Step‐on versus step‐off signals in time‐domain controlled source electromagnetic methods using a grounded electric dipole

The time‐domain controlled source electromagnetic method is a geophysical prospecting tool applied to image the subsurface resistivity distribution on land and in the marine environment. In its most general set‐up, a square‐wave current is fed into a grounded horizontal electric dipole, and several electric and magnetic field receivers at defined offsets to the imposed current measure the electromagnetic response of the Earth. In the marine environment, the application often uses only inline electric field receivers that, for a 50% duty‐cycle current waveform, include both step‐on and step‐off signals. Here, forward and inverse 1D modelling is used to demonstrate limited sensitivity towards shallow resistive layers in the step‐off electric field when transmitter and receivers are surrounded by conductive seawater. This observation is explained by a masking effect of the direct current signal that flows through the seawater and primarily affects step‐off data. During a step‐off measurement, this direct current is orders of magnitude larger than the inductive response at early and intermediate times, limiting the step‐off sensitivity towards shallow resistive layers in the seafloor. Step‐on data measure the resistive layer at times preceding the arrival of the direct current signal leading to higher sensitivity compared to step‐off data. Such dichotomous behaviour between step‐on and step‐off data is less obvious in onshore experiments due to the lack of a strong overlying conductive zone and corresponding masking effect from direct current flow. Supported by synthetic 1D inversion studies, we conclude that time‐domain controlled source electromagnetic measurements on land should apply both step‐on and step‐off data in a combined inversion approach to maximize signal‐to‐noise ratios and utilize the sensitivity characteristics of each signal. In an isotropic marine environment, step‐off electric fields have inferior sensitivity towards shallow resistive layers compared to step‐on data, resulting in an increase of non‐uniqueness when interpreting step‐off data in a single or combined inversion.

(e.g. Kaufman and Keller, 1983;Keller et al., 1984;Constable, 2010), gas hydrate and methane seep detection (e.g. Weitemeyer et al., 2011;Gehrmann et al., 2016;Goswami et al., 2016;Schwalenberg et al., 2017;Attias et al., 2018), mineral exploration (e.g. Gehrmann et al., 2019;Mörbe et al., 2020) and environmental research such as mud volcano imaging (e.g. Haroon et al., 2015;Hölz et al., 2015) or offshore groundwater studies (e.g. Haroon et al., 2018b;Levi et al., 2018;Micallef et al., 2018;Gustafson et al., 2019;Lippert and Tezkan, 2020). In a CSEM survey, current is injected into the subsurface via a grounded horizontal electrical dipole (HED) antenna, and the response of the Earth is measured by one or more electric and/or magnetic field receivers located at various distances from the source. The received signal is a function of the input current, which is modified by the resistivity structure of the Earth between the transmitter and receiver, by the acquisition system itself; superimposed on this response are various sources of anthropogenic and natural noise (Strack, 1992).
CSEM applications are commonly conducted in either the time or the frequency domain. In a time-domain CSEM (TD-CSEM) experiment, a square-wave current with either a 50% (e.g. Cairns, 1997;Yuan and Edwards, 2000) or 100% duty cycle (e.g. Hördt et al., 1992;Schwalenberg et al., 2005) is commonly used. These current waveforms differ in the way that the amplitude switches from one polarity to the other, which occurs rapidly in a 100% duty cycle and is interrupted by a zero state in the 50% duty-cycle signal. Hence, the measured electric field contains both step-on and step-off signals when transmitting a 50% duty cycle and polarity reversals (negative to positive current switch or vice versa) in a 100% duty cycle.
For marine frequency-domain CSEM (FD-CSEM), the 100% duty-cycle current waveform is typically used and has been effectively applied in numerous academic and industrial surveys (Myer et al., 2011). Particularly in marine electromagnetic surveys targeting hydrocarbons, FD-CSEM is the method of choice due to its high efficiency. Yet, until very recently it was believed that seafloor-based FD-CSEM receivers lose sensitivity when applied in environments with limited water depth above the source and receivers (<300 m; e.g. Weiss, 2007) due to a masking effect of the air-sea interface, sometimes referred to as the airwave (Weidelt, 2007). However, Chave et al. (2017aChave et al. ( , 2017b have recently demonstrated using forward modelling that submerged FD-CSEM systems are effective in shallow marine environments. Alternatively, surfacetowed FD-CSEM systems are often applied to mitigate the effect of the air-sea interface (e.g. Sherman et al., 2017;Sherman and Constable, 2018;Gustafson et al., 2019). However, surface-towed CSEM suffers from a decrease in sensitivity due to signal attenuation in the conductive seawater and is mostly applied along continental shelves with limited water column thicknesses (e.g. Sherman et al., 2017;Gustafson et al., 2019).
To increase seafloor coupling and reduce the airwave signal contribution, academic CSEM surveys targeting shallow resistive structures (depth below seafloor ≤100 m) sometimes apply seafloor-towed TD-CSEM using either a 100% (e.g. Schwalenberg et al., 2017) or a 50% duty-cycle signal (e.g. Yuan and Edwards, 2000). These seafloor-based TD-CSEM applications generally have high sensitivity for sub-seafloor resistivity structures but are less efficient (compared to FD-CSEM) in terms of survey speed (only survey at an average speed of approximately 1 kn), and longer acquisition windows are needed to reach the direct current (DC) state. Here, we demonstrate that TD-CSEM applications show dissimilar behaviour between step-on and step-off data. A short comparison to FD-CSEM systems in an equivalent transmitterreceiver set-up indicates that signal amplitudes acquired in the frequency domain behave similar to step-on data (Appendix A1). However, we note that the comparison between FD-CSEM and TD-CSEM is included here only for completeness but should not be over-interpreted due to the reasons explained in Appendix A1. For an in-depth comparison between TD-CSEM and FD-CSEM, we refer to, for example Andreis and MacGregor (2007), Connell (2011), Connell and Key (2013), and Mörbe (2020).
TD-CSEM applications often apply a 50% duty-cycle current to make use of the superior ramp characteristics in the switch-off step (e.g. Lippert and Tezkan, 2020;Micallef et al., 2020). Non-linear signal distortions such as overshoots, spikes and drifts are commonly less pronounced in the step-off current making them favourable for interpretation. However, we demonstrate here that restricting the interpretation to step-off data affects not only signal-to-noise considerations, but also limits the sensitivity of the TD-CSEM method to resolve shallow resistive structures in the seafloor. This is not a statistical consequence but originates instead from the physical differences between the step-on and the step-off electric fields.
For land-based TD-CSEM acquisition, Kaufman and Keller (1983, p. 385) discuss fundamental physical differences between step-on and step-off electric fields. They illustrate that step-on and frequency-domain soundings are screened by a layer of infinite resistivity in the subsurface, whereas stepoff signals become practically horizontal and do not create charges on the surfaces of the resistive layer. Hence, step-off signals can detect layers located at greater depth than the resistive layer, whereas step-on signals cannot. These fundamental differences between step-on and step-off electric fields are often neglected, since the common opinion is that both current excitations are equivalent in terms of sensitivity. This paper reiterates sensitivity characteristics of step-on and step-off electric fields on land and translates them to the deep marine (infinite water depth) and shallow marine (50 m water depth) environments, where differences in sensitivity are even more severe. It should be noted that multiple definitions of shallow marine environment exist (e.g. Weiss, 2007;Sommer et al., 2013). We constrain water column thickness for the shallow marine models to 50 m, which satisfies the conditions of both above-mentioned publications. Haroon (2016) shows that the detectability of a shallow 1D marine resistor (i.e. applicable to offshore groundwater or gas hydrate investigations) is orders of magnitude larger when measuring the electric field from a step-on signal compared to signals from a step-off current step. Although he uses this observation to design a TD-CSEM system for offshore groundwater exploration, no explanation is given regarding the physical principles that dictate the sensitivity differences between step-on and step-off data. Here, we use 1D modelling to demonstrate these sensitivity differences and describe the physical processes that lead to this dichotomous behaviour between the two signals in a marine setting. Different noise considerations are used to illustrate the relationship between sensitivity and data errors before implications of using either step-on or step-off data (or a combination of both) are investigated using 1D inversion.

