Combining borehole images with deep shear wave imaging technology

A major challenge of integrating borehole image and geophysical measurements is to bridge the gaps between their dissimilar resolutions. Identifying and characterizing geological features like bedding contacts and fractures, by combining high-resolution borehole imaging (BHI) with deep shear wave imaging (DSWI) technology, leads to an improved understanding of the subsurface. 

INTRODUCTION

High-resolution borehole images are suited to identify fractures, bedding, dip and azimuth information, facies types and other properties along the borehole. Besides coring, this evaluation method reveals the highest-resolution geological details, resolving features down to c. 0.2-in. (Paillet 1990). However, due to its small wavelength (in the sub-inch scale) ultrasonic waves, for example, are strongly affected by attenuation when propagating into the formation. Consequently, this method does not allow for the imaging of geological features away from the wellbore.

In recent times, the development of borehole acoustic array tools enabled the application of new techniques that are able to derive structural information away from the wellbore. This is especially true for single-well imaging (SWI), first discussed by Hornby (1989). Hornby has used monopole excitations to measure compressional waves, could provide information in the sub-seismic scale. Another way to illuminate the surrounding formation, and origin of the DSWI, is based on reflection data generated by a cross-dipole source (Tang 2004). These data do not only allow determination of the structural lateral extend and dip magnitude of a formation feature, but they also are able to give information about the strike direction of the reflector surface (Tang and Patterson 2009). The root for this determination lies in the directional nature of the dipole source.

In comparison to the borehole imaging measurements, the excited acoustic shear waves are much lower in frequency and, therefore, allow for deeper penetration into the formation. In particular, wireline dipole sources generate formation shear waves at frequencies as low as 1 kHz. Because of their relatively large wavelengths, they can, in fact, propagate as much as 100 ft into the formation, reflect, and still be detected across the receiver array. Thereby, the associated vertical and horizontal resolution is approximately 3 to 3½ ft, as opposed to the earlier mentioned borehole image resolution of c. 0.2-in.

THEORY AND METHOD

Borehole imaging technology provides a wealth of geological, petrophysical and geomechanical information of the formation surrounding the borehole. It is, therefore, crucial to use the most appropriate imaging system for the expected geology (Lagraba 2010). The two most common techniques in this connection are acoustic and electrical/resistivity imaging. Other imaging principles, especially acquired during logging while drilling (LWD) acquisitions, incorporate the usage e.g. of gamma ray, density or photo electric measurements (Liu 2017). In respect to the context of combining wireline DSWI with BHI, the focus lies on the usage of wireline acoustic and electrical imaging technology.

The best way to combine images of the borehole wall with DSWI would be the usage of acoustic BHI technology. The reason lies in the same physical approach that is used for both measurements, as a reflector surface occurs only if a sufficiently high impedance contrast exists, e.g. between formations or within faulting zones. Therefore, an amplitude image that contains the first reflected wave responses is the primary source for interpretations. Moreover, a travel-time image can be derived from the arrival times of the reflected waves. In combination with a correct borehole fluid slowness, this image can yield a picture of the wellbore shape.

It needs to be mentioned that the reflection at the borehole wall occurs directly at the interface to the borehole fluid. This implies that the amplitude and travel-time images solely contain information about the borehole wall and not of the formation behind it. Hence the depth of investigation can be assumed as zero. The measurement, itself, uses an ultrasonic transducer that acts as a source and receiver, which will cover the whole 360° of the borehole wall.

Electrical wireline imaging tools measure the resistivity of the formation surrounding the wellbore. In contrast to the acoustic BHI measurement, electrical imaging uses multiple electrodes that are located on pad devices, which are attached on arms to the tool. These arms will press the pads onto the borehole wall, to minimize the distance between formation and electrode. The outcome of this measurement principle is that the borehole wall is not completely covered, and stripes of unknown resistivity values will occur.

Furthermore, electrical currents will not only flow along the interface of the wall to the borehole fluid, but also within the formation. Thereby, the depth of investigation strongly depends on the conductivity of the surrounding formation and is approximately 2 in. or less. The resistivity values are commonly displayed by either a static or dynamic image. Static means that values will be statically normalized by a single mapping, based on a whole section of image data, whereas dynamic represents a local normalization of the data within a sliding window of a few feet (Hansen and Buczak, 2010).

