signals having a same polarization and are provided with such signals from the frequency transmitters  78  and  80 , respectively. The transmitters  78  and  80  are controlled by a digital signal processor or DSP  92 . A suitable DSP  92  is AD2181 manufactured by Analog Devices. DSP&#39;s are also available from Texas Instruments. Signals received by receiver coils  74  and  76 , mounted on the resistivity measuring tool in planes parallel to the plane(s) of the transmitter coil(s)  70 ,  72  (FIGS.  1 - 3 ), pass through filters  84  and  86 , respectively, and may then be sampled by the analog to digital converters  88  and  90 , respectively, at a rate at least twice the frequency of the highest frequency prior to being input into DSP  92  for separation and analysis. A multiple output oscillator circuit  82  is operatively connected to both the transmitter (e.g. via synchronization lines  83 ,  85 ) and the receiver elements of the circuit as shown in FIG.  4 . The multiple output oscillator circuit  82  may, for example, have two oscillators or two numerically controlled oscillators (NCO&#39;s) where the NCO outputs are added together with a resistor network before the final output amplifier in the transmitter; or one NCO where the sum of the two sinusoids (at the two different frequencies) are put in a lookup table and then go directly to the transmitter output amplifier. The DSP output at  94  comprises compensated phase and attenuation data at two radial depths of investigation. Such data is subsequently used to determine the resistivity and finally to empirically suggest the hydrocarbon saturation within the earth formation measured. 
     A suitable range of electromagnetic transmission frequencies which may be used in the invention is from about 100 kHz to about 10 MHz. By way of example, the first frequency may be 2 MHz and a second frequency used in the invention may be 500 MHz. 
     One advantage of the present invention is that the speed at which wellbore logging occurs may be increased without sacrificing accuracy. Prior MWD systems were functional moving axially through the wellbore at speeds of about 3 ft/min or 180 ft/hour based on one 5 second sample every ¼ ft. with an accuracy of 0.5 millisiemens per meter. The present invention may be functional at higher speeds. For example speeds may be increased from 3 ft/min to at least 6 ft/min for 2 simultaneous frequency operation while maintaining a measurement accuracy of 0.5 millisiemens per meter or better, or up to at least 9 ft/min for 3 simultaneous frequency operation without sacrificing accuracy. 
     MATHEMATICAL FORMALISM 
     The following mathematical formalism and convention will be used to describe the basic measurements of the system, and the parameter compensation methods. 
     The signal measured at each receiver of the system is 
       S =exp( i ø−α)exp( iωt )  (1) 
     where 
     S=the measured signal; 
     ø=the absolute phase with respect to the transmitter; 
     α=the absolute attenuation with respect to the transmitted signal; and 
     ω=the angular frequency of the signal. 
     The two transmitters, two receivers embodiment of the invention illustrated in FIGS. 1 and 2 will be used to illustrate the operation of the system. It should be understood, however, that a plurality of transmitter pairs as illustrated in FIG. 3 can be used, and the same data processing methodology can be used to obtain the desired compensated formation parameters. 
     During a time period ta, transmitter T 1  is turned on at frequency F 1  and transmitter T 2  is simultaneously turned on at frequency F 2 . The receivers measure eight parameters during this time interval which are 
     ø ijk  and 
     α ijk ; 
     where i=1, 2 and denotes the reference number of the transmitter generating the signal; 
     j=1, 2 and denotes the reference number of the receiver receiving the signal; and 
     k-1, 2 and denotes the frequency (1=high frequency and 2=low frequency)of the signal. 
     As an example, ø 121  is the phase of the signal from T 1  received at receiver R 2  at frequency F 1 . This notion will be user throughout the following discussions. 
     During a subsequent time period t b , transmitter T 1  is turned on at frequency F 2  and T 2  is simultaneously turned on at frequency F 1  and an additional eight parameters ø ijk  and α ijk  are measured. This yields a total of sixteen parameters from which compensated values of phase and attenuation are computed at two frequencies and consequently, two depths of investigation. Details of these computations will be discussed in the following section of this invention. 
     The steps taken in the time periods t a  and t b  are sequentially repeated as the logging tool is conveyed along the borehole thereby yielding a measure of parameters of interest as a function of depth within the well borehole. 
     FIG. 5 is a conceptual illustration of the timing sequence discussed above. A time line  100  represents events connected with the transmission of T 1 , and a time line  110  represents events connected with the transmission of T 2 . During the time interval t a  denoted at  122 , T 1  is turned on at time  102  and at frequency F 1 . Parameters illustrated are measured during this time interval. Also during t a  T 2  is simultaneously turned on at frequency F 2  and at time  102 , and the indicated parameters are measured during this time period. During the time interval t b  denoted by  124 , T 1  is turned on at frequency F 2  at time  107  and T 2  is turned on simultaneously at time  107  at frequency F 1 . The indicated parameters are measured during this time interval. The sequence is repeated, as indicated conceptually at  109 , as the tool is conveyed along the well borehole. 
     A time line  150  for one alternate embodiment of the invention is shown in FIG.  6 . In this embodiment, multiple frequencies are transmitted simultaneously at F 1  and F 2  at time  130 . The indicated parameters are made during time period  153 . During a time interval  153 , T 2  transmits at time  136  simultaneously at frequencies F 1  and F 2 . Parameters as indicated are measured during time interval  153 . The sequence is repeated, as indicated conceptually at  142 , as the tool is conveyed along the well borehole. 
     PARAMETER COMPENSATION 
     The present invention can be used for compensation to accomplish (a) a symmetric investigation of the formation and (b) to eliminate systematic errors. Absolute measures of φ and α are prone to error when the transmitter and receiver antennas and coils vary with the temperature and pressure as a result of operating in a borehole environment. As long as the measurement tool and the surrounding environs obey linear electromagnetic laws, the techniques of the invention can be used to correct for these “systematic” errors. A linear change in a circuit parameter will result in a phase or attenuation change in a received signal. This will result in an erroneous measure of true formation parameters, which are used to determine formation resistivity. 
     Compensation for systematic errors will be discussed for a single frequency for sake of brevity. The frequency indicating subscript will, therefore, be dropped from this discussion. It should be understood, however, that the same methodology is used for additional frequencies. The phase of the signal received at R 1  from T 1  is represented as 
     