M E T H O D O L O G Y
To derive the relationship between step-on and step-off electric fields of an horizontal electrical dipole (HED) source, let us first consider an external current step function I e (t) that at t = 0 seconds is instantaneously turned on (Fig. 1a). Hence, where (t) is the Heaviside function that equals unity for t > 0 seconds and zero for t < 0 seconds. |I| is the amplitude of the imposed external current oriented in a certain direction in space. Following Ward and Hohmann (1988), the stepresponse f(t) is given by the integral of the impulse h(t) that for a causal system is defined as When measuring the decay of the field after a constant current is turned off, that is, a negative step I e (-t) = 1 -I e (t) displayed in Fig. 1 where the integral of h from 0 to ∞ is the direct current (DC) response. We apply (4) to calculate the electric field of an HED after a constant current is shut off: Equation (5) shows that a step-on electric field of a dipole source can be transformed into a step-off electric field by subtracting it from the DC field and vice versa (Weidelt, 2000). Note that this relationship is theoretically efficient, but has practical implications as it requires sufficiently long acquisition times to guarantee adequate measurements of E DC .
The inline step-on and step-off electric fields at an offset of 300 m over a homogeneous subsurface of 1 Ωm are displayed in Fig. 1(c-e) for land-based, deep marine (water depth: 5000 m) and shallow marine (water depth: 50 m) environments, respectively. Offsets on the order of hundreds of metres are typically used in marine time-domain controlled source electromagnetic (TD-CSEM) surveys targeting shallow resistive structures in the seafloor (e.g. Schwalenberg et al., 2010). Note that we use the term subsurface to describe the volume of Earth beneath the air/ground or sea/seafloor interface. Figure 1 shows that the step-on and step-off electric field responses differ between land-and marine-based acquisitions. A land-based step-on transient measured at the surface of a homogeneous half-space is classified into three regions: (i) an early-time voltage where the field is nearly constant and equals 0.5 × E DC , (ii) an intermediate region where the electric field is changing and (iii) a late-time region where the field has reached its steady state (E DC ) (Caldwell and Bibby, 1998). In comparison, the land-based step-off data measured over a homogeneous subsurface have the same initial amplitude to the step-on field at early times. As time progresses, the step-off field decays depending on the resistivity of the lower half-space.
When submerged in conductive seawater (0.33 m) (Fig. 1d,e, respectively), the early-time voltages (t < 10 −3 seconds) of the step-on field equal zero. From (5) it follows that the step-off field must equal E DC . Edwards (2005) states that the time at which this zero-voltage changes depends on the resistivity of the surrounding environment, where a more resistive seafloor will entail amplitude changes at earlier times. One unique feature in marine TD-CSEM acquisition is that early times of the step-off data and late times of step-on data equal E DC. This is not observed on land where an immediate spreading of the signal along the air-ground interface is observed after the transmitter current is turned on or off. Transmitter and receiver dipoles are located at the interface between sea/air and subsurface with an offset of 300 m.