Fig. 1. Borehole imaging principle of a vertical borehole that is crossed by a slanted bedding plane. The cylindrical image will be unrolled at the north location, and the intersecting bedding plane will be displayed as a sinusoidal wave from which the intersection depth, apparent dip and azimuth can be derived.

BHI technology displays the borehole wall with different numbers of sectors, depending on the acquisition system, as a cylindrical image, Fig. 1. For interpretation purposes, this image will be unrolled, either at the north (vertical well) or at the top of hole (deviated/horizontal well) direction. Hence, the images are either displayed by the geographic directions north (0°/360°), east (90°), south (180°) and west (270°) or the position within the borehole up (0°/360°), right (90°), down (180°) and left (270°). 

If a bedding plane is not perpendicular to the borehole and crosses it at a certain depth, the result is a sinusoidal wave in the image. This wave can be described by the following equation:          

(1)

where a represents the offset in depth (z) direction, b the amplitude of the wave and c the offset in azimuthal (θ) direction. To retrieve these three variables, it is necessary to have at least three defined points on the sinusoid, such that a sine fit function can be applied.

The next step is the transformation of three sinusoid defining values into the intersection depth (z_int), apparent dip (ϕ_app) and apparent azimuth (θ_app) of the intersecting plane:

z_int = a      

(2)           

(3)

(4)

where r(z_int) represents the radius of the borehole at the intersection depth. Since we are not only interested in displaying the features with their apparent dips and azimuths, but also within the subsurface, we need to perform four coordinate transformations, incorporating the borehole azimuth (θ_hole) and inclination (ϕ_hole), as well as the apparent dip and azimuth of the intersecting plane. The four transformations can be described as two rotations around the z- and two rotations around the y-axes as follows:

(5)

(6)

(7)

(8)

To obtain the true dip (ϕ_true) and azimuth (θ_true) of the intersecting plane in the subsurface, all rotation matrices needs to be multiplied by each other:

R = R_a × R_b × R_c × R_d      

(9)

Thereby, we are able to extract both angles from the resulting rotation matrix R by the following equations:

(10)

(11)

where R_[3,3]represents the matrix entry in the third row and column.

Due to the fact that borehole images are orientated with references to the borehole trajectory, the calculation for the case if a vertical (orientated towards north direction) well is measured differs from the one of a deviated/horizontal (orientated towards top of hole direction) well. Hence the rotation matrix R_c (Cf. Eq. (7)) will be applied to the north orientated apparent azimuth

(12)

DEEP SHEAR WAVE IMAGING

The wireline multipole acoustic array tool, which is used to excite and measure the shear waves, consist of four sources located on the circumference and offset from each other by 90 degrees. To conduct the cross-dipole measurements the diametrically opposed sources are fired with opposite polarity and pairwise, such that two orthogonal dipole point sources in x- and Y- direction can be assumed. This assumption arises from the relatively low excitation frequencies, where the fluid wavelength is large compared to the tool radius. At the receiver array, eight four-component sensors will measure the responses and diametrically opposed receivers are subtracted from each other. This yields, in total, eight four-component receiver data matrices that can be expressed relative to the local base vectors by

(13)

where the measured receiver accelerations are denoted by a_◉,×. Thereby ◉ equals the fired source pair × and the recorded receiver direction.

Reflection surfaces that are measured by the cross-dipole excitation are defined by image points that lie in the so called “sagittal” plane, Fig. 2. This plane is defined by three points, the source position S, the receiver position R and the image point I. In principle, this plane can be located anywhere in space, as long as it contains the borehole symmetry axis. To measure a reflection from the surface Γ it is necessary that the elasto-dynamic properties (e.g. shear modulus) change across the interface. This could arise from a lithology change, an oil/gas contact, a mineralized fracture or something that has a sufficient contrast to the surrounding formation.

Fig. 2. Reflection principle of a surface measured with four-component receivers in the sagittal plane. Denoted are the incident and scattered wave with their corresponding polarization vectors, as well as the excitation and reception vectors.