       
         φ 11 =φ T1e +φ R1e +φ 11f   (2) 
       
     
     where 
     φ 11 =the measured quantity; 
     φ T1e =a phase error for transmitter T 1 ; 
     φ R1e =a phase error for receiver  1 ; and 
     φ 11f =the formation effect which is the parameter of interest. 
     Using the same notation convention, similar expression from equation (2) can be developed for measured quantities ø 12 , ø 21 , and ø 22 . The phase ø c1 , which is the phase at the specific frequency  1  and corrected for transmitter and receiver error, is 
     
       
         φ c1 =(φ 12 −φ 11 +φ 21 −φ 22 )/2  (3) 
       
     
     Substituting the set of equations represented by equation (2) into equation (3) yields 
     
       
         φ c1 =((φ 12f +φ t1ε +φ r2ε )−(φ 11f +φ t1ε +φ r2ε )+(φ 21f +φ t2ε +φ r1ε )−(φ 22f +φ t2ε +φ r2ε ))/2 
       
     
     Which reduces to: 
     
       
         φ c1 =(φ 12f +φ 11f +φ 21f −φ 22f )/2  (4) 
       
     
     where all error terms have canceled out. 
     Similar expressions can be developed for a compensated amplitude value αci at frequency i by substituting each phase value in set of equations (3) for a corresponding amplitude value using the notation convention developed throughout this disclosure. The invention, therefore, provides apparatus and methods for obtaining phase and amplitude parameters, which have been compensated for adverse effects of systematic errors. In addition, compensated values for these parameters at two or more frequencies can be obtained thereby yielding compensated parameters of interest at varying radial depths of investigation into the formation. These compensated parameters are then combined to yield formation resistivity values in which the adverse effects of formation fluid invasion and borehole perturbations have been reduced. 
     COMPENSATED RESISTIVITY METHODOLOGY 
     FIG. 7 is a flow chart summarizing the methodology of the compensated resistivity logging system. Transmitters transmit two frequencies simultaneously at block or step  160 . Receivers record the transmissions and yield eight independent absolute parametric measurements at step  162 . Transmitters again transmit simultaneously at two frequencies at step  164 . An additional eight independent parametric measurements are made with the receiver array at step  166 . Compensated phase values are computed for two different frequencies at step  168  using the parametric measurements. Compensated phase and attenuation measurements are combined at step  172  to obtain a value of formation resistivity, which is the parameter of interest used to compute hydrocarbon saturation of a logged formation. 
     While the foregoing is directed to the various embodiments, the claims are intended to cover the invention as broadly as legally possible in whatever form it may be utilized.