TA R G E T D E T E C TA B I L I T Y A NA LY S I S
We use a 1D resistivity model that has a resistive layer of 10 m and 10 m thickness buried in a conductive host rock (1 Ωm) at depth d 1 to illustrate signal characteristics of stepon and step-off electric field data (Fig. 2). Response curves are computed for variable target depths on land, in the deep marine environment and in the shallow marine environment. Figure 3 displays the step-on (green) and step-off (blue) source-normalized electric field transients for a variable target depth ranging between 30 and 100 m. The land-based acquisition is illustrated in Fig. 3(a), the deep marine acquisition in Fig. 3(b) and the shallow marine data in Fig. 3(c). The source and receivers are located on the interface between the air and Earth for the land case and on the seafloor in the marine cases. Figure 3(d-f) shows the corresponding target detectability defined after Goldman et al. (2015), also referred to as normalized response curves that are calculated as Figure 3(a) illustrates that step-on signals on land (green curves) behave similarly to the homogeneous half-space model when a target layer is introduced at a variable depth. During the very early times (t < 10 −3 seconds), initial amplitudes of the step-on electric field equal and depend only on offset (r), transmitter moment (Idl) and resistivity of the uppermost layer ρ 1 (Kaufman and Keller, 1983). Hence, the amplitudes for t < 10 −3 seconds are equivalent to the half-space response, which equals half the direct current Step-off data Step-on data Step-on and step-off electric fields are, respectively, plotted by different shades of green and blue depending on the depth of the resistive target layer. Measured noise data are displayed for reference using thin grey lines, whereas different theoretical time-dependent noise floors are displayed by the different shades of grey in the background. The dashed-grey line represents the time-dependent noise floor ( E abs ) that is used in the sensitivity and inverse modelling study. Panels (d-f) show normalized response curves for the land-based, deep marine and shallow marine scenario presented in the top panel, respectively. The curves in panels (d-f) are truncated at 2 for better representation of the detectability. Note that the normalized response curves for the marine step-on data increases exponentially until the host-rock response reaches numerical noise. Therefore, we neglect all step-on data for t < 10 −3 seconds.
(DC) value and is independent of the buried resistive target in the subsurface. This generalization holds for the specific transmitter-receiver separation and sufficiently large depths and low resistivities of the target but may need adjustments to earlier times if violated (i.e. shallower target or more resistive target). As time progresses (10 −3 ≤ t ≤ 10 −1 seconds), field amplitudes of the step-on signal increase at times dictated by the burial depth of the resistive target. At late times (approximately t > 10 −1 seconds), E DC is reached with the highest amplitudes observed for the shallowest target. The normalized response curves of all target depth variations deviate from unity at t > 10 −3 seconds, implying a sufficiently high detectability to accurately quantify the depth of the resistive layer in a noise-free environment (Fig. 3d). The step-off electric fields on land (Fig. 3a, blue curves) subtly depend on the burial depth of the resistive target at early times (t < 10 −3 seconds) causing an observable difference to the half-space response (dashed black line). As time progresses, the differences diminish and responses cannot be distinguished from the half-space solution at t > 3 × 10 −2 seconds. Hence, the target depth information is mainly contained in the early time data of the step-off signal and vanishes as time progresses.
In a deep marine environment (Fig. 3b), the step-on electric fields have an initial amplitude of zero (approximately t < 10 −3 seconds) and start to increase as the electromagnetic field diffuses through the seafloor. Following Edwards (2005), the time at which the amplitudes change from their zero state depends on the seafloor resistivity and occurs at earlier times for shallower burial depths. As no initial voltage is superimposed on the step-on data, all electric fields show an exceptionally high detectability, exceeding the detectability of land-based data by several orders of magnitude (Fig. 3e, green lines). In turn, step-off electric fields in the deep marine environment exhibit inferior detectability compared to landbased acquisition. The early-time amplitude that contributes largely to the high detectability on land is equivalent to E DC in the marine environment for all target depths and is therefore relatively insensitive to sub-seafloor resistivity (Swidinksy and Edwards, 2013). At intermediate times, variations in the normalized response curves of the step-off fields are observable (Fig. 3e, blue curves) but remain low compared to step-on data.
In a shallow marine environment (Fig. 3c), step-on electric fields exhibit comparable shapes to the deep-sea setting. In contrast, step-off transients resemble land-based data with a higher detectability observed in the DC voltages at early times. Yet, differences exist between land-based and shallow marine time-domain controlled source electromagnetic (TD-CSEM) acquisition, as early-time amplitudes of the step-off field in a marine setting equal E DC and not E DC − E ini . Therefore, earlytime marine step-off data have equal detectability to late-time marine step-on data, which is generally lower compared to the land-based acquisition.
Why does the detectability of the inline TD-CSEM electric field change between land and sea? A significant factor is the early-time amplitudes of the step-on data that are observable on land in form of E ini but equal zero within the marine environment. From (7) it is apparent that the early-time voltages (t < 10 −3 seconds) of the land-based step-on data are identical for all depth variations of the target and depend only on the resistivity of the uppermost subsurface. Contrarily, the DC voltages measured at late times of the step-on data are sensitive to the burial depth of the target layer. From Fig. 3(a), we see that the early-time transients of the step-on and step-off excitation are identical for a homogeneous subsurface but differ in the step-off signal when a resistive target is introduced. Furthermore, when applying (5) we see that early-time voltages of the step-off signal equal E DC − E on , where E on is equivalent to the half-space response for t < 10 −3 seconds. Hence, the earlytime amplitudes of the land-based step-off signal contain the subsurface information of E DC minus the background signal of E ini , resulting in an increased detectability of E off compared to E DC .
When translating these land-based observations to the deep and shallow marine environments, the obvious differences in the electric field data are the missing initial voltages of the early-time step-on responses. As (5) also applies within a marine setting, it directly follows that early-time step-off electric field data must equal E DC (Fig. 3b). The conductive seawater that surrounds transmitter and receiver mitigates an immediate signal spreading after the current switch. As a result, the initial amplitude increase of a marine step-on signal arrives at times that are dictated by the more resistive seafloor and contains the anomalous contribution from the shallow resistive layer (Weidelt, 2007). In contrast, marine step-off data contain the same anomalous contribution caused by the target layer but are superimposed by a much larger DC field at these times. Swidinsky and Edwards (2013) show that the DC field has limited sensitivity towards seafloor resistivity structure and, therefore, a masking effect is observed in the marine step-off data. This is purely a consequence of the highamplitude and low-sensitivity DC voltage that superimposes the low-amplitude and high-sensitivity inductive currents at early times of step-off data.
Since measured data are superimposed by natural and anthropogenic noise sources, detectability analyses are often limited in significance due to the following aspects. (i) Using normalized response curves to evaluate TD-CSEM signals does not consider noise, which is one of the driving factors in geophysical inversion. (ii) To image the subsurface using linearized inverse modelling, sensitivity is not defined by the ratio of signals with and without a target layer but rather evaluated for small perturbations of each model parameter. Hence, a high detectability does not imply a high sensitivity for specific model parameters, as parameter perturbations will have much smaller effects on the data. As a result, sensitivity may either be masked by the corresponding data error or exhibit intercorrelations between multiple model parameters; neither factor is considered when analysing normalized response curves.