Besides the direct waves arriving at the receiver array, the P-P, SV-SV and SH-SH reflections from the reflector surface will be recorded. Thereby, the amplitudes of the individual components are dependent on the location of the sagittal plane toward the dipole source excitation direction, with the corresponding arbitrary (non-zero) angle y₀ that defines the angle between the normal unit vector of the sagittal plane and the Y-source. In the special case that y₀ = 0 (red dashed arrows) the measured XX-component will only contain SH-SH reflections, whereas the YY-component will only contain P-P and SV-SV reflections. In theory, the cross-components (XY and YX) should, therefore, be free of any reflection. 

It should be mentioned that the SH-SH reflections are measurable in the borehole fluid, although only the radial component of the particle velocity is continuous at the borehole wall. This assumption is only valid for a low-frequency excitation, where the borehole fluid wavelength is large, compared to the borehole radius. The reason lies in the particle motion of the borehole fluid, as it will move in unison with the borehole. All of these described theoretical expectations lead to the fact that the cross-line components in the data matrix (Cf. Eq. (13)) can be minimized by a rotation over the angle y₀.

Therefore, the reason to apply this rotation lies not only in the minimization of the cross-line components, but also in the maximization of the induvial reflector surface amplitudes for the XX- and YY-component. A reflector, whose azimuth has been gathered from e.g. a borehole image, should, therefore, be maximized either in the wavefield in line with the sagittal plane (P-P & SV-SV) or in the wavefield perpendicular to the sagittal plane (SH-SH).

Because of their constant logging speed during the acquisition of data, acoustic wireline measurements offer the ability to perform a wave separation into an up- and downgoing wavefield. To achieve this, a three-step approach needs to be performed:

1. The direct wave (in case of a dipole excitation the formation flexural wave) will be modelled in the common source gather (CSG).
2. Afterwards, the modelled wave is subtracted from the recorded wavefield.
3. Finally, the resulting wavefield is filtered by a median filter in the common receiver gather (CRG) domain.

Accordingly, the CSG describes an array of recorded waves, which pertains to one shot at a certain tool location. These data are commonly used to perform the slowness processing. The CRG, instead, contains a single receiver array (e.g. the first receiver array) for all measured depths. This display form allows the user to visually distinguish between the direct arrivals and the reflections from the surroundings.

Fig. 3. Description of the receiver (Panel A) and transmitter (Panel B) array, where the receiver array contains the recorded waveforms from the actual source excitation (■)and the transmitter array is assembled to a reflect virtual source excitation (■).

To obtain the up- and downgoing wavefield, it is necessary to order the recorded waveforms into a receiver and transmitter array, Fig. 3. Thereby, the receiver array (Panel A) contains all receivers that belong to one shot at a certain tool location. For the transmitter array, the constant logging speed of the wireline acquisition comes into account. Due to this fact, a constant spatial frequency can be assumed that reflects the inter-receiver spacing of the tool. If this holds true, N equidistant tool positions are vertically offset from each other by the inter-receiver spacing (Panel B).

The next step is the grouping of the individual receiver waveforms and tool positions to the transmitter array. Starting with the N-th receiver of the first tool position,

followed by receiver N-1 for the second tool position 

and finalized by the 1st receiver for the N-th tool position.

Now the reciprocity principle allows us to exchange the transmitter and receiver locations (blue dashed arrows) for the same tool position (e.g. for the first tool position transmitter T switches its position with the last receiver ). If this is done for all N tool positions, the transmitter array is finalized, with a virtual source that has the same offset relative to the last receiver as the original transmitter has relative to the first receiver. Therefore the transmitter array will consist of the waveforms recorded at the receivers

while the receiver array will contain the receivers

(R₁,R₂, …,R_N).

Fig. 4. Measurement principle of the up- and downgoing wavefield under the usage of the transmitter and receiver array for a dipping bedding plane.

With the receiver and transmitter array, we are now able to extract the up- and downgoing wavefield from the recorded data (Fig. 4) as follows:

• Upgoing wavefield: If a bedding plane is located below the transmitter array and the virtual source is fired (Fig. 4), we are able to observe  direct waves, which are propagating from

The wave move-out is thereby positive (blue dashed line in Panel B of Fig. 3), whereas upgoing reflections from the bedding plane will propagate from

and therefore have a negative move-out (green dashed line).

• Downgoing wavefield: If a bedding plane is located above the receiver array, and the source is fired (Fig. 4), we are able to observe direct waves, which are propagating from

R₁ to R_N.