E L E C T RO M AG N E T I C N O I S E
Following the noise considerations of Connell and Key (2013) for controlled source electromagnetic (CSEM) data, the absolute ambient electric field noise E abs (t) can be defined as where E n (t) is a time dependent factor in volt per metre, Idl the source moment of the horizontal electrical dipole (HED) in Am and N represents the number of stacked measurements for the final transient. Note that noise decrease proportional to ÝN is only valid for white Gaussian noise (Munkholm and Auken, 1996). For the source-normalized synthetic data shown in Fig. 3 and the studies presented hereinafter, a source moment of 1 kAm (100 m source length with 10 A current) is used. From (8), it is apparent that the ambient noise can be reduced through a combination of higher source moments or an increased number of repeated measurements used for stacking. For the following consideration, we neglect error weighting due to repeated stacks (N = 1). Moreover, it should be mentioned that E n (t) contains noise contributions arising from both natural and cultural sources, as well as instrumental noise from system electronics and electrodes (Connell and Key, 2013). We restrain from quantifying different time-dependent noise contributions as these do not affect the results which follow. Repeated noise measurements from a single site acquired on land and in a shallow marine environment (water depth <50 m) recorded by the same device (KMS820 acquisition unit -KMS Technologies) are displayed in Fig. 3(a,c) by thin grey lines. In both cases, the 50 Hz (and odd harmonics) power grid contributions were filtered, and data were levelled so that the mean voltage of each period equals zero. Subsequently, the recorded 10 kHz data are log-gated following the processing of Munkholm and Auken (1996). Note that the individual noise measurements are not stacked to better exemplify the nature of the background noise for land and shallow marine environments. The presented noise measurements were conducted in different countries; land-based noise measurements are from Cuxhaven, Germany; the marine noise data were measured 4 km offshore Bat Yam, Israel.
For land-based acquisition displayed in Fig. 3(a), a time decay of the absolute noise is observable. This behaviour is consistent with Munkholm and Auken (1996) and should in theory decay with 1/ √ t for Gaussian noise (grey background shading in Fig. 3a,b). For the land-based data, we observe that the decay is slightly more gradual, but remains consistently below the 10 −12 V/(Am 2 ) source-normalized noise floor in the time range of interest. The measured noise data in a marine environment behave differently from the land-based case. Here, the 1/Ýt dependency of the noise floor is not observable within the relevant time range, and such non-Gaussian noise is presumably caused by flow noise (motionally induced noise due to water flow around the electrodes as investigated by Djanni, 2016) or cable strumming. But since measured noise data from land and shallow marine environments are predominantly below the absolute noise floor of E abs (t) = 10 −12 /Ýt (illustrated by the thick dashed line in Fig. 3), we define this relationship as adequate for the following 1D sensitivity and inverse modelling studies. We emphasize that the background noise for a specific survey area and measurement system should not be generalized from Fig. 3. The noise data presented here are used as a justification for possible electromagnetic noise encountered in land-and marine-based acquisition. However, noise considerations are survey-specific and should be carefully in-corporated in a sensitivity analysis prior to inversion as data errors represent one of the driving factors for resolution.
The absolute electric field noise E abs are further superimposed by errors from incorrect survey geometry, synchronization and sensor calibration that have a systematic influence on the measured voltage and cannot be improved by increasing the number of stacks, or using larger transmitter moments (Connell and Key, 2013). Instead, these errors typically scale with the measured voltage and are incorporated by a relative error factor E rel . Studies conducted by Gehrmann et al. (2020) show that a quasi-static scaling does not hold true for frequency-domain controlled source electromagnetic (FD-CSEM) applications towed within the water column, where geometrical distortions can be frequency or time dependent. However, such distortions do not concern synthetic data so that a first-order assumption for the total source-normalized error E(t) can be defined as where E(t) is the source-normalized electric field for a given transmitter-receiver configuration. In the following, we refer to the studies of Hölz et al. (2015) and apply a 1% relative error ( E rel = 0.01).

TA R G E T S E N S I T I V I T Y A NA LY S I S
Sensitivities of electromagnetic data are defined by the change of the response curve due to a perturbation (typically 10%) of a logarithmically transformed model parameter. Since this does not include any information regarding data errors, the sensitivity matrix (J) is commonly weighted by an error matrix (W), resulting in a dimensionless quantity that makes up the weighted Jacobian matrix (J W ). For electric field data, the weighted Jacobian is defined as where W ii = 1/ E i . i refers to the data sample at a specific time and p j to each model parameter.
The weighted sensitivities of step-on and step-off data are strongly dependent on the characteristics of the data error. Figure 4 illustrates how sensitivity curves for perturbations in target-relevant parameters (i.e. depth: d 1 ; resistivity: ρ 2 ; thickness: d 2 ) change based on relative error weighting in the top row, absolute error weighting from (8) in the second row and total error weighting according to (9) along the third row. Sensitivities are displayed for the land-based case in the left column, the deep marine setting in the centre and for the shal- Step-off data Step-on data Error-weighted sensitivity curves of (left) land-based, (centre) marine-based and (right) shallow marine-based inline electric field data for the relevant target parameters depth (d 1 ), thickness (d 2 ) and resistivity (ρ 2 ).
Step-on and step-off sensitivities are displayed by green and blue lines, respectively. The sensitivity of the target layer resistivity (ρ 2 ), depth (d 1 ) and thickness (d 2 ) are displayed by the different dashed lines. low marine setting along the right column. The green lines refer to the sensitivity of the step-on electric field data, the blue lines to the step-off data. Recall that the unperturbed model has a 10 m thick resistive layer of 10 m embedded in a 1 m host rock at a depth of 50 m. Weighting the Jacobian with a relative error (Fig. 4a-c) enforces the sensitivity data to resemble the general shape of the normalized response curves shown in Fig. 3(d-f). Note that sensitivity curves of target depth (d 1 ) have a reversed sign compared to the normalized response curves in Fig. 3 due to the nature of the +10% perturbation, meaning that the target is deeper in the perturbed model and step-on signal amplitudes decrease compared to the unperturbed model. For land-based acquisition, sensitivities of step-off and step-on data are comparable in terms of amplitude. The main sensitivity contributions for target thickness and resistivity are observable at early times in the step-off field and at intermediate to late times in the step-on field.
Step-on data are slightly more sensitive to target depth (d 1 ) compared to step-off data, which exhibit a sign reversal in the sensitivity at approximately 5 × 10 −3 seconds (Fig. 4a).
Step-on electric fields acquired in the marine environment exhibit proportionally higher sensitivities compared to stepoff fields when weighted by a relative data error, suggesting superior sensitivity (Fig. 4b). This is attributed to the relative error weighting that does not account for an overweighting of sensitivities at times where signal amplitudes are small. In this case, small electric field amplitudes are weighted equivalently to large amplitudes implying a high target sensitivity at early times of the step-on data. But since step-on signals in the marine environment (deep and shallow) are generally orders of magnitude smaller at early times compared to the late-time direct current (DC) field, they are also more susceptible to the superimposed background noise (cf. measured noise data in Fig. 3).
Weighting the sensitivity matrix with an absolute noise floor incorporates the ambient noise and mitigates irregularly high sensitivities caused by small electric field amplitudes ( Fig. 4d-f). In turn, absolute error weighting does not consider relative errors that scale linearly with electric field amplitude and, therefore, the sensitivity of the late-time step-on data increase significantly by Ýt although signal amplitudes are constant. Further differences between relative and absolute error weighting are (i) sensitivities of the early-time step-on data in marine acquisition equal zero since electric field amplitudes are below the absolute noise floor before 2 × 10 −3 seconds; (ii) step-off data show a sensitivity decline during early-time windows due to a decrease in signal-to-noise ratios. This re-sults in sensitivity reduction between 10 −4 and 10 −3 seconds for both land-and marine-based acquisition although signal amplitudes are constant within this time window. Figure 4(g-i) illustrates the sensitivity of time-domain controlled source electromagnetic data weighted by the total error defined in (9). By combining relative and absolute error weighting, characteristics of each are manifested in the sensitivity curves. This error weighting is considered most realistic as measured data typically exhibit both relative and absolute error contributions. The sensitivity curves show an inferior step-off sensitivity towards shallow resistive layers in the deep marine (Fig. 4h) and shallow marine (Fig. 4i) environments. Maximum values of step-on sensitivity exceed step-off sensitivity by a factor of 2 to 3 for all relevant target parameters including depth, thickness and resistivity. These inferior sensitivities observed in the step-off data are due to the superimposing DC contributions at early times that mask the inductive response and only slowly deteriorates. Due to their limited sensitivity to the seafloor resistivity structure, DC voltages suppress the sensitivity of the low-amplitude inductive signal when interpreting step-off data. In comparison to the marine case, step-off data on land are comparable to step-on data in terms of sensitivity since early-time amplitudes are sensitive to variations of the subsurface resistivity structure.
To illustrate sensitivity differences more clearly, the normalized cumulative sensitivity (S n ) defined as (e.g. Martin, 2009) is displayed as a 2D cross-section in Fig. 5. The weighted sensitivity data are computed for the 1D resistivity model displayed in Fig. 2 using a time-domain adaptation of MARE2DEM (Key, 2016) developed by Haroon et al. (2018a). In (11), A j defines the area of each finite element cell, and J W i j is the weighted Jacobian matrix calculated for the unstructured finite-element grid. Normalized cumulative sensitivities are dimensionless quantities that illustrate the sum of error-weighted sensitivities for a specific time range. Here, we consider sensitivities between 10 −3 and 10 −1 seconds, where variations in electric field amplitudes are strongest and bias from the static field or early-time voltages is minimized. Figure 5 shows cumulative sensitivities for (left) step-on data and (right) step-off data in (top) land-based, (middle) deep marine and (bottom) shallow marine settings. The colour bar in Fig. 5 highlights regions of high sensitivity by light shading, whereas regions of low sensitivity remain dark. Step-off sensitivity Step-on sensitivity Cumulative sensitivity cross-sections calculated according to equation (11) and plotted for the (top) land-based, (middle) deep marine and (bottom) shallow marine inline electric fields. The step-on and step-off sensitivities are displayed in the left and right panels, respectively. The transmitter and receiver are assumed to be point dipoles located 300 m apart at ±150 m. The interface between the air/sea and subsurface is depicted by a solid black line. Figure 5(a,b) shows that sensitivities of the resistive target layer are practically equivalent between step-on and step-off data for land-based acquisition. Contrarily, sections located above and below the resistive layer exhibit observable sensitivity differences. On land, the step-on electric field is less sensitive in the section below the resistive layer, which is interpreted as a reduced screening effect following the descriptions of Kaufman and Keller (1983, p. 385). Although the resistivity of the considered target layer is not infinite, a comparable screening effect with decreased significance is observed, where the vortex part of the electromagnetic field becomes insignificant at late times of the step-on signal due to a su-perimposed relative data error (1% is considered significant). For a step-off field, the vortex character dominates at late times and the field becomes practically horizontal. As a result, resistive layers do not screen regions located at greater depths (Kaufman and Keller, 1983) and imaging these sections is mainly dependent on the magnitude of the absolute noise floor. Sensitivity differences within the overburden between land-based step-on and step-off data are an effect of the considered time window. Here, the considered time window has practically removed E ini defined in (7), and as a result, the step-on data lose cumulative sensitivity towards the overburden.
When submerged in conductive seawater (Fig. 5c-f), sensitivity differences between step-on and step-off fields are mainly observable within the resistive target layer. The bright colouring indicates much higher sensitivity in deep and shallow marine environments when interpreting step-on data. The cumulative step-on sensitivities exceed those of step-off data by nearly one order of magnitude within the resistive target. In turn, sensitivities in sections located above and below the resistive layer appear relatively coherent between step-on and step-off data.