The wave moveout is, thereby, positive (blue dashed line in Panel A of (Fig. 3), whereas downgoing reflections from the bedding plane will propagate from

R_N to R₁

and thus have a negative move-out (green dashed line).

To remove the direct wave from the data in the CSG, without removing the reflections from reflector surfaces, it works best if the move-out of the reflections is opposed to the direct wave. This means that for interpretation of recorded data, that upgoing reflections will occur in the transmitter array and downgoing reflections in the receiver array.

In the next step, both extracted wavefields will be migrated to create an image of the formation surrounding the borehole. The migration approach is based on the inverse generalized Radon transform that incorporates a background slowness model to image the recorded reflection events at their spatial point of origin. The method is based on the single-scattering Born approximation, which only accounts for primary reflections in the data and can be categorized under the general term “Kirchhoff-type” migration. Unfortunately, the tool receiver array aperture is too short, in comparison to the imaging distances, to enable the usage of tomography methods for the calculation of a complex velocity model. Therefore, the background slowness will be assumed constant, representing the calculated formation shear slowness parallel to the borehole.

Fig. 5. Measurement of a reflection surface intersecting the borehole (left) and not crossing the wellbore (right).

Reflections that occur in the sagittal plane can either cross the borehole at a certain depth or run in parallel to the wellbore and not intersecting it, Fig. 5. As this work is focused on the combination of borehole images with DSWI, only reflection surfaces that intersect the borehole are of interest. According to this, the primary information that can be captured from DSWI for the individual reflections are the apparent dip, intersection depth and lateral extend away from the wellbore. The correct azimuth, instead, can only be obtained with a 180° ambiguity. While it is possible to obtain the orientation of the sagittal plane, as described earlier, through the rotation of the source excitation direction by minimizing the cross-components, the reflector surface can occur either on the right- or left-hand side of the sagittal plane. The reason behind this uncertainty is, again, the fact that the borehole fluid wavelength is much larger than the tool radius, such that no phase or amplitude variations on the four-component receivers occur, which would allow for determination of the correct azimuth. Hence, the azimuth information needs to be extracted from borehole images.

To determine the intersection depth and angle of the reflection surface, it is necessary to define at least two points that cross the borehole. This means that one point needs to be defined in the upgoing, and one in the downgoing migrated image. Both image points will be specified by a measured depth (z_1,2) and lateral distance (x_1,2) away from the wellbore. With this information, the intersection depth (z_int) and apparent dip (ϕ_app) can be calculated as follows:  

(14)

(15)

In combination with an apparent azimuth, derived with BHI technology, the true dip (ϕ_true) and azimuth (θ_true) of the intersecting plane can again be calculated with the equations (5)-(12).

3D Visualization. The determination of the true dip and azimuth of complex geological features that intersect the borehole will lead to a more accurate structural model of the subsurface. To display the true dip and azimuth, in reference to a local coordinate system of the subsurface, requires further calculations and will be the subject of future publications. 

CONCLUSIONS 

The authors have demonstrated that combining borehole imaging (BHI) and deep shear wave imaging (DSWI) technology leads to a more accurate structural model of the subsurface. Borehole images represent a detailed localized view of the drilled formation at the wellbore, whereas deep shear wave images will propagate deeper in the formation resolving features in the sub-seismic scale. DSWI is not able to resolve the 180° ambiguity of reflectors occurring in the sagittal plane of the up- and down-going migrated image. For this reason the azimuth of an identified reflector surface is determined by a borehole image. In the case of a vertical well, the special interest lies in the detection of fault or fracture zones, which can lead to unforeseen problems during drilling or completion. Additionally, in horizontal wells, the knowledge of the exact position of bedding or formation boundaries can help to stay within the reservoir or to refine the reservoir model defined by the seismic.  

^{ACKNOWLEDGEMENTS} 

^{This article contains elements from a technical paper presented at the Society of Petrophysicists and Well Log Analysts (SPWLA) 60th Annual Logging Symposium, held in the Woodlands, Texas, June 17-19, 2019. The authors would like to thank Baker Hughes and Tullow Oil for permission to publish the images and work product contained in this article. They would also like to thank internal reviewers Tim Geerits and Anna Przebindowska for their contribution.}