D I N V E R S I O N O F S Y N T H E T I C DATA
The sensitivity studies presented above demonstrate differences between step-on and step-off fields on land, in the deep sea and within shallow marine environments. They highlight the enhanced sensitivity of step-on electric field data to image shallow resistive targets for deep and shallow marine timedomain controlled source electromagnetic (TD-CSEM) acquisition. However, step-off data are not completely insensitive to shallow resistive targets. The question remains if the higher step-on sensitivity leads to an improved resistivity-depth image through inversion. We perform synthetic inversion studies using an horizontal electrical dipole (HED) source and four inline electric field receivers located at equidistant offsets of 150, 300, 450 and 600 m from the source. Here, multiple receivers at different offsets are applied to (i) mimic a realistic marine TD-CSEM experiment and (ii) enforce a more robust analysis by reducing the ambiguity that would arise from a single source-receiver configuration (e.g. Gehrmann et al., 2016;Schwalenberg et al., 2017).
Before inversion, noise following (9) is added to the synthetic data to simulate realistic noise conditions. Subsequently, the data are inverted using 1D Occam-R1 (Constable et al., 1987) and Levenberg-Marquardt inversion schemes (e.g. Strack, 1992). The resulting models for step-on data, step-off data and a combination of the two data sets (hereinafter referred to as combined inversion) are displayed in Fig. 6. The black model represents the true subsurface resistivity model, the dark-shaded lines the Occam inversions and the light-shaded lines the equivalent Levenberg-Marquardt inversion models using randomly distributed starting models. To analyse a possible interpretation bias due to over-fitting and under-fitting specific receivers, an error-scaled inversion was additionally conducted for land-based and deep marine data where the final model fits all four receivers equally well (Fig. B1). As these error-scaled inversion models are coherent to the displayed models in Fig. 6, we interpret the models ob-tained from inversion using the original error model defined in (9).
The Occam models shown in Fig. 6 are all fitted to an error-weighted root mean square (RMS) of 1 and converged after seven to nine iterations. Three-layer starting models for the equivalent Levenberg-Marquardt inversions were randomly chosen and all resistivity models displayed in Fig. 6 achieve an error-weighted RMS ≤ 1.
With the exception of the step-off inversion for a shallow marine setting (Fig. 6f), the majority of the obtained resistivity models for both step-on and step-off, and combined inversion indicated the existence of a more resistive layer embedded in a conductive background environment. Overall, target depth, resistivity and thickness are imaged most accurately for the land-based acquisition (Fig. 6, left column) and are more ambiguous when inverting marine data (Fig. 6, centre and right columns).
Resistivity contrasts between the target layer and the background are least pronounced in the marine step-off Occam inversion (Fig. 6e), which is indicative of inferior sensitivity compared to the step-on data (Fig. 6b). This inferior sensitivity is most obvious when analysing the Occam inversion model in a shallow marine environment (Fig. 6f). Here, the step-off data are fit by a homogeneous seafloor model with slightly increased resistivity, whereas the step-on inversion detects the resistive target layer at the correct depth (Fig. 6c). These increased ambiguities within the marine stepoff data are further supported by the equivalent Levenberg-Marquardt models that demonstrate a higher variability in the single and combined inversion.
To further illustrate the implications of sensitivity on nonuniqueness of the inversion, target resistivity and thickness are varied between realistic minimum and maximum values. The corresponding error-weighted RMS is shown as a function of ρ 2 and d 2 in Fig. 7. The top row displays the equivalence domain of the step-on data for (a) land, (b) deep marine and (c) shallow marine settings. The bottom row shows the corresponding equivalence domains for step-off data. All images show that target resistivity and thickness are intercorrelated parameters, enabling equivalent data fits for constant resistivity-thickness products if the layer thickness remains ≤30 m on land and ≤70 m in the marine environment. Overall, step-off data exhibit notable limitations when resolving the resistivity-thickness product compared to step-on data in a marine setting. Equivalent domains (for both shallow and deep marine environments) are notably larger indicating more ambiguity in the target parameters. 10 -1 10 0 10 1 10 2 Step-on inversion 10 -1 10 0 10 1 10 2 Step-on inversion Step-on inversion

(c)
Step Step-off inversion Step-off inversion Step-off inversion

Figure 7
Equivalence domain modelling study of the target layer resistivity (ρ 2 ) and thickness (d 2 ) for (left) land, (centre) deep marine and (right) shallow marine environments. The step-on data is displayed on the top, the step-off data along the bottom panels, respectively. The colour scale is chosen so that black colours are considered equivalent within an error-weighted RMS ≤ 1, red colours (RMS ≤ 2) represent parameter combinations with inferior fitting and light/white colours represent parameter combinations that do not fit the data. environment. However, inter-correlations to other model parameters are not considered here and Fig. 6(f) shows that a shallow marine TD-CSEM acquisition is most affected by its inferior sensitivity. The sensitivity, inversion and equivalence studies shown in Figs. 5-7 confirm an inferior sensitivity in the marine stepoff electric field data when exploring shallow resistive targets in the sub-seafloor. This sensitivity decrease is notable for simple three-layer models, but is even more pronounced when the resistivity-depth structure of the seafloor is more complex. To illustrate this, a final inversion study shows a five-layer resistivity model, where an additional resistive layer of 30 Ωm is introduced at a depth of 100 m beneath the subsurface with a thickness of 50 m (black lines in Fig. 8).
For the inversion of the synthetic five-layer model data, the noise model of (9) is applied for four receivers located at offsets of 150, 300, 450 and 600 m. Figure 8 shows the resulting Occam-R1 and Levenberg-Marquardt inversion models that all achieve an error-weighted RMS = 1 and RMS ≤ 1, respectively. The colour scheme corresponds to Fig. 6.
The left column of Fig. 8 displays the inversion models for land-based acquisition. Here, both step-on and step-off data are able to detect both the shallow and deep resistive layer (Fig. 8a,d, respectively). Resistivity and thickness of the two resistive layers are equally well determined. The equivalent models indicate that the step-on data (Fig. 8a) are superior in resolving the resistivity of the overburden (ρ 1 ) due to the defined amplitude of E ini , which is only dependent on the resistivity of the uppermost metres of the subsurface. In turn, the equivalent step-off models indicate superior resolution for the lower terminating half-space. A combined inversion of stepon and step-off data on land (Fig. 8e) includes the resolution characteristics of both data sets. The overburden in the combined inversion is well resolved due to the information content of the step-on data, whereas the lower terminating half-space is well resolved through the step-off data. Additionally, the ambiguities of the combined inversion models for land-based acquisition are further reduced through the increased amount of data in the inversion process (Vozoff and Jupp, 1975). If feasible, a combined inversion of step-on and step-off data is advisable for land-based TD-CSEM applications.
In deep and shallow marine environments, step-on data are more efficient in deriving the true resistivity structure of the subsurface (Fig. 8, centre and right columns). Both stepon and step-off data image the deeper (thicker) resistive layer, but only step-on data can resolve the upper resistive layer. For both data sets the equivalent models express a high ambiguity that is more severe in the step-off inversion. A combined inversion of marine step-on and step-off data shows no significant improvement compared to the single step-on inversion. Thus, we expect that a combined inversion approach for marine data increases non-uniqueness as over-fitted step-off data Step-on inversion Step-on inversion Step-on inversion

(c)
Step Step-off inversion Step-off inversion Step-off inversion

(f)
Step will enforce quicker convergence. However, this assumption is not clearly confirmed by analysis of the equivalent models in Fig. 8(c,i). Still, the analysis indicates that a combined inversion approach does not enhance model parameter resolution for an isotropic marine environment.

D I S C U S S I O N
Due to the preferable step characteristics of a switch-off current function in modern instrumentation, step-off data are widely interpreted in time-domain controlled source electromagnetic (TD-CSEM) experiments. Contrarily, step-on data are often neglected in the interpretation due to non-linear signal distortions caused by the transmitter, which are challenging to account for in processing and inversion. Here, we demonstrate that limiting the interpretation to step-off data prevents TD-CSEM from reaching its maximum potential, particularly when detecting shallow resistive bodies in the marine environment. When submerged in conductive seawater, TD-CSEM data exhibit a notable decrease in step-off sensitivity compared to step-on data. A resistive layer embedded in a conductive seafloor is imaged more precisely using step-on data, especially when resistivity structures are more complex than three-layer models. As a result, the use of stepoff data in a single or combined inversion approach appears to be redundant in an isotropic marine environment, as nonuniqueness is increased and resistivity models are more susceptible to misinterpretation. Contrarily, a combined inversion approach on land improves the overall resolution to all subsurface model parameters. Resolution characteristics of both signals are manifested in the best-fit inversion model. Most continental shelf sedimentary formations are known to exhibit vertically transverse isotropic electrical resistivity (Ramananjaona et al., 2011). Here, we restrict the analysis to isotropic resistivity models to focus on the differences observed between step-on and step-off sensitivities. These demonstrated sensitivity differences are not limited to isotropic resistivity models.
Theoretically, the proposition of only using step-on data in marine TD-CSEM acquisition is easy to recommend. Yet practically, removing non-linear distortions in step-on current functions poses technical challenges that might not find a trivial solution. Hence, measured marine step-on data can contain distortions that prevent an analysis or introduce bias, especially for the shorter offset receivers. In this case, an alternative strategy is imaginable. Transforming the measured step-off data into step-on data using (5) as shown by Mörbe et al. (2020) is feasible. However, it is worth clarifying that the data quality of such derived step-on transient will be inferior due to error propagation. Additionally, the requirement of sufficiently long acquisition times to obtain stable direct current (DC) plateaus can further jeopardize TD-CSEM survey efficiency. This is particularly critical in marine applications where the high cost of ship time is a critical (limiting) factor.
This study focuses on inline electric fields as these are commonly applied in the marine environment to detect shallow resistive structures such as offshore freshened groundwater or gas hydrates. The basic principles presented here also apply to other transmitter-receiver geometries. However, in these cases the implications of possible masking due to superimposed DC amplitudes should be investigated closely. This can be of interest for broadside electric fields, which exhibit a sign reversal in step-off data within the marine environment (e.g. Lippert and Tezkan, 2020). We suggest a thorough analysis of the most effective current function and survey geometry prior to data acquisition.

C O N C L U S I O N
We compare the sensitivity of inline step-on and step-off timedomain controlled source electromagnetic (TD-CSEM) electric field data towards a shallow resistive layer embedded in a more conductive host rock on land and in deep/shallow marine environments. Marine data indicate significantly higher detectability towards shallow resistive layers in the step-on signals compared to step-off signals. By defining realistic data errors for land-based, deep marine and shallow marine TD-CSEM acquisition, we are able to demonstrate that this detectability increase is also observed in the sensitivity, which has implications on geophysical inversion and geological inference. Overall, the inferior sensitivities observed in marine stepoff data are explained by the early-time step-off amplitudes, which are sensitive to subsurface resistivity variations on land, but insensitive to resistivity variations in the marine environment. Accordingly, this steady-state response masks the inductive response of the electromagnetic step-off field in the marine environment, substantially reducing sensitivity. In contrast, the step-on signal registered by a marine receiver measures the inductive field component prior to the signal arrival of the steady-state response and contains information about the more resistive seafloor structure. Therefore, the masking effect of the steady-state signal is less significant, resulting in significantly higher sensitivity in comparison.
Synthetic 1D inverse modelling studies indicate that both step-on and step-off electric field data can be used to detect a shallow resistive layer embedded in a conductive host rock. However, step-off data have inferior sensitivity to these shallow resistive layers in a marine environment, which increases ambiguity of the inversion. Moreover, this inferior sensitivity is further magnified when the resistivity-depth structure of the seafloor is more complex than a three-layer model. Only inversion models that include step-on data can accurately discriminate between two resistive layers embedded in the seafloor at different depths.

AC K N OW L E D G E M E N T S
We would like to thank the associate editor Rita Streich, Katrin Schwalenberg and one anonymous reviewer for their constructive criticism that helped us to improve the contents of this publication. Further, we would like to thank Wiebke Mörbe (University of Cologne) and Tillman Hanstein (KMS Technologies) for insightful discussions on time-domain CSEM. Amir Haroon is funded by the German Research Foundation grant no. 389727048 and by a Bridging Postdoc within the framework of the Digital Earth Project at the Helmholtz Association. Sebastian Hölz was funded by the German Federal Ministry for Economic Affairs and Energy (BMWI) and co-funded by European Union's Horizon 2020 research and innovation programme under the framework of ERA-NET Co-fund MarTERA (Maritime and Marine Technologies for a New Era). Open access funding enabled and organized by Projekt DEAL.

DATA AVA I L A B I L I T Y S TAT E M E N T
Data sharing is not applicable to this paper as no new data were created or analysed in this study.

A P P E N D I X A : C O M PA R I S O N TO F R E QU E N C Y -D O M A I N E L E C T RO M AG N E T I C S
The vast majority of controlled source electromagnetics (CSEM) applications that are conducted in the marine environment are practiced in the frequency domain. Commercial exploration for hydrocarbon reservoirs at several kilometres deep below the seafloor uses frequency-domain CSEM (FD-CSEM) due to its effectiveness. Applications in academia are generally confined to shallower resistive structures associated with gas hydrates or offshore freshened groundwater, and CSEM is used in both time and frequency domains. For completeness, we analyse a frequency-domain response based on the forward modelling studies presented in Fig. 3. The resistivity model is displayed in Fig. 2 and the corresponding transmitter-receiver configuration is consistent with the TD-CSEM study we present in the main body of this paper. Note that this study has only limited significance as FD-CSEM systems are generally not seafloor-based with both transmitter and receivers, use a higher variety of offsets to obtain greater depth information and are generally limited to a narrower frequency bandwidth compared to what is presented here. The aim of this study is to demonstrate that a broadband frequency-domain signal is consistent with a step-on timedomain signal as presented above. Figure A1 shows the FD-CSEM signal magnitudes for an inline electric field receiver at an offset of 300 m from the source. The computed frequency bandwidth is from 10 4 to 10 −1 Hz. Although the curves are not completely identical with the TD-CSEM step-on signal, the general shape and detectability of the resistive target are consistent. Therefore, the sensitivity of FD-CSEM to shallow resistive layers will behave similarly to the step-on response, provided that error estimations are consistent between time and frequency domains. Yet, it is important to consider the following aspects when comparing the FD-CSEM to TD-CSEM applications. We purposely omit a thorough comparison between time-and frequency-domain CSEM as numerous studies have previously done this. Please refer to Andreis and MacGregor (2007), Connell (2011), Connell andKey (2013) or Mörbe (2020) for detailed comparisons between TD-and FD-CSEM. 1. FD-CSEM applications generally use a smaller frequency bandwidth compared to Fig. A1. Therefore, depth resolution for a single source and receiver pair is limited and such resolution is commonly achieved by using an array of multiple receivers that are located at different offsets from the towed source. When using very large offsets of several kilometres, FD-CSEM applications are capable of investigating targets at several hundred metres to kilometres depth but may have insufficient resolution for very shallow structures. 2. Marine TD-CSEM applications often use several (few) fixed-offset receivers in a seafloor-based system. Increased depth of investigation is obtained through longer acquisition times and by applying larger source-receiver offsets. As a result, TD-CSEM applications are capable of detecting shallow and deep resistive targets in the seafloor. 3. Since FD-CSEM applications do not require the signal to reach a direct current state, they are much more efficient in terms of surveyed profile kilometres. 4. FD-CSEM systems have been applied in both shallow marine (e.g. Sherman et al., 2017;Du and Key, 2018;Gustafson et al., 2019;Attias et al., 2019) and deep marine (e.g. Constable, 2010) environments. Due to its efficiency, a higher lateral data sampling and presumably higher lateral resolution should be achievable using a FD-CSEM system compared to any TD-CSEM for a predefined time frame. Yet, instances exist where TD-CSEM applications may be more suitable, for example in confined coastal areas where only limited offset variations are feasible. Suitability of any CSEM system (TD or FD) for a specific exploration task is survey-specific and also somewhat subjective (e.g. depending on available acquisition hardware, processing and interpretation software, etc.) 10 -1 10 0 10 1 10 2 10 3 10 4 Figure A1 Frequency-domain response for inline electric field data in (a) land-based, (b) deep marine and (c) shallow marine environments using the three-layer subsurface resistivity model presented in Fig. 2. The different shades of green represent varying burial depth of the target layer as indicated in the legend. Panels (d-f) show normalized response curves for the land-based, deep marine and shallow marine scenario, respectively. A normalized response of 1 indicates no detectability towards the target formation at that frequency. but can be assessed prior to each measuring campaign using forward modelling and error analysis.

A P P E N D I X B : I N V E R S I O N B I A S D U E TO OV E R / U N D E R -F I T T I N G O F D I F F E R E N T R E C E I V E R S
In has been observed that TD-CSEM applications using one source and multiple receivers at various offsets suffer from bias in 1D inversions caused by over-fitting and under-fitting different receivers. Although the overall root mean square (RMS) ≤1, the introduced bias can lead to misinterpretation of the obtained resistivity models. An accepted approach to reducing such bias is to conduct multiple hypothesis testing as discussed for magnetotelluric data by Chave (2017). For CSEM data, Schwalenberg et al. (2017) propose a simpler approach based on rescaling the data errors at each receiver so that a resistivity model is obtained where all receivers have an RMS of approximately 1 and the total RMS ≤ 1. We apply the latter approach here. To rule out possible misinterpretation in our inversion studies, we compare inversion results from the original Occam models presented in Fig. 6 to an error-scaled inversion as described above. The inversion models for landbased and marine settings are displayed in Fig. B1. The darkshaded models are the original inversion models from Fig. 6, and the light-shaded models are the newly computed inversion models. Based on this short analysis, we can conclude that the differences between step-on and step-off resistivity models are not caused by bias of over/under-fitting individual receivers. 10 -1 10 0 10 1 10 2 Step-on inversion Step-on inversion

(b)
Step-on data Step-off inversion Step-off inversion

(d)
Step-off data